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Core

Definitions of the core classes: Problem, Solution, and SolutionBatch.

ActorSeeds (tuple)

ActorSeeds(py_global, np_global, torch_global, problem)

__getnewargs__(self) special

Return self as a plain tuple. Used by copy and pickle.

Source code in evotorch/core.py
def __getnewargs__(self):
    'Return self as a plain tuple.  Used by copy and pickle.'
    return _tuple(self)

__new__(_cls, py_global, np_global, torch_global, problem) special staticmethod

Create new instance of ActorSeeds(py_global, np_global, torch_global, problem)

__repr__(self) special

Return a nicely formatted representation string

Source code in evotorch/core.py
def __repr__(self):
    'Return a nicely formatted representation string'
    return self.__class__.__name__ + repr_fmt % self

AllRemoteEnvs

Representation of all remote reinforcement learning instances stored by the ray actors.

An instance of this class is to be obtained from a main (i.e. non-remote) Problem object, as follows:

remote_envs = my_problem.all_remote_envs()

A remote method f() on all remote environments can then be executed as follows:

results = remote_envs.f()

Given that there are n actors, results contains n objects, the i-th object being the method's result from the i-th actor. An alternative to the example above is like this:

results = my_problem.all_remote_envs().f()
Source code in evotorch/core.py
class AllRemoteEnvs:
    """
    Representation of all remote reinforcement learning instances
    stored by the ray actors.

    An instance of this class is to be obtained from a main
    (i.e. non-remote) Problem object, as follows:

        remote_envs = my_problem.all_remote_envs()

    A remote method f() on all remote environments can then
    be executed as follows:

        results = remote_envs.f()

    Given that there are `n` actors, `results` contains `n` objects,
    the i-th object being the method's result from the i-th actor.
    An alternative to the example above is like this:

        results = my_problem.all_remote_envs().f()
    """

    def __init__(self, actors: list):
        self._actors = actors

    def __getattr__(self, attr_name: str) -> Any:
        return RemoteMethod(attr_name, self._actors, on_env=True)

AllRemoteProblems

Representation of all remote problem instances stored by the ray actors.

An instance of this class is to be obtained from a main (i.e. non-remote) Problem object, as follows:

remote_probs = my_problem.all_remote_problems()

A remote method f() on all remote Problem instances can then be executed as follows:

results = remote_probs.f()

Given that there are n actors, results contains n objects, the i-th object being the method's result from the i-th actor. An alternative to the example above is like this:

results = my_problem.all_remote_problems().f()
Source code in evotorch/core.py
class AllRemoteProblems:
    """
    Representation of all remote problem instances stored by the ray actors.

    An instance of this class is to be obtained from a main
    (i.e. non-remote) Problem object, as follows:

        remote_probs = my_problem.all_remote_problems()

    A remote method f() on all remote Problem instances can then
    be executed as follows:

        results = remote_probs.f()

    Given that there are `n` actors, `results` contains `n` objects,
    the i-th object being the method's result from the i-th actor.
    An alternative to the example above is like this:

        results = my_problem.all_remote_problems().f()
    """

    def __init__(self, actors: list):
        self._actors = actors

    def __getattr__(self, attr_name: str) -> Any:
        return RemoteMethod(attr_name, self._actors)

BoundsPair (tuple)

BoundsPair(lb, ub)

__getnewargs__(self) special

Return self as a plain tuple. Used by copy and pickle.

Source code in evotorch/core.py
def __getnewargs__(self):
    'Return self as a plain tuple.  Used by copy and pickle.'
    return _tuple(self)

__new__(_cls, lb, ub) special staticmethod

Create new instance of BoundsPair(lb, ub)

__repr__(self) special

Return a nicely formatted representation string

Source code in evotorch/core.py
def __repr__(self):
    'Return a nicely formatted representation string'
    return self.__class__.__name__ + repr_fmt % self

ParetoInfo (tuple)

ParetoInfo(fronts, ranks)

__getnewargs__(self) special

Return self as a plain tuple. Used by copy and pickle.

Source code in evotorch/core.py
def __getnewargs__(self):
    'Return self as a plain tuple.  Used by copy and pickle.'
    return _tuple(self)

__new__(_cls, fronts, ranks) special staticmethod

Create new instance of ParetoInfo(fronts, ranks)

__repr__(self) special

Return a nicely formatted representation string

Source code in evotorch/core.py
def __repr__(self):
    'Return a nicely formatted representation string'
    return self.__class__.__name__ + repr_fmt % self

Problem (TensorMakerMixin, Serializable)

Representation of a problem to be optimized.

The simplest way to use this class is to instantiate it with an external fitness function.

Let us imagine that we have the following fitness function:

import torch

def f(solution: torch.Tensor) -> torch.Tensor:
    return torch.linalg.norm(solution)

A problem definition can be made around this fitness function as follows:

from evotorch import Problem

problem = Problem(
    "min", f,  # Goal is to minimize f (would be "max" for maximization)
    solution_length=10,  # Length of a solution is 10
    initial_bounds=(-5.0, 5.0),  # Bounds for sampling a new solution
    dtype=torch.float32,  # dtype of a solution
)

Vectorized problem definitions. To boost the runtime performance, one might want to define a vectorized fitness function where the fitnesses of multiple solutions are computed in a batched manner using the vectorization capabilities of PyTorch. A vectorized problem definition can be made as follows:

from evotorch.decorators import vectorized

@vectorized
def vf(solutions: torch.Tensor) -> torch.Tensor:
    return torch.linalg.norm(solutions ** 2, dim=-1)

problem = Problem(
    "min", vf,  # Goal is to minimize vf (would be "max" for maximization)
    solution_length=10,  # Length of a solution is 10
    initial_bounds=(-5.0, 5.0),  # Bounds for sampling a new solution
    dtype=torch.float32,  # dtype of a solution
)

Parallelization across multiple CPUs. An optimization problem can be configured to parallelize its evaluation operations across multiple CPUs as follows:

problem = Problem("min", f, ..., num_actors=4)  # will use 4 actors

Exploiting hardware accelerators. As an alternative to CPU-based parallelization, one might prefer to use the parallelized computation capabilities of a hardware accelerator such as CUDA. To load the problem onto a cuda device (for example, onto "cuda:0"), one can do:

from evotorch.decorators import vectorized


@vectorized
def vf(solutions: torch.Tensor) -> torch.Tensor:
    return ...


problem = Problem("min", vf, ..., device="cuda:0")

Exploiting multiple GPUs in parallel. One can also keep the entire population on the CPU, and split and distribute it to multiple GPUs for GPU-accelerated and parallelized fitness evaluation. For this, the main device of the problem is set as CPU, but the fitness function is decorated with evotorch.decorators.on_cuda.

from evotorch.decorators import on_cuda, vectorized


@on_cuda
@vectorized
def vf(solutions: torch.Tensor) -> torch.Tensor:
    return ...


problem = Problem(
    "min",
    vf,
    ...,
    num_actors=N,  # where N>1 and equal to the number of GPUs
    # Note: if you are on a computer or on a ray cluster with multiple
    # GPUs, you might prefer to use the string "num_gpus" instead of an
    # integer N, which will cause the number of available GPUs to be
    # counted, and the number of actors to be configured as that count.
    #
    num_gpus_per_actor=1,  # each GPU is assigned to an actor
    device="cpu",
)

Defining problems via inheritance. A problem can also be defined via inheritance. Using inheritance, one can define problems which carry their own additional data, and/or update their states as more solutions are evaluated, and/or have custom procedures for sampling new solutions, etc.

As a first example, let us define a parameterized problem. In this example problem, the goal is to minimize x^(2q), q being a parameter of the problem. The definition of such a problem can be as follows:

from evotorch import Problem, Solution


class MyProblem(Problem):
    def __init__(self, q: float):
        self.q = float(q)

        super().__init__(
            objective_sense="min",  # the goal is to minimize
            solution_length=10,  # a solution has the length 10
            initial_bounds=(-5.0, 5.0),  # sample new solutions from within [-5, 5]
            dtype=torch.float32,  # the dtype of a solution is float32
            # num_actors=...,  # if parallelization via multiple actors is desired
        )

    def _evaluate(self, solution: Solution):
        # This is where we declare the procedure of evaluating a solution

        # Get the decision values of the solution as a PyTorch tensor
        x = solution.values

        # Compute the fitness
        fitness = torch.sum(x ** (2 * self.q))

        # Register the fitness into the Solution object
        solution.set_evaluation(fitness)

This parameterized problem can be instantiated as follows (let's say with q=3):

problem = MyProblem(q=3)

Defining vectorized problems via inheritance. Vectorization can be used with inheritance-based problem definitions as well. Please see the following example where the method _evaluate_batch is used instead of _evaluate for vectorization:

from evotorch import Problem, SolutionBatch


class MyVectorizedProblem(Problem):
    def __init__(self, q: float):
        self.q = float(q)

        super().__init__(
            objective_sense="min",  # the goal is to minimize
            solution_length=10,  # a solution has the length 10
            initial_bounds=(-5.0, 5.0),  # sample new solutions from within [-5, 5]
            dtype=torch.float32,  # the dtype of a solution is float32
            # num_actors=...,  # if parallelization via multiple actors is desired
            # device="cuda:0",  # if hardware acceleration is desired
        )

    def _evaluate_batch(self, solutions: SolutionBatch):
        # Get the decision values of all the solutions in a 2D PyTorch tensor:
        xs = solutions.values

        # Compute the fitnesses
        fitnesses = torch.sum(x ** (2 * self.q), dim=-1)

        # Register the fitness into the Solution object
        solutions.set_evals(fitnesses)

Using multiple GPUs from a problem defined via inheritance. The previous example demonstrating the use of multiple GPUs showed how an independent fitness function can be decorated via evotorch.decorators.on_cuda. Instead of using an independent fitness function, if one wishes to define a problem by subclassing Problem, the overriden method _evaluate_batch(...) has to be decorated by evotorch.decorators.on_cuda. Like in the previous multi-GPU example, let us assume that we want to parallelize the fitness evaluation across N GPUs (where N>1). The inheritance-based code to achieve this can look like this:

from evotorch import Problem, SolutionBatch
from evotorch.decorators import on_cuda


class MyMultiGPUProblem(Problem):
    def __init__(self):
        ...
        super().__init__(
            objective_sense="min",  # the goal is to minimize
            solution_length=10,  # a solution has the length 10
            initial_bounds=(-5.0, 5.0),  # sample new solutions from within [-5, 5]
            dtype=torch.float32,  # the dtype of a solution is float32
            num_actors=N,  # allocate N actors
            # Note: if you are on a computer or on a ray cluster with multiple
            # GPUs, you might prefer to use the string "num_gpus" instead of an
            # integer N, which will cause the number of available GPUs to be
            # counted, and the number of actors to be configured as that count.
            #
            num_gpus_per_actor=1,  # for each actor, assign a cuda device
            device="cpu",  # keep the main population on the CPU
        )

    @on_cuda
    def _evaluate_batch(self, solutions: SolutionBatch):
        # Get the decision values of all the solutions in a 2D PyTorch tensor:
        xs = solutions.values

        # Compute the fitnesses
        fitnesses = ...

        # Register the fitness into the Solution object
        solutions.set_evals(fitnesses)

Customizing how initial solutions are sampled. Instead of sampling solutions from within an interval, one might wish to define a special procedure for generating new solutions. This can be achieved by overriding the _fill(...) method of the Problem class. Please see the example below.

class MyProblemWithCustomizedFilling(Problem):
    def __init__(self):
        super().__init__(
            objective_sense="min",
            solution_length=10,
            dtype=torch.float32,
            # we do not set initial_bounds because we have a manual procedure
            # for initializing solutions
        )

    def _evaluate_batch(self, solutions: SolutionBatch):
        ...  # code to compute and fill the fitnesses goes here

    def _fill(self, values: torch.Tensor):
        # `values` is an empty tensor of shape (n, m) where n is the number
        # of solutions and m is the solution length.
        # The responsibility of this method is to fill this tensor.
        # In the case of this example, let us say that we wish the new
        # solutions to have values sampled from a standard normal distribution.
        values.normal_()

Defining manually-structured optimization problems. The dtype of an optimization problem can be set as object. When the dtype is set as an object, it means that a solution's value can be a PyTorch tensor, or a numpy array, or a Python list, or a Python dictionary, or a string, or a scalar, or None. This gives the user enough flexibility to express non-numeric optimization problems and/or problems where each solution has its own length, or even its own structure.

In the example below, we define an optimization problem where a solution is represented by a Python list and where each solution can have its own length. For simplicity, we define the fitness function as the sum of the values of a solution.

from evotorch import Problem, SolutionBatch
from evotorch.tools import ObjectArray
import random
import torch


class MyCustomStructuredProblem(Problem):
    def __init__(self):
        super().__init__(
            objective_sense="min",
            dtype=object,
        )

    def _evaluate_batch(self, solutions: SolutionBatch):
        # Get the number of solutions
        n = len(solutions)

        # Allocate a PyTorch tensor that will store the fitnesses
        fitnesses = torch.empty(n, dtype=torch.float32)

        # Fitness is computed as the sum of numeric values stored
        # by a solution.
        for i in range(n):
            # Get the values stored by a solution (which, in the case of
            # this example, is a Python list, because we initialize them
            # so in the _fill method).
            sln_values = solutions[i].values
            fitnesses[i] = sum(sln_values)

        # Set the fitnesses
        solutions.set_evals(fitnesses)

    def _fill(self, values: ObjectArray):
        # At this point, we have an ObjectArray of length `n`.
        # This means, we need to fill the values of `n` solutions.
        # `values[i]` represents the values of the i-th solution.
        # Initially, `values[i]` is None.
        # It is up to us how `values[i]` will be filled.
        # Let us make each solution be initialized as a list of
        # random length, containing random real numbers.

        for i in range(len(values)):
            ith_solution_length = random.randint(1, 10)
            ith_solution_values = [random.random() for _ in range(ith_solution_length)]
            values[i] = ith_solution_values

Multi-objective optimization. A multi-objective optimization problem can be expressed by using multiple objective senses. As an example, let us consider an optimization problem where the first objective sense is minimization and the second objective sense is maximization. When working with an external fitness function, the code to express such an optimization problem would look like this:

from evotorch import Problem
from evotorch.decorators import vectorized
import torch


@vectorized
def f(x: torch.Tensor) -> torch.Tensor:
    # (Note that if dtype is object, x will be of type ObjectArray,
    # and not a PyTorch tensor)

    # Code to compute the fitnesses goes here.
    # Our resulting tensor `fitnesses` is expected to have a shape (n, m)
    # where n is the number of solutions and m is the number of objectives
    # (which is 2 in the case of this example).
    # `fitnesses[i, k]` is expected to store the fitness value belonging
    # to the i-th solution according to the k-th objective.
    fitnesses: torch.Tensor = ...
    return fitnesses


problem = Problem(["min", "max"], f, ...)

A multi-objective problem defined via class inheritance would look like this:

from evotorch import Problem, SolutionBatch


class MyMultiObjectiveProblem(Problem):
    def __init__(self):
        super().__init__(objective_sense=["min", "max"], ...)

    def _evaluate_batch(self, solutions: SolutionBatch):
        # Code to compute the fitnesses goes here.
        # `fitnesses[i, k]` is expected to store the fitness value belonging
        # to the i-th solution according to the k-th objective.
        fitnesses: torch.Tensor = ...

        # Set the fitnesses
        solutions.set_evals(fitnesses)

How to solve a problem. If the optimization problem is single-objective and its dtype is a float (e.g. torch.float32, torch.float64, etc.), then it can be solved using any search algorithm implemented in EvoTorch. Let us assume that we have such an optimization problem stored by the variable prob. We could use the cross entropy method) to solve it:

from evotorch import Problem
from evotorch.algorithms import CEM
from evotorch.logging import StdOutLogger


def f(x: torch.Tensor) -> torch.Tensor:
    ...


prob = Problem("min", f, solution_length=..., dtype=torch.float32)

searcher = CEM(
    problem,
    # The keyword arguments below refer to hyperparameters specific to the
    # cross entropy method algorithm. It is recommended to tune these
    # hyperparameters according to the problem at hand.
    popsize=100,  # population size
    parenthood_ratio=0.5,  # 0.5 means better half of solutions become parents
    stdev_init=10.0,  # initial standard deviation of the search distribution
)

_ = StdOutLogger(searcher)  # to report the progress onto the screen
searcher.run(50)  # run for 50 generations

print("Center of the search distribution:", searcher.status["center"])
print("Solution with best fitness ever:", searcher.status["best"])

See the namespace evotorch.algorithms to see the algorithms implemented within EvoTorch.

If the optimization problem at hand has an integer dtype (e.g. torch.int64), or has the object dtype, or has multiple objectives, then distribution-based search algorithms such as CEM cannot be used (since those algorithms were implemented with continuous decision variables and with single-objective problems in mind). In such cases, one can use the algorithm named SteadyState. Please also note that, while using SteadyStateGA on a problem with an integer dtype or with the object dtype, one will have to define manual cross-over and mutation operators specialized to the solution structure of the problem at hand. Please see the documentation of SteadyStateGA for details.

Source code in evotorch/core.py
class Problem(TensorMakerMixin, Serializable):
    """
    Representation of a problem to be optimized.

    The simplest way to use this class is to instantiate it with an
    external fitness function.

    Let us imagine that we have the following fitness function:

    ```
    import torch

    def f(solution: torch.Tensor) -> torch.Tensor:
        return torch.linalg.norm(solution)
    ```

    A problem definition can be made around this fitness function as follows:

    ```
    from evotorch import Problem

    problem = Problem(
        "min", f,  # Goal is to minimize f (would be "max" for maximization)
        solution_length=10,  # Length of a solution is 10
        initial_bounds=(-5.0, 5.0),  # Bounds for sampling a new solution
        dtype=torch.float32,  # dtype of a solution
    )
    ```

    **Vectorized problem definitions.**
    To boost the runtime performance, one might want to define a vectorized
    fitness function where the fitnesses of multiple solutions are computed
    in a batched manner using the vectorization capabilities of PyTorch.
    A vectorized problem definition can be made as follows:

    ```
    from evotorch.decorators import vectorized

    @vectorized
    def vf(solutions: torch.Tensor) -> torch.Tensor:
        return torch.linalg.norm(solutions ** 2, dim=-1)

    problem = Problem(
        "min", vf,  # Goal is to minimize vf (would be "max" for maximization)
        solution_length=10,  # Length of a solution is 10
        initial_bounds=(-5.0, 5.0),  # Bounds for sampling a new solution
        dtype=torch.float32,  # dtype of a solution
    )
    ```

    **Parallelization across multiple CPUs.**
    An optimization problem can be configured to parallelize its evaluation
    operations across multiple CPUs as follows:

    ```python
    problem = Problem("min", f, ..., num_actors=4)  # will use 4 actors
    ```

    **Exploiting hardware accelerators.**
    As an alternative to CPU-based parallelization, one might prefer to use
    the parallelized computation capabilities of a hardware accelerator such
    as CUDA. To load the problem onto a cuda device (for example, onto
    "cuda:0"), one can do:

    ```python
    from evotorch.decorators import vectorized


    @vectorized
    def vf(solutions: torch.Tensor) -> torch.Tensor:
        return ...


    problem = Problem("min", vf, ..., device="cuda:0")
    ```

    **Exploiting multiple GPUs in parallel.**
    One can also keep the entire population on the CPU, and split and distribute
    it to multiple GPUs for GPU-accelerated and parallelized fitness evaluation.
    For this, the main device of the problem is set as CPU, but the fitness
    function is decorated with `evotorch.decorators.on_cuda`.

    ```python
    from evotorch.decorators import on_cuda, vectorized


    @on_cuda
    @vectorized
    def vf(solutions: torch.Tensor) -> torch.Tensor:
        return ...


    problem = Problem(
        "min",
        vf,
        ...,
        num_actors=N,  # where N>1 and equal to the number of GPUs
        # Note: if you are on a computer or on a ray cluster with multiple
        # GPUs, you might prefer to use the string "num_gpus" instead of an
        # integer N, which will cause the number of available GPUs to be
        # counted, and the number of actors to be configured as that count.
        #
        num_gpus_per_actor=1,  # each GPU is assigned to an actor
        device="cpu",
    )
    ```

    **Defining problems via inheritance.**
    A problem can also be defined via inheritance.
    Using inheritance, one can define problems which carry their own additional
    data, and/or update their states as more solutions are evaluated,
    and/or have custom procedures for sampling new solutions, etc.

    As a first example, let us define a parameterized problem. In this example
    problem, the goal is to minimize `x^(2q)`, `q` being a parameter of the
    problem. The definition of such a problem can be as follows:

    ```python
    from evotorch import Problem, Solution


    class MyProblem(Problem):
        def __init__(self, q: float):
            self.q = float(q)

            super().__init__(
                objective_sense="min",  # the goal is to minimize
                solution_length=10,  # a solution has the length 10
                initial_bounds=(-5.0, 5.0),  # sample new solutions from within [-5, 5]
                dtype=torch.float32,  # the dtype of a solution is float32
                # num_actors=...,  # if parallelization via multiple actors is desired
            )

        def _evaluate(self, solution: Solution):
            # This is where we declare the procedure of evaluating a solution

            # Get the decision values of the solution as a PyTorch tensor
            x = solution.values

            # Compute the fitness
            fitness = torch.sum(x ** (2 * self.q))

            # Register the fitness into the Solution object
            solution.set_evaluation(fitness)
    ```

    This parameterized problem can be instantiated as follows (let's say with q=3):

    ```python
    problem = MyProblem(q=3)
    ```

    **Defining vectorized problems via inheritance.**
    Vectorization can be used with inheritance-based problem definitions as well.
    Please see the following example where the method `_evaluate_batch`
    is used instead of `_evaluate` for vectorization:

    ```python
    from evotorch import Problem, SolutionBatch


    class MyVectorizedProblem(Problem):
        def __init__(self, q: float):
            self.q = float(q)

            super().__init__(
                objective_sense="min",  # the goal is to minimize
                solution_length=10,  # a solution has the length 10
                initial_bounds=(-5.0, 5.0),  # sample new solutions from within [-5, 5]
                dtype=torch.float32,  # the dtype of a solution is float32
                # num_actors=...,  # if parallelization via multiple actors is desired
                # device="cuda:0",  # if hardware acceleration is desired
            )

        def _evaluate_batch(self, solutions: SolutionBatch):
            # Get the decision values of all the solutions in a 2D PyTorch tensor:
            xs = solutions.values

            # Compute the fitnesses
            fitnesses = torch.sum(x ** (2 * self.q), dim=-1)

            # Register the fitness into the Solution object
            solutions.set_evals(fitnesses)
    ```

    **Using multiple GPUs from a problem defined via inheritance.**
    The previous example demonstrating the use of multiple GPUs showed how
    an independent fitness function can be decorated via
    `evotorch.decorators.on_cuda`. Instead of using an independent fitness
    function, if one wishes to define a problem by subclassing `Problem`,
    the overriden method `_evaluate_batch(...)` has to be decorated by
    `evotorch.decorators.on_cuda`. Like in the previous multi-GPU example,
    let us assume that we want to parallelize the fitness evaluation
    across N GPUs (where N>1). The inheritance-based code to achieve this
    can look like this:

    ```python
    from evotorch import Problem, SolutionBatch
    from evotorch.decorators import on_cuda


    class MyMultiGPUProblem(Problem):
        def __init__(self):
            ...
            super().__init__(
                objective_sense="min",  # the goal is to minimize
                solution_length=10,  # a solution has the length 10
                initial_bounds=(-5.0, 5.0),  # sample new solutions from within [-5, 5]
                dtype=torch.float32,  # the dtype of a solution is float32
                num_actors=N,  # allocate N actors
                # Note: if you are on a computer or on a ray cluster with multiple
                # GPUs, you might prefer to use the string "num_gpus" instead of an
                # integer N, which will cause the number of available GPUs to be
                # counted, and the number of actors to be configured as that count.
                #
                num_gpus_per_actor=1,  # for each actor, assign a cuda device
                device="cpu",  # keep the main population on the CPU
            )

        @on_cuda
        def _evaluate_batch(self, solutions: SolutionBatch):
            # Get the decision values of all the solutions in a 2D PyTorch tensor:
            xs = solutions.values

            # Compute the fitnesses
            fitnesses = ...

            # Register the fitness into the Solution object
            solutions.set_evals(fitnesses)
    ```

    **Customizing how initial solutions are sampled.**
    Instead of sampling solutions from within an interval, one might wish to
    define a special procedure for generating new solutions. This can be
    achieved by overriding the `_fill(...)` method of the Problem class.
    Please see the example below.

    ```python
    class MyProblemWithCustomizedFilling(Problem):
        def __init__(self):
            super().__init__(
                objective_sense="min",
                solution_length=10,
                dtype=torch.float32,
                # we do not set initial_bounds because we have a manual procedure
                # for initializing solutions
            )

        def _evaluate_batch(self, solutions: SolutionBatch):
            ...  # code to compute and fill the fitnesses goes here

        def _fill(self, values: torch.Tensor):
            # `values` is an empty tensor of shape (n, m) where n is the number
            # of solutions and m is the solution length.
            # The responsibility of this method is to fill this tensor.
            # In the case of this example, let us say that we wish the new
            # solutions to have values sampled from a standard normal distribution.
            values.normal_()
    ```

    **Defining manually-structured optimization problems.**
    The `dtype` of an optimization problem can be set as `object`.
    When the `dtype` is set as an `object`, it means that a solution's
    value can be a PyTorch tensor, or a numpy array, or a Python list,
    or a Python dictionary, or a string, or a scalar, or `None`.
    This gives the user enough flexibility to express non-numeric
    optimization problems and/or problems where each solution has its
    own length, or even its own structure.

    In the example below, we define an optimization problem where a
    solution is represented by a Python list and where each solution can
    have its own length. For simplicity, we define the fitness function
    as the sum of the values of a solution.

    ```python
    from evotorch import Problem, SolutionBatch
    from evotorch.tools import ObjectArray
    import random
    import torch


    class MyCustomStructuredProblem(Problem):
        def __init__(self):
            super().__init__(
                objective_sense="min",
                dtype=object,
            )

        def _evaluate_batch(self, solutions: SolutionBatch):
            # Get the number of solutions
            n = len(solutions)

            # Allocate a PyTorch tensor that will store the fitnesses
            fitnesses = torch.empty(n, dtype=torch.float32)

            # Fitness is computed as the sum of numeric values stored
            # by a solution.
            for i in range(n):
                # Get the values stored by a solution (which, in the case of
                # this example, is a Python list, because we initialize them
                # so in the _fill method).
                sln_values = solutions[i].values
                fitnesses[i] = sum(sln_values)

            # Set the fitnesses
            solutions.set_evals(fitnesses)

        def _fill(self, values: ObjectArray):
            # At this point, we have an ObjectArray of length `n`.
            # This means, we need to fill the values of `n` solutions.
            # `values[i]` represents the values of the i-th solution.
            # Initially, `values[i]` is None.
            # It is up to us how `values[i]` will be filled.
            # Let us make each solution be initialized as a list of
            # random length, containing random real numbers.

            for i in range(len(values)):
                ith_solution_length = random.randint(1, 10)
                ith_solution_values = [random.random() for _ in range(ith_solution_length)]
                values[i] = ith_solution_values
    ```

    **Multi-objective optimization.**
    A multi-objective optimization problem can be expressed by using multiple
    objective senses. As an example, let us consider an optimization problem
    where the first objective sense is minimization and the second objective
    sense is maximization. When working with an external fitness function,
    the code to express such an optimization problem would look like this:

    ```python
    from evotorch import Problem
    from evotorch.decorators import vectorized
    import torch


    @vectorized
    def f(x: torch.Tensor) -> torch.Tensor:
        # (Note that if dtype is object, x will be of type ObjectArray,
        # and not a PyTorch tensor)

        # Code to compute the fitnesses goes here.
        # Our resulting tensor `fitnesses` is expected to have a shape (n, m)
        # where n is the number of solutions and m is the number of objectives
        # (which is 2 in the case of this example).
        # `fitnesses[i, k]` is expected to store the fitness value belonging
        # to the i-th solution according to the k-th objective.
        fitnesses: torch.Tensor = ...
        return fitnesses


    problem = Problem(["min", "max"], f, ...)
    ```

    A multi-objective problem defined via class inheritance would look like this:

    ```python
    from evotorch import Problem, SolutionBatch


    class MyMultiObjectiveProblem(Problem):
        def __init__(self):
            super().__init__(objective_sense=["min", "max"], ...)

        def _evaluate_batch(self, solutions: SolutionBatch):
            # Code to compute the fitnesses goes here.
            # `fitnesses[i, k]` is expected to store the fitness value belonging
            # to the i-th solution according to the k-th objective.
            fitnesses: torch.Tensor = ...

            # Set the fitnesses
            solutions.set_evals(fitnesses)
    ```

    **How to solve a problem.**
    If the optimization problem is single-objective and its dtype is a float
    (e.g. torch.float32, torch.float64, etc.), then it can be solved using
    any search algorithm implemented in EvoTorch. Let us assume that we have
    such an optimization problem stored by the variable `prob`. We could use
    the [cross entropy method][evotorch.algorithms.distributed.gaussian.CEM])
    to solve it:

    ```python
    from evotorch import Problem
    from evotorch.algorithms import CEM
    from evotorch.logging import StdOutLogger


    def f(x: torch.Tensor) -> torch.Tensor:
        ...


    prob = Problem("min", f, solution_length=..., dtype=torch.float32)

    searcher = CEM(
        problem,
        # The keyword arguments below refer to hyperparameters specific to the
        # cross entropy method algorithm. It is recommended to tune these
        # hyperparameters according to the problem at hand.
        popsize=100,  # population size
        parenthood_ratio=0.5,  # 0.5 means better half of solutions become parents
        stdev_init=10.0,  # initial standard deviation of the search distribution
    )

    _ = StdOutLogger(searcher)  # to report the progress onto the screen
    searcher.run(50)  # run for 50 generations

    print("Center of the search distribution:", searcher.status["center"])
    print("Solution with best fitness ever:", searcher.status["best"])
    ```

    See the namespace [evotorch.algorithms][evotorch.algorithms] to see the
    algorithms implemented within EvoTorch.

    If the optimization problem at hand has an integer dtype (e.g. torch.int64),
    or has the `object` dtype, or has multiple objectives, then distribution-based
    search algorithms such as CEM cannot be used (since those algorithms were
    implemented with continuous decision variables and with single-objective
    problems in mind). In such cases, one can use the algorithm named
    [SteadyState][evotorch.algorithms.ga.SteadyStateGA].
    Please also note that, while using
    [SteadyStateGA][evotorch.algorithms.ga.SteadyStateGA] on a problem with an
    integer dtype or with the `object` dtype, one will have to define manual
    cross-over and mutation operators specialized to the solution structure
    of the problem at hand. Please see the documentation of
    [SteadyStateGA][evotorch.algorithms.ga.SteadyStateGA] for details.
    """

    def __init__(
        self,
        objective_sense: ObjectiveSense,
        objective_func: Optional[Callable] = None,
        *,
        initial_bounds: Optional[BoundsPairLike] = None,
        bounds: Optional[BoundsPairLike] = None,
        solution_length: Optional[int] = None,
        dtype: Optional[DType] = None,
        eval_dtype: Optional[DType] = None,
        device: Optional[Device] = None,
        eval_data_length: Optional[int] = None,
        seed: Optional[int] = None,
        num_actors: Optional[Union[int, str]] = None,
        actor_config: Optional[dict] = None,
        num_gpus_per_actor: Optional[Union[int, float, str]] = None,
        num_subbatches: Optional[int] = None,
        subbatch_size: Optional[int] = None,
        store_solution_stats: Optional[bool] = None,
        vectorized: Optional[bool] = None,
    ):
        """
        `__init__(...)`: Initialize the Problem object.

        Args:
            objective_sense: A string, or a sequence of strings.
                For a single-objective problem, a single string
                ("min" or "max", for minimization or maximization)
                is enough.
                For a problem with `n` objectives, a sequence
                of strings (e.g. a list of strings) of length `n` is
                required, each string in the sequence being "min" or
                "max". This argument specifies the goal of the
                optimization.
            initial_bounds: In which interval will the values of a
                new solution will be initialized.
                Expected as a tuple, each element being either a
                scalar, or a vector of length `n`, `n` being the
                length of a solution.
                If a manual solution initialization is preferred
                (instead of an interval-based initialization),
                one can leave `initial_bounds` as None, and override
                the `_fill(...)` method in the inheriting subclass.
            bounds: Interval in which all the solutions must always
                reside.
                Expected as a tuple, each element being either a
                scalar, or a vector of length `n`, `n` being the
                length of a solution.
                This argument is optional, and can be left as None
                if one does not wish to declare hard bounds on the
                decision values of the problem.
                If `bounds` is specified, `initial_bounds` is missing,
                and `_fill(...)` is not overriden, then `bounds` will
                also serve as the `initial_bounds`.
            solution_length: Length of a solution.
                Required for all fixed-length numeric optimization
                problems.
                For variable-length problems (which might or might not
                be numeric), one is expected to leave `solution_length`
                as None, and declare `dtype` as `object`.
            dtype: dtype (data type) of the data stored by a solution.
                Can be given as a string (e.g. "float32"),
                or as a numpy dtype (e.g. `numpy.dtype("float32")`),
                or as a PyTorch dtype (e.g. `torch.float32`).
                Alternatively, if the problem is variable-length
                and/or non-numeric, one is expected to declare `dtype`
                as `object`.
            eval_dtype: dtype to be used for storing the evaluations
                (or fitnesses, or scores, or costs, or losses)
                of the solutions.
                Can be given as a string (e.g. "float32"),
                or as a numpy dtype (e.g. `numpy.dtype("float32")`),
                or as a PyTorch dtype (e.g. `torch.float32`).
                `eval_dtype` must always refer to a "float" data type,
                therefore, `object` is not accepted as a valid `eval_dtype`.
                If `eval_dtype` is not specified (i.e. left as None),
                then the following actions are taken to determine the
                `eval_dtype`:
                if `dtype` is "float16", `eval_dtype` becomes "float16";
                if `dtype` is "bfloat16", `eval_dtype` becomes "bfloat16";
                if `dtype` is "float32", `eval_dtype` becomes "float32";
                if `dtype` is "float64", `eval_dtype` becomes "float64";
                and for any other `dtype`, `eval_dtype` becomes "float32".
            device: Default device in which a new population will be
                generated. For non-numeric problems, this must be "cpu".
                For numeric problems, this can be any device supported
                by PyTorch (e.g. "cuda").
                Note that, if the number of actors of the problem is configured
                to be more than 1, `device` has to be "cpu" (or, equivalently,
                left as None).
            eval_data_length: In addition to evaluation results
                (which are (un)fitnesses, or scores, or costs, or losses),
                each solution can store extra evaluation data.
                If storage of such extra evaluation data is required,
                one can set this argument to an integer bigger than 0.
            seed: Random seed to be used by the random number generator
                attached to the problem object.
                If left as None, no random number generator will be
                attached, and the global random number generator of
                PyTorch will be used instead.
            num_actors: Number of actors to create for parallelized
                evaluation of the solutions.
                Certain string values are also accepted.
                When given as "max" or as "num_cpus", the number of actors
                will be equal to the number of all available CPUs in the ray
                cluster.
                When given as "num_gpus", the number of actors will be
                equal to the number of all available GPUs in the ray
                cluster, and each actor will be assigned a GPU.
                There is also an option, "num_devices", which means that
                both the numbers of CPUs and GPUs will be analyzed, and
                new actors and GPUs for them will be allocated,
                in a one-to-one mapping manner, if possible.
                In more details, with `num_actors="num_devices"`, if
                `device` is given as a GPU device, then it will be inferred
                that the user wishes to put everything (including the
                population) on a single GPU, and therefore there won't be
                any allocation of actors nor GPUs.
                With `num_actors="num_devices"` and with `device` set as
                "cpu" (or as left as None), if there are multiple CPUs
                and multiple GPUs, then `n` actors will be allocated
                where `n` is the minimum among the number of CPUs
                and the number of GPUs, so that there can be one-to-one
                mapping between CPUs and GPUs (i.e. such that each actor
                can be assigned an entire GPU).
                If `num_actors` is given as "num_gpus" or "num_devices",
                the argument `num_gpus_per_actor` must not be used,
                and the `actor_config` dictionary must not contain the
                key "num_gpus".
                If `num_actors` is given as something other than "num_gpus"
                or "num_devices", and if you wish to assign GPUs to each
                actor, then please see the argument `num_gpus_per_actor`.
            actor_config: A dictionary, representing the keyword arguments
                to be passed to the options(...) used when creating the
                ray actor objects. To be used for explicitly allocating
                resources per each actor.
                For example, for declaring that each actor is to use a GPU,
                one can pass `actor_config=dict(num_gpus=1)`.
                Can also be given as None (which is the default),
                if no such options are to be passed.
            num_gpus_per_actor: Number of GPUs to be allocated by each
                remote actor.
                The default behavior is to NOT allocate any GPU at all
                (which is the default behavior of the ray library as well).
                When given as a number `n`, each actor will be given
                `n` GPUs (where `n` can be an integer, or can be a `float`
                for fractional allocation).
                When given as a string "max", then the available GPUs
                across the entire ray cluster (or within the local computer
                in the simplest cases) will be equally distributed among
                the actors.
                When given as a string "all", then each actor will have
                access to all the GPUs (this will be achieved by suppressing
                the environment variable `CUDA_VISIBLE_DEVICES` for each
                actor).
                When the problem is not distributed (i.e. when there are
                no actors), this argument is expected to be left as None.
            num_subbatches: If `num_subbatches` is None (assuming that
                `subbatch_size` is also None), then, when evaluating a
                population, the population will be split into n pieces, `n`
                being the number of actors, and each actor will evaluate
                its assigned piece. If `num_subbatches` is an integer `m`,
                then the population will be split into `m` pieces,
                and actors will continually accept the next unevaluated
                piece as they finish their current tasks.
                The arguments `num_subbatches` and `subbatch_size` cannot
                be given values other than None at the same time.
                While using a distributed algorithm, this argument determines
                how many sub-batches will be generated, and therefore,
                how many gradients will be computed by the remote actors.
            subbatch_size: If `subbatch_size` is None (assuming that
                `num_subbatches` is also None), then, when evaluating a
                population, the population will be split into `n` pieces, `n`
                being the number of actors, and each actor will evaluate its
                assigned piece. If `subbatch_size` is an integer `m`,
                then the population will be split into pieces of size `m`,
                and actors will continually accept the next unevaluated
                piece as they finish their current tasks.
                When there can be significant difference across the solutions
                in terms of computational requirements, specifying a
                `subbatch_size` can be beneficial, because, while one
                actor is busy with a subbatch containing computationally
                challenging solutions, other actors can accept more
                tasks and save time.
                The arguments `num_subbatches` and `subbatch_size` cannot
                be given values other than None at the same time.
                While using a distributed algorithm, this argument determines
                the size of a sub-batch (or sub-population) sampled by a
                remote actor for computing a gradient.
                In distributed mode, it is expected that the population size
                is divisible by `subbatch_size`.
            store_solution_stats: Whether or not the problem object should
                keep track of the best and worst solutions.
                Can also be left as None (which is the default behavior),
                in which case, it will store the best and worst solutions
                only when the first solution batch it encounters is on the
                cpu. This default behavior is to ensure that there is no
                transfer between the cpu and a foreign computation device
                (like the gpu) just for the sake of keeping the best and
                the worst solutions.
            vectorized: Set this to True if the provided fitness function
                is vectorized but is not decorated via `@vectorized`.
        """

        # Set the dtype for the decision variables of the Problem
        if dtype is None:
            self._dtype = torch.float32
        elif is_dtype_object(dtype):
            self._dtype = object
        else:
            self._dtype = to_torch_dtype(dtype)

        _evolog.info(message_from(self, f"The `dtype` for the problem's decision variables is set as {self._dtype}"))

        # Set the dtype for the solution evaluations (i.e. fitnesses and evaluation data)
        if eval_dtype is not None:
            # If an `eval_dtype` is explicitly stated, then accept it as the `_eval_dtype` of the Problem
            self._eval_dtype = to_torch_dtype(eval_dtype)
        else:
            # This is the case where an `eval_dtype` is not explicitly stated by the user.
            # We need to choose a default.
            if self._dtype in (torch.float16, torch.bfloat16, torch.float64):
                # If the `dtype` of the problem is a non-32-bit float type (i.e. float16, bfloat16, float64)
                # then we use that as our `_eval_dtype` as well.
                self._eval_dtype = self._dtype
            else:
                # For any other `dtype`, we use float32 as our `_eval_dtype`.
                self._eval_dtype = torch.float32

            _evolog.info(
                message_from(
                    self, f"`eval_dtype` (the dtype of the fitnesses and evaluation data) is set as {self._eval_dtype}"
                )
            )

        # Set the main device of the Problem object
        self._device = torch.device("cpu") if device is None else torch.device(device)
        _evolog.info(message_from(self, f"The `device` of the problem is set as {self._device}"))

        # Declare the internal variable that might store the random number generator
        self._generator: Optional[torch.Generator] = None

        # Set the seed of the Problem object, if a seed is provided
        self.manual_seed(seed)

        # Declare the internal variables that will store the bounds and the solution length
        self._initial_lower_bounds: Optional[torch.Tensor] = None
        self._initial_upper_bounds: Optional[torch.Tensor] = None
        self._lower_bounds: Optional[torch.Tensor] = None
        self._upper_bounds: Optional[torch.Tensor] = None
        self._solution_length: Optional[int] = None

        if self._dtype is object:
            # If dtype is given as `object`, then there are some runtime sanity checks to perform
            if bounds is not None or initial_bounds is not None:
                # With dtype as object, if bounds are given then we raise an error.
                # This is because the `object` dtype implies that the decision values are not necessarily numeric,
                # and therefore, we cannot have the guarantee of satisfying numeric bounds.
                raise ValueError(
                    f"With dtype as {repr(dtype)}, expected to receive `initial_bounds` and/or `bounds` as None."
                    f" However, one or both of them is/are set as value(s) other than None."
                )
            if solution_length is not None:
                # With dtype as object, if `solution_length` is provided, then we raise an error.
                # This is because the `object` dtype implies that the solutions can be expressed via various
                # containers, each with its own length, and therefore, a fixed solution length cannot be guaranteed.
                raise ValueError(
                    f"With dtype as {repr(dtype)}, expected to receive `solution_length` as None."
                    f" However, received `solution_length` as {repr(solution_length)}."
                )
            if str(self._device) != "cpu":
                # With dtype as object, if `device` is something other than "cpu", then we raise an error.
                # This is because the `object` dtype implies that the decision values are stored by an ObjectArray,
                # whose device is always "cpu".
                raise ValueError(
                    f"With dtype as {repr(dtype)}, expected to receive `device` as 'cpu'."
                    f" However, received `device` as {repr(device)}."
                )
        else:
            # If dtype is something other than `object`, then we need to make sure that we have a valid length for
            # solutions, and also properly store the given numeric bounds.

            if solution_length is None:
                # With a numeric dtype, if solution length is missing, then we raise an error.
                raise ValueError(
                    f"Together with a numeric dtype ({repr(dtype)}),"
                    f" expected to receive `solution_length` as an integer."
                    f" However, `solution_length` is None."
                )
            else:
                # With a numeric dtype, if a solution length is provided, we make sure that it is integer.
                solution_length = int(solution_length)

            # Store the solution length
            self._solution_length = solution_length

            if (bounds is not None) or (initial_bounds is not None):
                # This is the case where we have a dtype other than `object`, and either `bounds` or `initial_bounds`
                # was provided.
                initbnd_tuple_name = "initial_bounds"
                bnd_tuple_name = "bounds"

                if (bounds is not None) and (initial_bounds is None):
                    # With a numeric dtype, if strict bounds are given but initial bounds are not given, then we assume
                    # that the strict bounds also serve as the initial bounds.
                    # Therefore, we take clones of the strict bounds and use this clones as the initial bounds.
                    initial_bounds = clone(bounds)
                    initbnd_tuple_name = "bounds"

                # Below is an internal helper function for some common operations for the (strict) bounds
                # and for the initial bounds.
                def process_bounds(bounds_tuple: BoundsPairLike, tuple_name: str) -> BoundsPair:
                    # This function receives the bounds_tuple (a tuple containing lower and upper bounds),
                    # and the string name of the bounds argument ("bounds" or "initial_bounds").
                    # What is returned is the bounds expressed as PyTorch tensors in the correct dtype and device.

                    nonlocal solution_length

                    # Extract the lower and upper bounds from the received bounds tuple.
                    lb, ub = bounds_tuple

                    # Make sure that the lower and upper bounds are expressed as tensors of correct dtype and device.
                    lb = self.make_tensor(lb)
                    ub = self.make_tensor(ub)

                    for bound_array in (lb, ub):  # For each boundary tensor (lb and ub)
                        if bound_array.ndim not in (0, 1):
                            # If the boundary tensor is not as scalar and is not a 1-dimensional vector, then raise an
                            # error.
                            raise ValueError(
                                f"Lower and upper bounds are expected as scalars or as 1-dimensional vectors."
                                f" However, these given boundaries have incompatible shape:"
                                f" {bound_array} (of shape {bound_array.shape})."
                            )
                        if bound_array.ndim == 1:
                            if len(bound_array) != solution_length:
                                # In the case where the boundary tensor is a 1-dimensional vector, if this vector's length
                                # is not equal to the solution length, then we raise an error.
                                raise ValueError(
                                    f"When boundaries are expressed as 1-dimensional vectors, their length are"
                                    f" expected as the solution length of the Problem object."
                                    f" However, while the problem's solution length is {solution_length},"
                                    f" these given boundaries have incompatible length:"
                                    f" {bound_array} (of length {len(bound_array)})."
                                )

                    # Return the processed forms of the lower and upper boundary tensors.
                    return lb, ub

                # Process the initial bounds with the help of the internal function `process_bounds(...)`
                init_lb, init_ub = process_bounds(initial_bounds, initbnd_tuple_name)

                # Store the processed initial bounds
                self._initial_lower_bounds = init_lb
                self._initial_upper_bounds = init_ub

                if bounds is not None:
                    # If there are strict bounds, then process those bounds with the help of `process_bounds(...)`.
                    lb, ub = process_bounds(bounds, bnd_tuple_name)
                    # Store the processed bounds
                    self._lower_bounds = lb
                    self._upper_bounds = ub

        # Annotate the variable that will store the objective sense(s) of the problem
        self._objective_sense: ObjectiveSense

        # Below is an internal function which makes sure that a provided objective sense has a valid value
        # (where valid values are "min" or "max")
        def validate_sense(s: str):
            if s not in ("min", "max"):
                raise ValueError(
                    f"Invalid objective sense: {repr(s)}."
                    f"Instead, please provide the objective sense as 'min' or 'max'."
                )

        if not is_sequence(objective_sense):
            # If the provided objective sense is not a sequence, then convert it to a single-element list
            senses = [objective_sense]
            num_senses = 1
        else:
            # If the provided objective sense is a sequence, then take a list copy of it
            senses = list(objective_sense)
            num_senses = len(objective_sense)

            # Ensure that each provided objective sense is valid
            for sense in senses:
                validate_sense(sense)

            if num_senses == 0:
                # If the given sequence of objective senses is empty, then we raise an error.
                raise ValueError(
                    "Encountered an empty sequence via `objective_sense`."
                    " For a single-objective problem, please set `objective_sense` as 'min' or 'max'."
                    " For a multi-objective problem, please set `objective_sense` as a sequence,"
                    " each element being 'min' or 'max'."
                )

        # Store the objective senses
        self._senses: Iterable[str] = senses

        # Store the provided objective function (which can be None)
        self._objective_func: Optional[Callable] = objective_func

        # Declare the instance variable that will store whether or not the external fitness function is
        # vectorized, if such an external fitness function is given.
        self._vectorized: Optional[bool]

        # Store the information which indicates whether or not the given objective function is vectorized
        if self._objective_func is None:
            # This is the case where an external fitness function is not given.
            # In this case, we expect the keyword argument `vectorized` to be left as None.

            if vectorized is not None:
                # If the keyword argument `vectorized` is something other than None, then we raise an error
                # to let the user know.
                raise ValueError(
                    f"This problem object received no external fitness function."
                    f" When not using an external fitness function, the keyword argument `vectorized`"
                    f" is expected to be left as None."
                    f" However, the value of the keyword argument `vectorized` is {vectorized}."
                )

            # At this point, we know that we do not have an external fitness function.
            # The variable which is supposed to tell us whether or not the external fitness function is vectorized
            # is therefore irrelevant. We just set it as None.
            self._vectorized = None
        else:
            # This is the case where an external fitness function is given.

            if (
                hasattr(self._objective_func, "__evotorch_vectorized__")
                and self._objective_func.__evotorch_vectorized__
            ):
                # If the external fitness function has an attribute `__evotorch_vectorized__`, and the value of this
                # attribute evaluates to True, then this is an indication that the fitness function was decorated
                # with `@vectorized`.

                if vectorized is not None:
                    # At this point, we know (or at least have the assumption) that the fitness function was decorated
                    # with `@vectorized`. Any boolean value given via the keyword argument `vectorized` would therefore
                    # be either redundant or conflicting.
                    # Therefore, in this case, if the keyword argument `vectorized` is anything other than None, we
                    # raise an error to inform the user.

                    raise ValueError(
                        f"Received a fitness function that was decorated via @vectorized."
                        f" When using such a fitness function, the keyword argument `vectorized`"
                        f" is expected to be left as None."
                        f" However, the value of the keyword argument `vectorized` is {vectorized}."
                    )

                # Since we know that our fitness function declares itself as vectorized, we set the instance variable
                # _vectorized as True.
                self._vectorized = True
            else:
                # This is the case in which the fitness function does not appear to be decorated via `@vectorized`.
                # In this case, if the keyword argument `vectorized` has a value that is equivalent to True,
                # then the value of `_vectorized` becomes True. On the other hand, if the keyword argument `vectorized`
                # was left as None or if it has a value that is equivalent to False, `_vectorized` becomes False.
                self._vectorized = bool(vectorized)

        # If the evaluation data length is explicitly stated, then convert it to an integer and store it.
        # Otherwise, store the evaluation data length as 0.
        self._eval_data_length = 0 if eval_data_length is None else int(eval_data_length)

        # Initialize the actor index.
        # If the problem is configured to be parallelized and the parallelization is triggered, then each remote
        # copy will have a different integer value for `_actor_index`.
        self._actor_index: Optional[int] = None

        # Initialize the variable that might store the list of actors as None.
        # If the problem is configured to be parallelized and the parallelization is triggered, then this variable
        # will store references to the remote actors (each remote actor storing its own copy of this Problem
        # instance).
        self._actors: Optional[list] = None

        # Initialize the variable that might store the ray ActorPool.
        # If the problem is configured to be parallelized and the parallelization is triggered, then this variable
        # will store the ray ActorPool that is generated out of the remote actors.
        self._actor_pool: Optional[ActorPool] = None

        # Store the ray actor configuration dictionary provided by the user (if any).
        # When (or if) the parallelization is triggered, each actor will be created with this given configuration.
        self._actor_config: Optional[dict] = None if actor_config is None else deepcopy(dict(actor_config))

        # If given, store the sub-batch size or number of sub-batches.
        # When the problem is parallelized, a sub-batch size determines the maximum size for a SolutionBatch
        # that will be sent to a remote actor for parallel solution evaluation.
        # Alternatively, num_subbatches determines into how many pieces will a SolutionBatch be split
        # for parallelization.
        # If both are None, then the main SolutionBatch will be split among the actors.
        if (num_subbatches is not None) and (subbatch_size is not None):
            raise ValueError(
                f"Encountered both `num_subbatches` and `subbatch_size` as values other than None."
                f" num_subbatches={num_subbatches}, subbatch_size={subbatch_size}."
                f" Having both of them as values other than None cannot be accepted."
            )
        self._num_subbatches: Optional[int] = None if num_subbatches is None else int(num_subbatches)
        self._subbatch_size: Optional[int] = None if subbatch_size is None else int(subbatch_size)

        # Initialize the additional states to be loaded by the remote actor as None.
        # If there are such additional states for remote actors, the inheriting class can fill this as a list
        # of dictionaries.
        self._remote_states: Optional[Iterable[dict]] = None

        # Initialize a temporary internal variable which stores the resources available in the ray cluster.
        # Most probably, we are interested in the resources "CPU" and "GPU".
        ray_resources: Optional[dict] = None

        # The following is an internal helper function which returns the amount of availability for a given
        # resource in the ray cluster.
        # If the requested resource is not available at all, None will be returned.
        def get_ray_resource(resource_name: str) -> Any:
            # Ensure that the ray cluster is initialized
            ensure_ray()
            nonlocal ray_resources
            if ray_resources is None:
                # If the ray resource information was not fetched, then fetch them and store them.
                ray_resources = ray.available_resources()
            # Return the information regarding the requested resource from the fetched resource information.
            # If it turns out that the requested resource is not available at all, the result will be None.
            return ray_resources.get(resource_name, None)

        # Annotate the variable that will store the number of actors (to be created when the parallelization
        # is triggered).
        self._num_actors: int

        if num_actors is None:
            # If the argument `num_actors` is left as None, then we set `_num_actors` as 0, which means that
            # there will be no parallelization.
            self._num_actors = 0
        elif isinstance(num_actors, str):
            # This is the case where `num_actors` has a string value
            if num_actors in ("max", "num_cpus"):
                # If the `num_actors` argument was given as "max" or as "num_cpus", then we first read how many CPUs
                # are available in the ray cluster, then convert it to integer (via computing its ceil value), and
                # finally set `_num_actors` as this integer.
                self._num_actors = math.ceil(get_ray_resource("CPU"))
            elif num_actors == "num_gpus":
                # If the `num_actors` argument was given as "num_gpus", then we first read how many GPUs are
                # available in the ray cluster.
                num_gpus = get_ray_resource("GPU")
                if num_gpus is None:
                    # If there are no GPUs at all, then we raise an error
                    raise ValueError(
                        "The argument `num_actors` was encountered as 'num_gpus'."
                        " However, there does not seem to be any GPU available."
                    )
                if num_gpus < 1e-4:
                    # If the number of available GPUs are 0 or close to 0, then we raise an error
                    raise ValueError(
                        f"The argument `num_actors` was encountered as 'num_gpus'."
                        f" However, the number of available GPUs are either 0 or close to 0 (= {num_gpus})."
                    )
                if (actor_config is not None) and ("num_gpus" in actor_config):
                    # With `num_actors` argument given as "num_gpus", we will also allocate each GPU to an actor.
                    # If `actor_config` contains an item with key "num_gpus", then that configuration item would
                    # conflict with the GPU allocation we are about to do here.
                    # So, we raise an error.
                    raise ValueError(
                        "The argument `num_actors` was encountered as 'num_gpus'."
                        " With this configuration, the number of GPUs assigned to an actor is automatically determined."
                        " However, at the same time, the `actor_config` argument was received with the key 'num_gpus',"
                        " which causes a conflict."
                    )
                if num_gpus_per_actor is not None:
                    # With `num_actors` argument given as "num_gpus", we will also allocate each GPU to an actor.
                    # If the argument `num_gpus_per_actor` is also stated, then such a configuration item would
                    # conflict with the GPU allocation we are about to do here.
                    # So, we raise an error.
                    raise ValueError(
                        f"The argument `num_actors` was encountered as 'num_gpus'."
                        f" With this configuration, the number of GPUs assigned to an actor is automatically determined."
                        f" However, at the same time, the `num_gpus_per_actor` argument was received with a value other"
                        f" than None ({repr(num_gpus_per_actor)}), which causes a conflict."
                    )
                # Set the number of actors as the ceiled integer counterpart of the number of available GPUs
                self._num_actors = math.ceil(num_gpus)
                # We assign a GPU for each actor (by overriding the value for the argument `num_gpus_per_actor`).
                num_gpus_per_actor = num_gpus / self._num_actors
            elif num_actors == "num_devices":
                # This is the case where `num_actors` has the string value "num_devices".

                # With `num_actors` set as "num_devices", if there are any GPUs, the behavior is to assign a GPU
                # to each actor. If there are conflicting configurations regarding how many GPUs are to be assigned
                # to each actor, then we raise an error.
                if (actor_config is not None) and ("num_gpus" in actor_config):
                    raise ValueError(
                        "The argument `num_actors` was encountered as 'num_devices'."
                        " With this configuration, the number of GPUs assigned to an actor is automatically determined."
                        " However, at the same time, the `actor_config` argument was received with the key 'num_gpus',"
                        " which causes a conflict."
                    )
                if num_gpus_per_actor is not None:
                    raise ValueError(
                        f"The argument `num_actors` was encountered as 'num_devices'."
                        f" With this configuration, the number of GPUs assigned to an actor is automatically determined."
                        f" However, at the same time, the `num_gpus_per_actor` argument was received with a value other"
                        f" than None ({repr(num_gpus_per_actor)}), which causes a conflict."
                    )

                if self._device != torch.device("cpu"):
                    # If the main device is not CPU, then the user most probably wishes to put all the
                    # computations (both evaluations and the population) on the GPU, without allocating
                    # any actor.
                    # So, we set `_num_actors` as None, and overwrite `num_gpus_per_actor` with None.
                    self._num_actors = None
                    num_gpus_per_actor = None
                else:
                    # If the device argument is "cpu" or left as None, then we assume that actor allocations
                    # might be desired.

                    # Read how many CPUs and GPUs are available in the ray cluster.
                    num_cpus = get_ray_resource("CPU")
                    num_gpus = get_ray_resource("GPU")

                    # If we have multiple CPUs, then we continue with the actor allocation procedures.
                    if (num_gpus is None) or (num_gpus < 1e-4):
                        # If there are no GPUs, then we set the number of actors as the number of CPUs, and we
                        # set the number of GPUs per actor as None (which means that there will be no GPU
                        # assignment)
                        self._num_actors = math.ceil(num_cpus)
                        num_gpus_per_actor = None
                    else:
                        # If there are GPUs available, then we compute the minimum among the number of CPUs and
                        # GPUs, and this minimum value becomes the number of actors (so that there can be
                        # one-to-one mapping between actors and GPUs).
                        self._num_actors = math.ceil(min(num_cpus, num_gpus))

                        # We assign a GPU for each actor (by overriding the value for the argument
                        # `num_gpus_per_actor`).
                        if self._num_actors <= num_gpus:
                            num_gpus_per_actor = 1
                        else:
                            num_gpus_per_actor = num_gpus / self._num_actors
            else:
                # This is the case where `num_actors` is given as an unexpected string. We raise an error here.
                raise ValueError(
                    f"Invalid string value for `num_actors`: {repr(num_actors)}."
                    f" The acceptable string values for `num_actors` are 'max', 'num_cpus', 'num_gpus', 'num_devices'."
                )
        else:
            # This is the case where `num_actors` has a value which is not a string.
            # In this case, we make sure that the given value is an integer, and then use this integer as our
            # number of actors.
            self._num_actors = int(num_actors)

        if self._num_actors == 1:
            _evolog.info(
                message_from(
                    self,
                    (
                        "The number of actors that will be allocated for parallelized evaluation was encountered as 1."
                        " This number is automatically dropped to 0,"
                        " because having only 1 actor does not bring any benefit in terms of parallelization."
                    ),
                )
            )
            # Creating a single actor does not bring any benefit of parallelization.
            # Therefore, at the end of all the computations above regarding the number of actors, if it turns out
            # that the target number of actors is 1, we reduce it to 0 (meaning that no actor will be initialized).
            self._num_actors = 0

            # Since we are to allocate no actor, the value of the argument `num_gpus_per_actor` is meaningless.
            # We therefore overwrite the value of that argument with None.
            num_gpus_per_actor = None

        _evolog.info(
            message_from(
                self, f"The number of actors that will be allocated for parallelized evaluation is {self._num_actors}"
            )
        )

        if (self._num_actors >= 2) and (self._device != torch.device("cpu")):
            detailed_error_msg = (
                f"The number of actors that will be allocated for parallelized evaluation is {self._num_actors}."
                " When the number of actors is at least 2,"
                ' the only supported value for the `device` argument is "cpu".'
                f" However, `device` was received as {self._device}."
                "\n\n---- Possible ways to fix the error: ----"
                "\n\n"
                "(1)"
                " If both the population and the fitness evaluation operations can fit into the same device,"
                f" try setting `device={self._device}` and `num_actors=0`."
                "\n\n"
                "(2)"
                " If you would like to use N number of GPUs in parallel for fitness evaluation (where N>1),"
                ' set `device="cpu"` (so that the main process will keep the population on the cpu), set'
                " `num_actors=N` and `num_gpus_per_actor=1` (to allocate an actor for each of the `N` GPUs),"
                " and then, decorate your fitness function using `evotorch.decorators.on_cuda`"
                " so that the fitness evaluation will be performed on the cuda device assigned to the actor."
                " The code for achieving this can look like this:"
                "\n\n"
                "    from evotorch import Problem\n"
                "    from evotorch.decorators import on_cuda, vectorized\n"
                "    import torch\n"
                "\n"
                "    @on_cuda\n"
                "    @vectorized\n"
                "    def f(x: torch.Tensor) -> torch.Tensor:\n"
                "        ...\n"
                "\n"
                '    problem = Problem("min", f, device="cpu", num_actors=N, num_gpus_per_actor=1)\n'
                "\n"
                "Or, it can look like this:\n"
                "\n"
                "    from evotorch import Problem, SolutionBatch\n"
                "    from evotorch.decorators import on_cuda\n"
                "    import torch\n"
                "\n"
                "    class MyProblem(Problem):\n"
                "        def __init__(self, ...):\n"
                "            super().__init__(\n"
                '                objective_sense="min", device="cpu", num_actors=N, num_gpus_per_actor=1, ...\n'
                "            )\n"
                "\n"
                "        @on_cuda\n"
                "        def _evaluate_batch(self, batch: SolutionBatch):\n"
                "            ...\n"
                "\n"
                "    problem = MyProblem(...)\n"
                "\n"
                "\n"
                "(3)"
                " Similarly to option (2), for when you wish to use N number of GPUs for fitness evaluation,"
                ' set `device="cpu"`, set `num_actors=N` and `num_gpus_per_actor=1`, then, within the evaluation'
                ' function, manually use the device `"cuda"` to accelerate the computation.'
                "\n\n"
                "--------------\n"
                "Note for cases (2) and (3): if you are on a computer or on a ray cluster with multiple GPUs, you"
                ' might prefer to set `num_actors` as the string "num_gpus" instead of an integer N,'
                " which will cause the number of available GPUs to be counted, and the number of actors to be"
                " configured as that count."
            )

            raise ValueError(detailed_error_msg)

        # Annotate the variable which will determine how many GPUs are to be assigned to each actor.
        self._num_gpus_per_actor: Optional[Union[str, int, float]]

        if (actor_config is not None) and ("num_gpus" in actor_config) and (num_gpus_per_actor is not None):
            # If `actor_config` dictionary has the item "num_gpus" and also `num_gpus_per_actor` is not None,
            # then there is a conflicting (or redundant) configuration. We raise an error here.
            raise ValueError(
                'The `actor_config` dictionary contains the key "num_gpus".'
                " At the same time, `num_gpus_per_actor` has a value other than None."
                " These two configurations are conflicting."
                " Please specify the number of GPUs per actor either via the `actor_config` dictionary,"
                " or via the `num_gpus_per_actor` argument, but not via both."
            )

        if num_gpus_per_actor is None:
            # If the argument `num_gpus_per_actor` is not specified, then we set the attribute
            # `_num_gpus_per_actor` as None, which means that no GPUs will be assigned to the actors.
            self._num_gpus_per_actor = None
        elif isinstance(num_gpus_per_actor, str):
            # This is the case where `num_gpus_per_actor` is given as a string.
            if num_gpus_per_actor == "max":
                # This is the case where `num_gpus_per_actor` is given as "max".
                num_gpus = get_ray_resource("GPU")
                if num_gpus is None:
                    # With `num_gpus_per_actor` as "max", if there is no GPU available, then we set the attribute
                    # `_num_gpus_per_actor` as None, which means there will be no GPU assignment to the actors.
                    self._num_gpus_per_actor = None
                else:
                    # With `num_gpus_per_actor` as "max", if there are GPUs available, then the available GPUs will
                    # be shared among the actors.
                    self._num_gpus_per_actor = num_gpus / self._num_actors
            elif num_gpus_per_actor == "all":
                # When `num_gpus_per_actor` is "all", we also set the attribute `_num_gpus_per_actor` as "all".
                # When a remote actor is initialized, the remote actor will see that the Problem instance has its
                # `_num_gpus_per_actor` set as "all", and it will remove the environment variable named
                # "CUDA_VISIBLE_DEVICES" in its own environment.
                # With "CUDA_VISIBLE_DEVICES" removed, an actor will see all the GPUs available in its own
                # environment.
                self._num_gpus_per_actor = "all"
            else:
                # This is the case where `num_gpus_per_actor` argument has an unexpected string value.
                # We raise an error.
                raise ValueError(
                    f"Invalid string value for `num_gpus_per_actor`: {repr(num_gpus_per_actor)}."
                    f' Acceptable string values for `num_gpus_per_actor` are: "max", "all".'
                )
        elif isinstance(num_gpus_per_actor, int):
            # When the argument `num_gpus_per_actor` is set as an integer we just set the attribute
            # `_num_gpus_per_actor` as this integer.
            self._num_gpus_per_actor = num_gpus_per_actor
        else:
            # For anything else, we assume that `num_gpus_per_actor` is an object that is convertible to float.
            # Therefore, we convert it to float and store it in the attribute `_num_gpus_per_actor`.
            # Also, remember that, when `num_actors` is given as "num_gpus" or as "num_devices",
            # the code above overrides the value for the argument `num_gpus_per_actor`, which means,
            # this is the case that is activated when `num_actors` is "num_gpus" or "num_devices".
            self._num_gpus_per_actor = float(num_gpus_per_actor)

        if self._num_actors > 0:
            _evolog.info(
                message_from(self, f"Number of GPUs that will be allocated per actor is {self._num_gpus_per_actor}")
            )

        # Initialize the Hook instances (and the related status dictionary for the `_after_eval_hook`)
        self._before_eval_hook: Hook = Hook()
        self._after_eval_hook: Hook = Hook()
        self._after_eval_status: dict = {}
        self._remote_hook: Hook = Hook()
        self._before_grad_hook: Hook = Hook()
        self._after_grad_hook: Hook = Hook()

        # Initialize various stats regarding the solutions encountered by this Problem instance.
        self._store_solution_stats = None if store_solution_stats is None else bool(store_solution_stats)
        self._best: Optional[list] = None
        self._worst: Optional[list] = None
        self._best_evals: Optional[torch.Tensor] = None
        self._worst_evals: Optional[torch.Tensor] = None

        # Initialize the boolean attribute which indicates whether or not this Problem instance (which can be
        # the main instance or a remote instance on an actor) is "prepared" via the `_prepare` method.
        self._prepared: bool = False

    def manual_seed(self, seed: Optional[int] = None):
        """
        Provide a manual seed for the Problem object.

        If the given seed is None, then the Problem object will remove
        its own stored generator, and start using the global generator
        of PyTorch instead.
        If the given seed is an integer, then the Problem object will
        instantiate its own generator with the given seed.

        Args:
            seed: None for using the global PyTorch generator; an integer
                for instantiating a new PyTorch generator with this given
                integer seed, specific to this Problem object.
        """
        if seed is None:
            self._generator = None
        else:
            if self._generator is None:
                self._generator = torch.Generator(device=self.device)
            self._generator.manual_seed(seed)

    @property
    def dtype(self) -> DType:
        """
        dtype of the Problem object.

        The decision variables of the optimization problem are of this dtype.
        """
        return self._dtype

    @property
    def device(self) -> Device:
        """
        device of the Problem object.

        New solutions and populations will be generated in this device.
        """
        return self._device

    @property
    def aux_device(self) -> Device:
        """
        Auxiliary device to help with the computations, most commonly for
        speeding up the solution evaluations.

        An auxiliary device is different than the main device of the Problem
        object (the main device being expressed by the `device` property).
        While the main device of the Problem object determines where the
        solutions and the populations are stored (and also using which device
        should a SearchAlgorithm instance communicate with the problem),
        an auxiliary device is a device that might be used by the Problem
        instance itself for its own computations (e.g. computations defined
        within the methods `_evaluate(...)` or `_evaluate_batch(...)`).

        If the problem's main device is something other than "cpu", that main
        device is also seen as the auxiliary device, and therefore returned
        by this property.

        If the problem's main device is "cpu", then the auxiliary device
        is decided as follows. If `num_gpus_per_actor` of the Problem object
        was set as "all" and if this instance is a remote instance, then the
        auxiliary device is guessed as "cuda:N" where N is the actor index.
        In all other cases, the auxiliary device is "cuda" if cuda is
        available, and "cpu" otherwise.
        """
        cpu_device = torch.device("cpu")
        if torch.device(self.device) == cpu_device:
            if torch.cuda.is_available():
                if isinstance(self._num_gpus_per_actor, str) and (self._num_gpus_per_actor == "all") and self.is_remote:
                    return torch.device("cuda", self.actor_index)
                else:
                    return torch.device("cuda")
            else:
                return cpu_device
        else:
            return self.device

    @property
    def eval_dtype(self) -> DType:
        """
        evaluation dtype of the Problem object.

        The evaluation results of the solutions are stored according to this
        dtype.
        """
        return self._eval_dtype

    @property
    def generator(self) -> Optional[torch.Generator]:
        """
        Random generator used by this Problem object.

        Can also be None, which means that the Problem object will use the
        global random generator of PyTorch.
        """
        return self._generator

    @property
    def has_own_generator(self) -> bool:
        """
        Whether or not the Problem object has its own random generator.

        If this is True, then the Problem object will use its own
        random generator when creating random values or tensors.
        If this is False, then the Problem object will use the global
        random generator when creating random values or tensors.
        """
        return self.generator is not None

    @property
    def objective_sense(self) -> ObjectiveSense:
        """
        Get the objective sense.

        If the problem is single-objective, then a single string is returned.
        If the problem is multi-objective, then the objective senses will be
        returned in a list.

        The returned string in the single-objective case, or each returned
        string in the multi-objective case, is "min" or "max".
        """
        if len(self.senses) == 1:
            return self.senses[0]
        else:
            return self.senses

    @property
    def senses(self) -> Iterable[str]:
        """
        Get the objective senses.

        The return value is a list of strings, each string being
        "min" or "max".
        """
        return self._senses

    @property
    def is_single_objective(self) -> bool:
        """Whether or not the problem is single-objective"""
        return len(self.senses) == 1

    @property
    def is_multi_objective(self) -> bool:
        """Whether or not the problem is multi-objective"""
        return len(self.senses) > 1

    def get_obj_order_descending(self) -> Iterable[bool]:
        """When sorting the solutions from best to worst according to each objective i, is the ordering descending?"""
        result = []
        for s in self.senses:
            if s == "min":
                result.append(False)
            elif s == "max":
                result.append(True)
            else:
                raise ValueError(f"Invalid sense: {repr(s)}")
        return result

    @property
    def solution_length(self) -> Optional[int]:
        """
        Get the solution length.

        Problems with `dtype=None` do not have solution lengths.
        For such problems, this property returns None.
        """
        return self._solution_length

    @property
    def eval_data_length(self) -> int:
        """
        Length of the extra evaluation data vector for each solution.
        """
        return self._eval_data_length

    @property
    def initial_lower_bounds(self) -> Optional[torch.Tensor]:
        """
        Initial lower bounds, for when initializing a new solution.

        If such a bound was declared during the initialization phase,
        the returned value is a torch tensor (in the form of a vector
        or in the form of a scalar).
        If no such bound was declared, the returned value is None.
        """
        return self._initial_lower_bounds

    @property
    def initial_upper_bounds(self) -> Optional[torch.Tensor]:
        """
        Initial upper bounds, for when initializing a new solution.

        If such a bound was declared during the initialization phase,
        the returned value is a torch tensor (in the form of a vector
        or in the form of a scalar).
        If no such bound was declared, the returned value is None.
        """
        return self._initial_upper_bounds

    @property
    def lower_bounds(self) -> Optional[torch.Tensor]:
        """
        Lower bounds for the allowed values of a solution.

        If such a bound was declared during the initialization phase,
        the returned value is a torch tensor (in the form of a vector
        or in the form of a scalar).
        If no such bound was declared, the returned value is None.
        """
        return self._lower_bounds

    @property
    def upper_bounds(self) -> Optional[torch.Tensor]:
        """
        Upper bounds for the allowed values of a solution.

        If such a bound was declared during the initialization phase,
        the returned value is a torch tensor (in the form of a vector
        or in the form of a scalar).
        If no such bound was declared, the returned value is None.
        """
        return self._upper_bounds

    def generate_values(self, num_solutions: int) -> Union[torch.Tensor, ObjectArray]:
        """
        Generate decision values.

        This function returns a tensor containing the decision values
        for `n` new solutions, `n` being the integer passed as the `num_rows`
        argument.

        For numeric problems, this function generates the decision values
        which respect `initial_bounds` (or `bounds`, if `initial_bounds`
        was not provided).
        If this type of initialization is not desired, one can override
        this function and define a manual initialization scheme in the
        inheriting subclass.

        For non-numeric problems, it is expected that the inheriting subclass
        will override the method `_fill(...)`.

        Args:
            num_solutions: For how many solutions will new decision values be
                generated.
        Returns:
            A PyTorch tensor for numeric problems, an ObjectArray for
            non-numeric problems.
        """
        result = self.make_empty(num_solutions=num_solutions)
        self._fill(result)
        return result

    def _fill(self, values: Iterable):
        """
        Fill the provided `values` tensor with new decision values.

        Inheriting subclasses can override this method to specialize how
        new solutions are generated.

        For numeric problems, this method already has an implementation
        which samples the initial decision values uniformly from the
        interval expressed by `initial_bounds` attribute.
        For non-numeric problems, overriding this method is mandatory.

        Args:
            values: The tensor which is to be filled with the new decision
                values.
        """
        if self.dtype is object:
            raise NotImplementedError(
                "The dtype of this problem is object, therefore a manual implementation of the"
                " method `_fill(...)` needs to be provided by the inheriting class."
            )
        else:
            if (self.initial_lower_bounds is None) or (self.initial_upper_bounds is None):
                raise RuntimeError(
                    "The default implementation of the method `_fill(...)` does not know how to initialize solutions"
                    " because it appears that this Problem object was not given neither `initial_bounds` nor `bounds`"
                    " during the moment of initialization."
                    " Please either instantiate this Problem object with `initial_bounds` and/or `bounds`, or override"
                    " the method `_fill(...)` to specify how solutions should be initialized."
                )
            else:
                return self.make_uniform(
                    out=values,
                    lb=self.initial_lower_bounds,
                    ub=self.initial_upper_bounds,
                )

    def generate_batch(
        self,
        popsize: Optional[int] = None,
        *,
        empty: bool = False,
        center: Optional[RealOrVector] = None,
        stdev: Optional[RealOrVector] = None,
        symmetric: bool = False,
    ) -> "SolutionBatch":
        """
        Generate a new SolutionBatch.

        Args:
            popsize: Number of solutions that will be contained in the new
                batch.
            empty: Set this as True if you would like to receive the solutions
                un-initialized.
            center: Center point of the Gaussian distribution from which
                the decision values will be sampled, as a scalar or as a
                1-dimensional vector.
                Can also be left as None.
                If `center` is None and `stdev` is None, all the decision
                values will be sampled from the interval specified by
                `initial_bounds` (or by `bounds` if `initial_bounds` was not
                specified).
                If `center` is None and `stdev` is not None, a center point
                will be sampled from within the interval specified by
                `initial_bounds` or `bounds`, and the decision values will be
                sampled from a Gaussian distribution around this center point.
            stdev: Can be None (default) if the SolutionBatch is to contain
                decision values sampled from the interval specified by
                `initial_bounds` (or by `bounds` if `initial_bounds` was not
                provided during the initialization phase).
                Alternatively, a scalar or a 1-dimensional vector specifying
                the standard deviation of the Gaussian distribution from which
                the decision values will be sampled.
            symmetric: To be used only when `stdev` is not None.
                If `symmetric` is True, decision values will be sampled from
                the Gaussian distribution in a symmetric (i.e. antithetic)
                manner.
                Otherwise, the decision values will be sampled in the
                non-antithetic manner.
        """
        if (center is None) and (stdev is None):
            if symmetric:
                raise ValueError(
                    f"The argument `symmetric` can be set as True only when `center` and `stdev` are provided."
                    f" Although `center` and `stdev` are None, `symmetric` was received as {symmetric}."
                )
            return SolutionBatch(self, popsize, empty=empty, device=self.device)
        elif (center is not None) and (stdev is not None):
            if empty:
                raise ValueError(
                    f"When `center` and `stdev` are provided, the argument `empty` must be False."
                    f" However, the received value for `empty` is {empty}."
                )
            result = SolutionBatch(self, popsize, device=self.device, empty=True)
            self.make_gaussian(out=result.access_values(), center=center, stdev=stdev, symmetric=symmetric)
            return result
        else:
            raise ValueError(
                f"The arguments `center` and `stdev` were expected to be None or non-None at the same time."
                f" Received `center`: {center}."
                f" Received `stdev`: {stdev}."
            )

    def _parallelize(self):
        """Create ray actors for parallelizing the solution evaluations."""

        # If the problem was explicitly configured for
        # NOT having parallelization, leave this function.
        if (not isinstance(self._num_actors, str)) and (self._num_actors <= 0):
            return

        # If this problem object is a remote one,
        # leave this function
        # (because we do not want the remote worker
        # to parallelize itself further)
        if self._actor_index is not None:
            return

        # If the actors list is not None, then this means
        # that the initialization of the parallelization mechanism
        # was already completed. So, leave this function.
        if self._actors is not None:
            return

        # Make sure that ray is initialized
        ensure_ray()
        number_of_actors = self._num_actors

        # numpy's RandomState uses 32-bit unsigned integers
        # for random seeds.
        # So, the following value is the exclusive upper bound
        # for a random seed.
        supremum_seed = 2**32

        # Generate an integer from the main problem object's
        # random_state. From this integer, further seed integers
        # will be computed, and these generated seeds will be
        # used by the remote actors.
        base_seed = int(self.make_randint(tuple(), n=supremum_seed))

        # The following function returns a seed number for the actor
        # number i.
        def generate_actor_seed(i):
            nonlocal base_seed, supremum_seed
            return (base_seed + (i + 1)) % supremum_seed

        all_seeds = []
        j = 0
        for i in range(number_of_actors):
            actor_seeds = []
            for _ in range(4):
                actor_seeds.append(generate_actor_seed(j))
                j += 1
            all_seeds.append(tuple(actor_seeds))

        if self._remote_states is None:
            remote_states = [{} for _ in range(number_of_actors)]
        else:
            remote_states = self._remote_states

        # Prepare the necessary actor config
        config_per_actor = {}
        if self._actor_config is not None:
            config_per_actor.update(self._actor_config)
        if isinstance(self._num_gpus_per_actor, (int, float)):
            config_per_actor["num_gpus"] = self._num_gpus_per_actor

        # Generate the actors, each with a unique seed.
        if config_per_actor is None:
            actors = [EvaluationActor.remote(self, i, all_seeds[i], remote_states[i]) for i in range(number_of_actors)]
        else:
            actors = [
                EvaluationActor.options(**config_per_actor).remote(self, i, all_seeds[i], remote_states[i])
                for i in range(number_of_actors)
            ]

        self._actors = actors
        self._actor_pool = ActorPool(self._actors)
        self._remote_states = None

    def all_remote_problems(self) -> AllRemoteProblems:
        """
        Get an accessor which is used for running a method
        on all remote clones of this Problem object.

        For example, given a Problem object named `my_problem`,
        also assuming that this Problem object is parallelized,
        and therefore has `n` remote actors, a method `f()`
        can be executed on all the remote instances as follows:

            results = my_problem.all_remote_problems().f()

        The variable `results` is a list of length `n`, the i-th
        item of the list belonging to the method f's result
        from the i-th actor.

        Returns:
            A method accessor for all the remote Problem objects.
        """
        self._parallelize()
        if self.is_remote:
            raise RuntimeError(
                "The method `all_remote_problems()` can only be used on the main (i.e. non-remote)"
                " Problem instance."
                " However, this Problem instance is on a remote actor."
            )
        return AllRemoteProblems(self._actors)

    def all_remote_envs(self) -> AllRemoteEnvs:
        """
        Get an accessor which is used for running a method
        on all remote reinforcement learning environments.

        This method can only be used on parallelized Problem
        objects which have their `get_env()` methods defined.
        For example, one can use this feature on a parallelized
        GymProblem.

        As an example, let us consider a parallelized GymProblem
        object named `my_problem`. Given that `my_problem` has
        `n` remote actors, a method `f()` can be executed
        on all remote reinforcement learning environments as
        follows:

            results = my_problem.all_remote_envs().f()

        The variable `results` is a list of length `n`, the i-th
        item of the list belonging to the method f's result
        from the i-th actor.

        Returns:
            A method accessor for all the remote reinforcement
            learning environments.
        """
        self._parallelize()
        if self.is_remote:
            raise RuntimeError(
                "The method `all_remote_envs()` can only be used on the main (i.e. non-remote)"
                " Problem instance."
                " However, this Problem instance is on a remote actor."
            )
        return AllRemoteEnvs(self._actors)

    def kill_actors(self):
        """
        Kill all the remote actors used by the Problem instance.

        One might use this method to release the resources used by the
        remote actors.
        """
        if not self.is_main:
            raise RuntimeError(
                "The method `kill_actors()` can only be used on the main (i.e. non-remote)"
                " Problem instance."
                " However, this Problem instance is on a remote actor."
            )
        for actor in self._actors:
            ray.kill(actor)
        self._actors = None
        self._actor_pool = None

    @property
    def num_actors(self) -> int:
        """
        Number of actors (to be) used for parallelization.
        If the problem is configured for no parallelization,
        the result will be 0.
        """
        return self._num_actors

    @property
    def actors(self) -> Optional[list]:
        """
        Get the ray actors, if the Problem object is distributed.
        If the Problem object is not distributed and therefore
        has no actors, then, the result will be None.
        """
        return self._actors

    @property
    def actor_index(self) -> Optional[int]:
        """Return the actor index if this is a remote worker.
        If this is not a remote worker, return None.
        """
        return self._actor_index

    @property
    def is_remote(self) -> bool:
        """Returns True if this problem object lives in a remote ray actor.
        Otherwise, returns False.
        """
        return self._actor_index is not None

    @property
    def is_main(self) -> bool:
        """Returns True if this problem object lives in the main process
        and not in a remote actor.
        Otherwise, returns False.
        """
        return self._actor_index is None

    @property
    def before_eval_hook(self) -> Hook:
        """
        Get the Hook which stores the functions to call just before
        evaluating a SolutionBatch.

        The functions to be stored in this hook are expected to
        accept one positional argument, that one argument being the
        SolutionBatch which is about to be evaluated.
        """
        return self._before_eval_hook

    @property
    def after_eval_hook(self) -> Hook:
        """
        Get the Hook which stores the functions to call just after
        evaluating a SolutionBatch.

        The functions to be stored in this hook are expected to
        accept one argument, that one argument being the SolutionBatch
        whose evaluation has just been completed.

        The dictionaries returned by the functions in this hook
        are accumulated, and reported in the status dictionary of this
        problem object.
        """
        return self._after_eval_hook

    @property
    def before_grad_hook(self) -> Hook:
        """
        Get the Hook which stores the functions to call just before
        its `sample_and_compute_gradients(...)` operation.
        """
        return self._before_grad_hook

    @property
    def after_grad_hook(self) -> Hook:
        """
        Get the Hook which stores the functions to call just after
        its `sample_and_compute_gradients(...)` operation.

        The functions to be stored in this hook are expected to
        accept one argument, that one argument being the gradients
        dictionary (which was produced by the Problem object,
        but not yet followed by the search algorithm).

        The dictionaries returned by the functions in this hook
        are accumulated, and reported in the status dictionary of this
        problem object.
        """
        return self._after_grad_hook

    @property
    def remote_hook(self) -> Hook:
        """
        Get the Hook which stores the functions to call when this
        Problem object is (re)created on a remote actor.

        The functions in this hook should expect one positional
        argument, that is the Problem object itself.
        """
        return self._remote_hook

    def _make_sync_data_for_actors(self) -> Any:
        """
        Override this function for providing synchronization between
        the main process and the remote actors.

        The responsibility of this function is to prepare and return the
        data to be sent to the remote actors for synchronization.

        If this function returns NotImplemented, then there will be no
        syncing.
        If this function returns None, there will be no data sent to the
        actors for syncing, however, syncing will still be enabled, and
        the main actor will ask for sync data from the remote actors
        after their jobs are finished.
        """
        return NotImplemented

    def _use_sync_data_from_main(self, received: Any):
        """
        Override this function for providing synchronization between
        the main process and the remote actors.

        The responsibility of this function is to update the state
        of the remote Problem object according to the synchronization
        data received by the main process.
        """
        pass

    def _make_sync_data_for_main(self) -> Any:
        """
        Override this function for providing synchronization between
        the main process and the remote actors.

        The responsibility of this function is to prepare and return the
        data to be sent to the main Problem object by a remote actor.
        """
        return NotImplemented

    def _use_sync_data_from_actors(self, received: list):
        """
        Override this function for providing synchronization between
        the main process and the remote actors.

        The responsibility of this function is to update the state
        of the main Problem object according to the synchronization
        data received by the remote actors.
        """
        pass

    def _make_pickle_data_for_main(self) -> dict:
        """
        Override this function for preserving the state of a remote
        actor in the main state dictionary when pickling a parallelized
        problem.

        The responsibility of this function is to return the state
        of a problem object which lives in a remote actor.

        If the remote clones of this problem do not need to be stateful
        then you probably do not need to override this method.
        """
        return {}

    def _use_pickle_data_from_main(self, state: dict):
        """
        Override this function for re-creating the internal state of
        a problem instance living in a remote actor, by using the
        given state dictionary.

        If the remote clones of this problem do not need to be stateful
        then you probably do not need to override this method.
        """
        pass

    def _sync_before(self) -> bool:
        if self._actors is None:
            return False

        to_send = self._make_sync_data_for_actors()
        if to_send is NotImplemented:
            return False

        if to_send is not None:
            ray.get([actor.call.remote("_use_sync_data_from_main", [to_send], {}) for actor in self._actors])

        return True

    def _sync_after(self):
        if self._actors is None:
            return

        received = ray.get([actor.call.remote("_make_sync_data_for_main", [], {}) for actor in self._actors])

        self._use_sync_data_from_actors(received)

    @torch.no_grad()
    def _get_best_and_worst(self, batch: "SolutionBatch") -> Optional[dict]:
        if self._store_solution_stats is None:
            self._store_solution_stats = str(batch.device) == "cpu"

        if not self._store_solution_stats:
            return {}

        senses = self.senses
        nobjs = len(senses)

        if self._best is None:
            self._best_evals = self.make_empty(nobjs, device=batch.device, use_eval_dtype=True)
            self._worst_evals = self.make_empty(nobjs, device=batch.device, use_eval_dtype=True)
            for i_obj in range(nobjs):
                if senses[i_obj] == "min":
                    self._best_evals[i_obj] = float("inf")
                    self._worst_evals[i_obj] = float("-inf")
                elif senses[i_obj] == "max":
                    self._best_evals[i_obj] = float("-inf")
                    self._worst_evals[i_obj] = float("inf")
                else:
                    raise ValueError(f"Invalid sense: {senses[i_obj]}")
            self._best = [None] * nobjs
            self._worst = [None] * nobjs

        def first_is_better(a, b, i_obj):
            if senses[i_obj] == "min":
                return a < b
            elif senses[i_obj] == "max":
                return a > b
            else:
                raise ValueError(f"Invalid sense: {senses[i_obj]}")

        def first_is_worse(a, b, i_obj):
            if senses[i_obj] == "min":
                return a > b
            elif senses[i_obj] == "max":
                return a < b
            else:
                raise ValueError(f"Invalid sense: {senses[i_obj]}")

        best_sln_indices = [batch.argbest(i) for i in range(nobjs)]
        worst_sln_indices = [batch.argworst(i) for i in range(nobjs)]

        for i_obj in range(nobjs):
            best_sln_index = best_sln_indices[i_obj]
            worst_sln_index = worst_sln_indices[i_obj]
            scores = batch.access_evals(i_obj)
            best_score = scores[best_sln_index]
            worst_score = scores[worst_sln_index]
            if first_is_better(best_score, self._best_evals[i_obj], i_obj):
                self._best_evals[i_obj] = best_score
                self._best[i_obj] = batch[best_sln_index].clone()
            if first_is_worse(worst_score, self._worst_evals[i_obj], i_obj):
                self._worst_evals[i_obj] = worst_score
                self._worst[i_obj] = batch[worst_sln_index].clone()

        if len(senses) == 1:
            return dict(
                best=self._best[0],
                worst=self._worst[0],
                best_eval=float(self._best[0].evals[0]),
                worst_eval=float(self._worst[0].evals[0]),
            )
        else:
            return {"best": self._best, "worst": self._worst}

    def compare_solutions(self, a: "Solution", b: "Solution", obj_index: Optional[int] = None) -> float:
        """
        Compare two solutions.
        It is assumed that both solutions are already evaluated.

        Args:
            a: The first solution.
            b: The second solution.
            obj_index: The objective index according to which the comparison
                will be made.
                Can be left as None if the problem is single-objective.
        Returns:
            A positive number if `a` is better;
            a negative number if `b` is better;
            0 if there is a tie.
        """
        senses = self.senses
        obj_index = self.normalize_obj_index(obj_index)
        sense = senses[obj_index]

        def score(s: Solution):
            return s.evals[obj_index]

        if sense == "max":
            return score(a) - score(b)
        elif sense == "min":
            return score(b) - score(a)
        else:
            raise ValueError("Unrecognized sense: " + repr(sense))

    def is_better(self, a: "Solution", b: "Solution", obj_index: Optional[int] = None) -> bool:
        """
        Check whether or not the first solution is better.
        It is assumed that both solutions are already evaluated.

        Args:
            a: The first solution.
            b: The second solution.
            obj_index: The objective index according to which the comparison
                will be made.
                Can be left as None if the problem is single-objective.
        Returns:
            True if `a` is better; False otherwise.
        """
        return self.compare_solutions(a, b, obj_index) > 0

    def is_worse(self, a: "Solution", b: "Solution", obj_index: Optional[int] = None) -> bool:
        """
        Check whether or not the first solution is worse.
        It is assumed that both solutions are already evaluated.

        Args:
            a: The first solution.
            b: The second solution.
            obj_index: The objective index according to which the comparison
                will be made.
                Can be left as None if the problem is single-objective.
        Returns:
            True if `a` is worse; False otherwise.
        """
        return self.compare_solutions(a, b, obj_index) < 0

    def _prepare(self) -> None:
        """Prepare a worker instance of the problem for evaluation. To be overridden by the user"""
        pass

    def _prepare_main(self) -> None:
        """Prepare the main instance of the problem for evaluation."""
        self._share_attributes()

    def _start_preparations(self) -> None:
        """Prepare the problem for evaluation. Calls self._prepare() if the self._prepared flag is not True."""
        if not self._prepared:
            if self.actors is None or self._num_actors == 0:
                # Call prepare method for any problem class that is expected to do work
                self._prepare()
            if self.is_main:
                # Call share method to distribute shared attributes to actors
                self._prepare_main()

            self._prepared = True

    @property
    def _nonserialized_attribs(self) -> List[str]:
        return []

    def _share_attributes(self) -> None:
        if (self._actors is not None) and (len(self._actors) > 0):
            for attrib_name in self._shared_attribs:
                obj_ref = ray.put(getattr(self, attrib_name))
                for actor in self.actors:
                    actor.call.remote("put_ray_object", [], {"obj_ref": obj_ref, "attrib_name": attrib_name})

    def put_ray_object(self, obj_ref: ray.ObjectRef, attrib_name: str) -> None:
        setattr(self, attrib_name, ray.get(obj_ref))

    @property
    def _shared_attribs(self) -> List[str]:
        return []

    def _device_of_fitness_function(self) -> Optional[Device]:
        def device_of_fn(fn: Optional[Callable]) -> Optional[Device]:
            if fn is None:
                return None
            else:
                if hasattr(fn, "__evotorch_on_aux_device__") and fn.__evotorch_on_aux_device__:
                    return self.aux_device
                elif hasattr(fn, "device"):
                    return fn.device
                else:
                    return None

        for candidate_fn in (self._objective_func, self._evaluate_all, self._evaluate_batch, self._evaluate):
            device = device_of_fn(candidate_fn)
            if device is not None:
                if candidate_fn is self._evaluate_all:
                    raise RuntimeError(
                        "It seems that the `_evaluate_all(...)` method of this Problem object is either decorated"
                        " by @on_aux_device or by @on_device, or it is specifying a target device via a `device`"
                        " attribute. However, these decorators (or the `device` attribute) are not supported in the"
                        " case of `_evaluate_all(...)`."
                        " The reason is that the checking of the target device and the operations of moving the batch"
                        " onto the target device are handled by the default implementation of `_evaluate_all` itself."
                        " To specify a target device, consider decorating `_evaluate_batch(...)` or `_evaluate(...)`"
                        " instead."
                    )
                return device

        return None

    def evaluate(self, x: Union["SolutionBatch", "Solution"]):
        """
        Evaluate the given Solution or SolutionBatch.

        Args:
            x: The SolutionBatch to be evaluated.
        """

        if isinstance(x, Solution):
            batch = x.to_batch()
        elif isinstance(x, SolutionBatch):
            batch = x
        else:
            raise TypeError(
                f"The method `evaluate(...)` expected a Solution or a SolutionBatch as its argument."
                f" However, the received object is {repr(x)}, which is of type {repr(type(x))}."
            )

        self._parallelize()

        if self.is_main:
            self.before_eval_hook(batch)

        must_sync_after = self._sync_before()

        self._start_preparations()

        self._evaluate_all(batch)

        if must_sync_after:
            self._sync_after()

        if self.is_main:
            self._after_eval_status = {}

            best_and_worst = self._get_best_and_worst(batch)
            if best_and_worst is not None:
                self._after_eval_status.update(best_and_worst)

            self._after_eval_status.update(self.after_eval_hook.accumulate_dict(batch))

    def _evaluate_all(self, batch: "SolutionBatch"):
        if self._actors is None:
            fitness_device = self._device_of_fitness_function()
            if fitness_device is None:
                self._evaluate_batch(batch)
            else:
                original_device = batch.device
                moved_batch = batch.to(fitness_device)
                self._evaluate_batch(moved_batch)
                batch.set_evals(moved_batch.evals.to(original_device))
        else:
            if self._num_subbatches is not None:
                pieces = batch.split(self._num_subbatches)
            elif self._subbatch_size is not None:
                pieces = batch.split(max_size=self._subbatch_size)
            else:
                pieces = batch.split(len(self._actors))
            # mapresult = self._actor_pool.map(lambda a, v: a.evaluate_batch.remote(v), list(pieces))
            # for i, evals in enumerate(mapresult):
            #    row_begin, row_end = pieces.indices_of(i)
            #    batch._evdata[row_begin:row_end, :] = evals

            mapresult = self._actor_pool.map_unordered(
                lambda a, v: a.evaluate_batch_piece.remote(v[0], v[1]), list(enumerate(pieces))
            )
            for i, evals in mapresult:
                row_begin, row_end = pieces.indices_of(i)
                batch._evdata[row_begin:row_end, :] = evals

    def _evaluate_batch(self, batch: "SolutionBatch"):
        if self._vectorized and (self._objective_func is not None):
            result = self._objective_func(batch.values)
            if isinstance(result, tuple):
                batch.set_evals(*result)
            else:
                batch.set_evals(result)
        else:
            for sln in batch:
                self._evaluate(sln)

    def _evaluate(self, solution: "Solution"):
        if self._objective_func is not None:
            result = self._objective_func(solution.values)
            if isinstance(result, tuple):
                solution.set_evals(*result)
            else:
                solution.set_evals(result)
        else:
            raise NotImplementedError

    @property
    def stores_solution_stats(self) -> Optional[bool]:
        """
        Whether or not the best and worst solutions are kept.
        """
        return self._store_solution_stats

    @property
    def status(self) -> dict:
        """
        Status dictionary of the problem object, updated after the last
        evaluation operation.

        The dictionaries returned by the functions in `after_eval_hook`
        are accumulated, and reported in this status dictionary.
        """
        return self._after_eval_status

    def ensure_numeric(self):
        """
        Ensure that the problem has a numeric dtype.

        Raises:
            ValueError: if the problem has a non-numeric dtype.
        """
        if is_dtype_object(self.dtype):
            raise ValueError("Expected a problem with numeric dtype, but the dtype is object.")

    def ensure_unbounded(self):
        """
        Ensure that the problem has no strict lower and upper bounds.

        Raises:
            ValueError: if the problem has strict lower and upper bounds.
        """
        if not (self.lower_bounds is None and self.upper_bounds is None):
            raise ValueError("Expected an unbounded problem, but this problem has lower and/or upper bounds.")

    def ensure_single_objective(self):
        """
        Ensure that the problem has only one objective.

        Raises:
            ValueError: if the problem is multi-objective.
        """
        n = len(self.senses)
        if n > 1:
            raise ValueError(f"Expected a single-objective problem, but this problem has {n} objectives.")

    def normalize_obj_index(self, obj_index: Optional[int] = None) -> int:
        """
        Normalize the objective index.

        If the provided index is non-negative, it is ensured that the index
        is valid.

        If the provided index is negative, the objectives are counted in the
        reverse order, and the corresponding non-negative index is returned.
        For example, -1 is converted to a non-negative integer corresponding to
        the last objective.

        If the provided index is None and if the problem is single-objective,
        the returned value is 0, which represents the only objective.

        If the provided index is None and if the problem is multi-objective,
        an error is raised.

        Args:
            obj_index: The non-normalized objective index.
        Returns:
            The normalized objective index, as a non-negative integer.
        """
        if obj_index is None:
            if len(self.senses) == 1:
                return 0
            else:
                raise ValueError(
                    "This problem is multi-objective, therefore, an explicit objective index was expected."
                    " However, `obj_index` was found to be None."
                )
        else:
            obj_index = int(obj_index)
            if obj_index < 0:
                obj_index = len(self.senses) + obj_index
            if obj_index < 0 or obj_index >= len(self.senses):
                raise IndexError("Objective index out of range.")
            return obj_index

    def _get_cloned_state(self, *, memo: dict) -> dict:
        # Collect the inner states of the remote Problem clones
        if self._actors is not None:
            self._remote_states = ray.get(
                [actor.call.remote("_make_pickle_data_for_main", [], {}) for actor in self._actors]
            )

        # Prepare the main state dictionary
        result = {}
        for k, v in self.__dict__.items():
            if k in ("_actors", "_actor_pool") or k in self._nonserialized_attribs:
                result[k] = None
            else:
                v_id = id(v)
                if v_id in memo:
                    result[k] = memo[v_id]
                else:
                    with _no_grad_if_basic_dtype(self.dtype):
                        result[k] = deep_clone(
                            v,
                            otherwise_deepcopy=True,
                            memo=memo,
                        )
        return result

    def _get_local_interaction_count(self) -> int:
        """
        Get the number of simulator interactions this Problem encountered.

        For problems focused on reinforcement learning, it is expected
        that the subclass overrides this method to describe its own way
        of getting the local interaction count.

        When working on parallelized problems, what is returned here is
        not necessarily synchronized with the other parallelized instance.
        """
        raise NotImplementedError

    def _get_local_episode_count(self) -> int:
        """
        Get the number of episodes this Problem encountered.

        For problems focused on reinforcement learning, it is expected
        that the subclass overrides this method to describe its own way
        of getting the local episode count.

        When working on parallelized problems, what is returned here is
        not necessarily synchronized with the other parallelized instance.
        """
        raise NotImplementedError

    def sample_and_compute_gradients(
        self,
        distribution,
        popsize: int,
        *,
        num_interactions: Optional[int] = None,
        popsize_max: Optional[int] = None,
        obj_index: Optional[int] = None,
        ranking_method: Optional[str] = None,
        with_stats: bool = True,
        ensure_even_popsize: bool = False,
    ) -> Union[list, dict]:
        """
        Sample new solutions from the distribution and compute gradients.

        The distribution can then be updated according to the computed
        gradients.

        If the problem is not parallelized, and `with_stats` is False,
        then the result will be a single dictionary of gradients.
        For example, in the case of a Gaussian distribution, the returned
        gradients dictionary would look like this:

            {
                "mu": ...,     # the gradient for the mean
                "sigma": ...,  # the gradient for the standard deviation
            }

        If the problem is not parallelized, and `with_stats` is True,
        then the result will be a dictionary which contains in itself
        the gradients dictionary, and additional elements for providing
        further information. In the case of a Gaussian distribution,
        the returned dictionary with additional stats would look like
        this:

            {
                "gradients": {
                    "mu": ...,     # the gradient for the mean
                    "sigma": ...,  # the gradient for the standard deviation
                },
                "num_solutions": ...,  # how many solutions were sampled
                "mean_eval": ...,      # Mean of all evaluations
            }

        If the problem is parallelized, then the gradient computation will
        be distributed among the remote actors. In more details, each actor
        will sample its own solutions (such that the total population size
        across all remote actors will be near the provided `popsize`)
        and will compute its own gradients, and will produce its own
        additional stats (if `with_stats` is given as True).
        These remote results will then be collected by the main process,
        and the final result of this method will be a list of dictionaries,
        each dictionary being the result of a remote gradient computation.

        The sampled solutions are temporary, and will not be kept
        (and will not be returned).

        To customize how solutions are sampled and how gradients are
        computed, one is encouraged to override
        `_sample_and_compute_gradients(...)` (instead of overriding this
        method directly.

        Args:
            distribution: The search distribution from which the solutions
                will be sampled, and according to which the gradients will
                be computed.
            popsize: The number of solutions which will be sampled.
            num_interactions: Number of simulator interactions that must
                be completed (more solutions will be sampled until this
                threshold is reached). This argument is to be used when
                the problem has characteristics similar to reinforcement
                learning, and an adaptive population size, depending on
                the interactions made, is desired.
                Otherwise, one can leave this argument as None, in which
                case, there will not be any threshold based on number
                of interactions.
            popsize_max: To be used when `num_interactions` is provided,
                as an additional criterion for ending the solution sampling
                phase. This argument can be used to prevent the population
                size from growing too much while trying to satisfy the
                `num_interactions`. If not needed, `popsize_max` can be left
                as None.
            obj_index: Index of the objective according to which the gradients
                will be computed. Can be left as None if the problem has only
                one objective.
            ranking_method: The solution ranking method to be used when
                computing the gradients.
                If not specified, the raw fitnesses will be used.
            with_stats: If given as False, then the results dictionary will
                only contain the gradients information. If given as True,
                then the results dictionary will contain within itself
                the gradients dictionary, and also additional elements for
                providing further information.
                The default is True.
            ensure_even_popsize: If `ensure_even_popsize` is True and the
                problem is not parallelized, then a `popsize` given as an odd
                number will cause an error. If `ensure_even_popsize` is True
                and the problem is parallelized, then the remote actors will
                sample their own sub-populations in such a way that their
                sizes are even.
                If `ensure_even_popsize` is False, whether or not the
                `popsize` is even will not be checked.
                When the provided `distribution` is a symmetric (or
                "mirrored", or "antithetic"), then this argument must be
                given as True.
        Returns:
            A results dictionary when the problem is not parallelized,
            or list of results dictionaries when the problem is parallelized.
        """

        # For problems which are configured for parallelization, make sure that the actors are created.
        self._parallelize()

        # Below we check if there is an inconsistency in arguments.
        if (num_interactions is None) and (popsize_max is not None):
            # If `num_interactions` is None, then we assume that the user does not wish an adaptive population size.
            # However, at the same time, if `popsize_max` is not None, then there is an inconsistency,
            # because, `popsize_max` without `num_interactions` (therefore without adaptive population size)
            # does not make sense.
            # This is probably a configuration error, so, we inform the user by raising an error.
            raise ValueError(
                f"`popsize_max` was expected as None, because `num_interactions` is None."
                f" However, `popsize_max` was found as {popsize_max}."
            )

        # The problem instance in the main process should trigger the `before_grad_hook`.
        if self.is_main:
            self._before_grad_hook()

        if self.is_main and (self._actors is not None) and (len(self._actors) > 0):
            # If this is the main process and the problem is parallelized, then we need to split the request
            # into multiple tasks, and then execute those tasks in parallel using the problem's actor pool.

            if self._subbatch_size is not None:
                # If `subbatch_size` is provided, then we first make sure that `popsize` is divisible by
                # `subbatch_size`
                if (popsize % self._subbatch_size) != 0:
                    raise ValueError(
                        f"This Problem was created with `subbatch_size` as {self._subbatch_size}."
                        f" When doing remote gradient computation, the requested population size must be divisible by"
                        f" the `subbatch_size`."
                        f" However, the requested population size is {popsize}, and the remainder after dividing it"
                        f" by `subbatch_size` is not 0 (it is {popsize % self._subbatch_size})."
                    )
                # After making sure that `popsize` and `subbatch_size` configurations are compatible, we declare that
                # we are going to have n tasks, each task imposing a sample size of `subbatch_size`.
                n = int(popsize // self._subbatch_size)
                popsize_per_task = [self._subbatch_size for _ in range(n)]
            elif self._num_subbatches is not None:
                # If `num_subbatches` is provided, then we are going to have n tasks where n is equal to the given
                # `num_subbatches`.
                popsize_per_task = split_workload(popsize, self._num_subbatches)
            else:
                # If neither `subbatch_size` nor `num_subbatches` is given, then we will split the workload in such
                # a way that each actor will have its share.
                popsize_per_task = split_workload(popsize, len(self._actors))

            if ensure_even_popsize:
                # If `ensure_even_popsize` argument is True, then we need to make sure that each tasks's popsize is
                # an even number.
                for i in range(len(popsize_per_task)):
                    if (popsize_per_task[i] % 2) != 0:
                        # If the i-th actor's assigned popsize is not even, increase its assigned popsize by 1.
                        popsize_per_task[i] += 1

            # The number of tasks is finally determined by the length of `popsize_per_task` list we created above.
            num_tasks = len(popsize_per_task)

            if num_interactions is None:
                # If the argument `num_interactions` is not given, then, for each task, we declare that
                # `num_interactions` is None.
                num_inter_per_task = [None for _ in range(num_tasks)]
            else:
                # If the argument `num_interactions` is given, then we compute each task's target number of
                # interactions from its sample size.
                num_inter_per_task = [
                    math.ceil((popsize_per_task[i] / popsize) * num_interactions) for i in range(num_tasks)
                ]

            if popsize_max is None:
                # If the argument `popsize_max` is not given, then, for each task, we declare that
                # `popsize_max` is None.
                popsize_max_per_task = [None for _ in range(num_tasks)]
            else:
                # If the argument `popsize_max` is given, then we compute each task's target maximum population size
                # from its sample size.
                popsize_max_per_task = [
                    math.ceil((popsize_per_task[i] / popsize) * popsize_max) for i in range(num_tasks)
                ]

            # We trigger the synchronization between the main process and the remote actors.
            # If this problem instance has nothing to synchronize, then `must_sync_after` will be False.
            must_sync_after = self._sync_before()

            # Because we want to send the distribution to remote actors, we first copy the distribution to cpu
            # (unless it is already on cpu)
            dist_on_cpu = distribution.to("cpu")

            # Here, we use our actor pool to execute our tasks in parallel.
            result = list(
                self._actor_pool.map_unordered(
                    (
                        lambda a, v: a.call.remote(
                            "_sample_and_compute_gradients",
                            [dist_on_cpu, v[0]],
                            {
                                "obj_index": obj_index,
                                "num_interactions": v[1],
                                "popsize_max": v[2],
                                "ranking_method": ranking_method,
                            },
                        )
                    ),
                    list(zip(popsize_per_task, num_inter_per_task, popsize_max_per_task)),
                )
            )

            # At this point, all the tensors within our collected results are on the CPU.

            if torch.device(self.device) != torch.device("cpu"):
                # If the main device of this problem instance is not CPU, then we move the tensors to the main device.
                result = cast_tensors_in_container(result, device=self.device)

            if must_sync_after:
                # If a post-gradient synchronization is required, we trigger the synchronization operations.
                self._sync_after()

            # ####################################################
            # # If this is the main process and the problem is parallelized, then we need to split the workload among
            # # the remote actors, and then request each of them to compute their gradients.
            #
            # # We begin by getting the number of actors, and computing the `popsize` for each actor.
            # num_actors = len(self._actors)
            # popsize_per_actor = split_workload(popsize, num_actors)
            #
            # if ensure_even_popsize:
            #     # If `ensure_even_popsize` argument is True, then we need to make sure that each actor's popsize is
            #     # an even number.
            #     for i in range(len(popsize_per_actor)):
            #         if (popsize_per_actor[i] % 2) != 0:
            #             # If the i-th actor's assigned popsize is not even, increase its assigned popsize by 1.
            #             popsize_per_actor[i] += 1
            #
            # if num_interactions is None:
            #     # If `num_interactions` is None, then the `num_interactions` argument for each actor must also be
            #     # passed as None.
            #     num_int_per_actor = [None] * num_actors
            # else:
            #     # If `num_interactions` is not None, then we split the `num_interactions` workload among the actors.
            #     num_int_per_actor = split_workload(num_interactions, num_actors)
            #
            # if popsize_max is None:
            #     # If `popsize_max` is None, then the `popsize_max` argument for each actor must also be None.
            #     popsize_max_per_actor = [None] * num_actors
            # else:
            #     # If `popsize_max` is not None, then we split the `popsize_max` workload among the actors.
            #     popsize_max_per_actor = split_workload(popsize_max, num_actors)
            #
            # # We trigger the synchronization between the main process and the remote actors.
            # # If this problem instance has nothing to synchronize, then `must_sync_after` will be False.
            # must_sync_after = self._sync_before()
            #
            # # Because we want to send the distribution to remote actors, we first copy the distribution to cpu
            # # (unless it is already on cpu)
            # dist_on_cpu = distribution.to("cpu")
            #
            # # To each actor, we send the request of computing the gradients, and then collect the results
            # result = ray.get(
            #     [
            #         self._actors[i].call.remote(
            #             "_gradient_computation_helper",
            #             [dist_on_cpu, popsize_per_actor[i]],
            #             dict(
            #                 num_interactions=num_int_per_actor[i],
            #                 popsize_max=popsize_max_per_actor[i],
            #                 obj_index=obj_index,
            #                 ranking_method=ranking_method,
            #                 with_stats=with_stats,
            #                 move_results_to_device="cpu",
            #             ),
            #         )
            #         for i in range(num_actors)
            #     ]
            # )
            #
            # # At this point, all the tensors within our collected results are on the CPU.
            #
            # if torch.device(self.device) != torch.device("cpu"):
            #     # If the main device of this problem instance is not CPU, then we move the tensors to the main device.
            #     result = cast_tensors_in_container(result, device=device)
            #
            # if must_sync_after:
            #     # If a post-gradient synchronization is required, we trigger the synchronization operations.
            #     self._sync_after()
        else:
            # If the problem is not parallelized, then we request this instance itself to compute the gradients.
            result = self._gradient_computation_helper(
                distribution,
                popsize,
                popsize_max=popsize_max,
                obj_index=obj_index,
                ranking_method=ranking_method,
                num_interactions=num_interactions,
                with_stats=with_stats,
            )

        # The problem instance in the main process should trigger the `after_grad_hook`.
        if self.is_main:
            self._after_eval_status = self._after_grad_hook.accumulate_dict(result)

        # We finally return the results
        return result

    def _gradient_computation_helper(
        self,
        distribution,
        popsize: int,
        *,
        num_interactions: Optional[int] = None,
        popsize_max: Optional[int] = None,
        obj_index: Optional[int] = None,
        ranking_method: Optional[str] = None,
        with_stats: bool = True,
        move_results_to_device: Optional[Device] = None,
    ) -> dict:
        # This is a helper method which makes sure that the provided distribution is in the correct dtype and device.
        # This method also makes sure that the results are moved to the desired device.

        # At first, we make sure that the objective index is normalized
        # (for example, the objective -1 is converted to the index of the last objective).
        obj_index = self.normalize_obj_index(obj_index)

        if (distribution.dtype != self.dtype) or (distribution.device != self.device):
            # Make sure that the distribution is in the correct dtype and device
            distribution = distribution.modified_copy(dtype=self.dtype, device=self.device)

        # Call the protected method responsible for sampling solutions and computing the gradients
        result = self._sample_and_compute_gradients(
            distribution,
            popsize,
            popsize_max=popsize_max,
            obj_index=obj_index,
            num_interactions=num_interactions,
            ranking_method=ranking_method,
        )

        if move_results_to_device is not None:
            # If `move_results_to_device` is provided, move the results to the desired device
            result = cast_tensors_in_container(result, device=move_results_to_device)

        # Finally, return the result
        if with_stats:
            return result
        else:
            return result["gradients"]

    @property
    def _grad_device(self) -> Device:
        """
        Get the device in which new solutions will be made in distributed mode.

        In more details, in distributed mode, each actor creates its own
        sub-populations, evaluates them, and computes its own gradient
        (all such actor gradients eventually being collected by the
        distribution-based search algorithm in the main process).
        For some problem types, it can make sense for the remote actors to
        create their temporary sub-populations on another device
        (e.g. on the GPU that is allocated specifically for them).
        For such situations, one is encouraged to override this property
        and make it return whatever device is to be used.

        Note that this property is used by the default implementation of the
        method named `_sample_and_compute_grad(...)`. If the method named
        `_sample_and_compute_grad(...)` is overriden, this property might not
        be called at all.

        This is the default (i.e. not-yet-overriden) implementation in the
        Problem class, and performs the following operations to decide the
        device:
        (i) if the Problem object was given an external fitness function that
        is decorated by @[on_device][evotorch.decorators.on_device],
        or by @[on_aux_device][evotorch.decorators.on_aux_device],
        or has a `device` attribute, then return the device requested by that
        function; otherwise
        (ii) if either one of the methods `_evaluate_batch`, and `_evaluate`
        was decorated by @[on_device][evotorch.decorators.on_device]
        or by @[on_aux_device][evotorch.decorators.on_aux_device],
        or has a `device` attribute, then return the device requested by that
        method; otherwise
        (iii) return the main device of the Problem object.
        """
        fitness_device = self._device_of_fitness_function()
        return self.device if fitness_device is None else fitness_device

    def _sample_and_compute_gradients(
        self,
        distribution,
        popsize: int,
        *,
        obj_index: int,
        num_interactions: Optional[int] = None,
        popsize_max: Optional[int] = None,
        ranking_method: Optional[str] = None,
    ) -> dict:
        """
        This method contains the description of how the solutions are sampled
        and the gradients are computed according to the given distribution.

        One might override this method for customizing the procedure of
        sampling solutions and the gradient computation, but this method does
        have a default implementation.

        This returns a dictionary which contains the gradients for the given
        distribution, and also further information. For example, considering
        a Gaussian distribution with parameters 'mu' and 'sigma', the result
        is expected to look like this:

            {
                "gradients": {
                    "mu": ...,     # the gradient for the mean (tensor)
                    "sigma": ...,  # the gradient for the std.dev. (tensor)
                },
                "num_solutions": ...,  # how many solutions were sampled (int)
                "mean_eval": ...,      # Mean of all evaluations (float)
            }

        A customized version of this method can add more items to the outer
        dictionary.

        Args:
            distribution: The search distribution from which the solutions
                will be sampled and according to which the gradients will
                be computed. This method assumes that `distribution` is
                given with this problem instance's dtype, and in this problem
                instance's device.
            popsize: Number of solutions to sample.
            obj_index: Objective index, expected as an integer.
            num_interactions: Number of simulator interactions that must be
                reached before computing the gradients.
                Having this argument as an integer implies that adaptive
                population is requested: more solutions are to be sampled
                until this number of simulator interactions are made.
                Can also be None if this threshold is not needed.
            popsize_max: Maximum population size for when the population
                size is adaptive (where the adaptiveness is enabled when
                `num_interactions` is not None).
                Can be left as None if a maximum population size limit
                is not needed.
            ranking_method: Ranking method to be used when computing the
                gradients. Can be left as None, in which case the raw
                fitnesses will be used.
        Returns:
            A dictionary which contains the gradients, number of solutions,
            mean of all the evaluation results, and optionally further
            items (if customized to do so).
        """

        # Annotate the variable which will store the temporary SolutionBatch for computing the local gradient.
        resulting_batch: SolutionBatch

        # Get the device in which the new solutions will be made.
        grad_device = torch.device(self._grad_device)
        distribution = distribution.to(grad_device)

        # Below we define an inner utility function which samples and evaluates a new SolutionBatch.
        # This newly evaluated SolutionBatch is returned.
        def sample_evaluated_batch() -> SolutionBatch:
            batch = SolutionBatch(self, popsize, device=grad_device)
            distribution.sample(out=batch.access_values(), generator=self.generator)
            self.evaluate(batch)
            return batch

        if num_interactions is None:
            # If a `num_interactions` threshold is not given (i.e. is left as None), then we assume that an adaptive
            # population is not desired.
            # We therefore simply sample and evaluate a single SolutionBatch, and declare it as our main batch.
            resulting_batch = sample_evaluated_batch()
        else:
            # If we have a `num_interactions` threshold, then we might have to sample more than one SolutionBatch
            # (until `num_interactions` is reached).
            # We start by defining a list (`batches`) which is to store all the batches we will sample.
            batches = []

            # We will have to count the number of all simulator interactions that we have encountered during the
            # execution of this method. So, to count it correctly, we first get the interaction count that we already
            # have before sampling and evaluating our new solutions.
            interaction_count_at_first = self._get_local_interaction_count()

            # Below is an inner function which returns how many simulator interactions we have done so far.
            # It makes use of the variable `interaction_count_at_first` defined above.
            def current_num_interactions() -> int:
                return self._get_local_interaction_count() - interaction_count_at_first

            # We also keep track of the total number of solutions.
            # We might need this if there is a `popsize_max` threshold.
            current_popsize = 0

            # The main loop of the adaptive sampling.
            while True:
                # Sample and evaluate a new SolutionBatch, and add it to our batches list.
                batches.append(sample_evaluated_batch())

                # Increase our total population size by the size of the most recent batch.
                current_popsize += popsize

                if current_num_interactions() > num_interactions:
                    # If the number of interactions has reached or exceeded the `num_interactions` threshold,
                    # we exit the loop.
                    break
                if (popsize_max is not None) and (current_popsize >= popsize_max):
                    # If we have `popsize_max` threshold and our total population size have reached or exceeded
                    # the `popsize_max` threshold, we exit the loop.
                    break

            if len(batches) == 1:
                # If we have only one batch in our batches list, that batch can be declared as our main batch.
                resulting_batch = batches[0]
            else:
                # If we have multiple batches in our batches list, we concatenate all those batches and
                # declare the result of the concatenation as our main batch.
                resulting_batch = SolutionBatch.cat(batches)

        # We take the solutions (`samples`) and the fitnesses from our main batch.
        samples = resulting_batch.access_values(keep_evals=True)
        fitnesses = resulting_batch.access_evals(obj_index)

        # With the help of `samples` and `fitnesses`, we now compute our gradients.
        grads = distribution.compute_gradients(
            samples, fitnesses, objective_sense=self.senses[obj_index], ranking_method=ranking_method
        )

        if grad_device != self.device:
            grads = cast_tensors_in_container(grads, device=self.device)

        # Finally, we return the result, which is a dictionary containing the gradients and further information.
        return {
            "gradients": grads,
            "num_solutions": len(resulting_batch),
            "mean_eval": float(torch.mean(resulting_batch.access_evals(obj_index))),
        }

    def is_on_cpu(self) -> bool:
        """
        Whether or not the Problem object has its device set as "cpu".
        """
        return str(self.device) == "cpu"

actor_index: Optional[int] property readonly

Return the actor index if this is a remote worker. If this is not a remote worker, return None.

actors: Optional[list] property readonly

Get the ray actors, if the Problem object is distributed. If the Problem object is not distributed and therefore has no actors, then, the result will be None.

after_eval_hook: Hook property readonly

Get the Hook which stores the functions to call just after evaluating a SolutionBatch.

The functions to be stored in this hook are expected to accept one argument, that one argument being the SolutionBatch whose evaluation has just been completed.

The dictionaries returned by the functions in this hook are accumulated, and reported in the status dictionary of this problem object.

after_grad_hook: Hook property readonly

Get the Hook which stores the functions to call just after its sample_and_compute_gradients(...) operation.

The functions to be stored in this hook are expected to accept one argument, that one argument being the gradients dictionary (which was produced by the Problem object, but not yet followed by the search algorithm).

The dictionaries returned by the functions in this hook are accumulated, and reported in the status dictionary of this problem object.

aux_device: Union[str, torch.device] property readonly

Auxiliary device to help with the computations, most commonly for speeding up the solution evaluations.

An auxiliary device is different than the main device of the Problem object (the main device being expressed by the device property). While the main device of the Problem object determines where the solutions and the populations are stored (and also using which device should a SearchAlgorithm instance communicate with the problem), an auxiliary device is a device that might be used by the Problem instance itself for its own computations (e.g. computations defined within the methods _evaluate(...) or _evaluate_batch(...)).

If the problem's main device is something other than "cpu", that main device is also seen as the auxiliary device, and therefore returned by this property.

If the problem's main device is "cpu", then the auxiliary device is decided as follows. If num_gpus_per_actor of the Problem object was set as "all" and if this instance is a remote instance, then the auxiliary device is guessed as "cuda:N" where N is the actor index. In all other cases, the auxiliary device is "cuda" if cuda is available, and "cpu" otherwise.

before_eval_hook: Hook property readonly

Get the Hook which stores the functions to call just before evaluating a SolutionBatch.

The functions to be stored in this hook are expected to accept one positional argument, that one argument being the SolutionBatch which is about to be evaluated.

before_grad_hook: Hook property readonly

Get the Hook which stores the functions to call just before its sample_and_compute_gradients(...) operation.

device: Union[str, torch.device] property readonly

device of the Problem object.

New solutions and populations will be generated in this device.

dtype: Union[str, torch.dtype, numpy.dtype, Type] property readonly

dtype of the Problem object.

The decision variables of the optimization problem are of this dtype.

eval_data_length: int property readonly

Length of the extra evaluation data vector for each solution.

eval_dtype: Union[str, torch.dtype, numpy.dtype, Type] property readonly

evaluation dtype of the Problem object.

The evaluation results of the solutions are stored according to this dtype.

generator: Optional[torch._C.Generator] property readonly

Random generator used by this Problem object.

Can also be None, which means that the Problem object will use the global random generator of PyTorch.

has_own_generator: bool property readonly

Whether or not the Problem object has its own random generator.

If this is True, then the Problem object will use its own random generator when creating random values or tensors. If this is False, then the Problem object will use the global random generator when creating random values or tensors.

initial_lower_bounds: Optional[torch.Tensor] property readonly

Initial lower bounds, for when initializing a new solution.

If such a bound was declared during the initialization phase, the returned value is a torch tensor (in the form of a vector or in the form of a scalar). If no such bound was declared, the returned value is None.

initial_upper_bounds: Optional[torch.Tensor] property readonly

Initial upper bounds, for when initializing a new solution.

If such a bound was declared during the initialization phase, the returned value is a torch tensor (in the form of a vector or in the form of a scalar). If no such bound was declared, the returned value is None.

is_main: bool property readonly

Returns True if this problem object lives in the main process and not in a remote actor. Otherwise, returns False.

is_multi_objective: bool property readonly

Whether or not the problem is multi-objective

is_remote: bool property readonly

Returns True if this problem object lives in a remote ray actor. Otherwise, returns False.

is_single_objective: bool property readonly

Whether or not the problem is single-objective

lower_bounds: Optional[torch.Tensor] property readonly

Lower bounds for the allowed values of a solution.

If such a bound was declared during the initialization phase, the returned value is a torch tensor (in the form of a vector or in the form of a scalar). If no such bound was declared, the returned value is None.

num_actors: int property readonly

Number of actors (to be) used for parallelization. If the problem is configured for no parallelization, the result will be 0.

objective_sense: Union[str, Iterable[str]] property readonly

Get the objective sense.

If the problem is single-objective, then a single string is returned. If the problem is multi-objective, then the objective senses will be returned in a list.

The returned string in the single-objective case, or each returned string in the multi-objective case, is "min" or "max".

remote_hook: Hook property readonly

Get the Hook which stores the functions to call when this Problem object is (re)created on a remote actor.

The functions in this hook should expect one positional argument, that is the Problem object itself.

senses: Iterable[str] property readonly

Get the objective senses.

The return value is a list of strings, each string being "min" or "max".

solution_length: Optional[int] property readonly

Get the solution length.

Problems with dtype=None do not have solution lengths. For such problems, this property returns None.

status: dict property readonly

Status dictionary of the problem object, updated after the last evaluation operation.

The dictionaries returned by the functions in after_eval_hook are accumulated, and reported in this status dictionary.

stores_solution_stats: Optional[bool] property readonly

Whether or not the best and worst solutions are kept.

upper_bounds: Optional[torch.Tensor] property readonly

Upper bounds for the allowed values of a solution.

If such a bound was declared during the initialization phase, the returned value is a torch tensor (in the form of a vector or in the form of a scalar). If no such bound was declared, the returned value is None.

__init__(self, objective_sense, objective_func=None, *, initial_bounds=None, bounds=None, solution_length=None, dtype=None, eval_dtype=None, device=None, eval_data_length=None, seed=None, num_actors=None, actor_config=None, num_gpus_per_actor=None, num_subbatches=None, subbatch_size=None, store_solution_stats=None, vectorized=None) special

__init__(...): Initialize the Problem object.

Parameters:

Name Type Description Default
objective_sense Union[str, Iterable[str]]

A string, or a sequence of strings. For a single-objective problem, a single string ("min" or "max", for minimization or maximization) is enough. For a problem with n objectives, a sequence of strings (e.g. a list of strings) of length n is required, each string in the sequence being "min" or "max". This argument specifies the goal of the optimization.

required
initial_bounds Union[Iterable[Union[float, Iterable[float], torch.Tensor]], evotorch.core.BoundsPair]

In which interval will the values of a new solution will be initialized. Expected as a tuple, each element being either a scalar, or a vector of length n, n being the length of a solution. If a manual solution initialization is preferred (instead of an interval-based initialization), one can leave initial_bounds as None, and override the _fill(...) method in the inheriting subclass.

None
bounds Union[Iterable[Union[float, Iterable[float], torch.Tensor]], evotorch.core.BoundsPair]

Interval in which all the solutions must always reside. Expected as a tuple, each element being either a scalar, or a vector of length n, n being the length of a solution. This argument is optional, and can be left as None if one does not wish to declare hard bounds on the decision values of the problem. If bounds is specified, initial_bounds is missing, and _fill(...) is not overriden, then bounds will also serve as the initial_bounds.

None
solution_length Optional[int]

Length of a solution. Required for all fixed-length numeric optimization problems. For variable-length problems (which might or might not be numeric), one is expected to leave solution_length as None, and declare dtype as object.

None
dtype Union[str, torch.dtype, numpy.dtype, Type]

dtype (data type) of the data stored by a solution. Can be given as a string (e.g. "float32"), or as a numpy dtype (e.g. numpy.dtype("float32")), or as a PyTorch dtype (e.g. torch.float32). Alternatively, if the problem is variable-length and/or non-numeric, one is expected to declare dtype as object.

None
eval_dtype Union[str, torch.dtype, numpy.dtype, Type]

dtype to be used for storing the evaluations (or fitnesses, or scores, or costs, or losses) of the solutions. Can be given as a string (e.g. "float32"), or as a numpy dtype (e.g. numpy.dtype("float32")), or as a PyTorch dtype (e.g. torch.float32). eval_dtype must always refer to a "float" data type, therefore, object is not accepted as a valid eval_dtype. If eval_dtype is not specified (i.e. left as None), then the following actions are taken to determine the eval_dtype: if dtype is "float16", eval_dtype becomes "float16"; if dtype is "bfloat16", eval_dtype becomes "bfloat16"; if dtype is "float32", eval_dtype becomes "float32"; if dtype is "float64", eval_dtype becomes "float64"; and for any other dtype, eval_dtype becomes "float32".

None
device Union[str, torch.device]

Default device in which a new population will be generated. For non-numeric problems, this must be "cpu". For numeric problems, this can be any device supported by PyTorch (e.g. "cuda"). Note that, if the number of actors of the problem is configured to be more than 1, device has to be "cpu" (or, equivalently, left as None).

None
eval_data_length Optional[int]

In addition to evaluation results (which are (un)fitnesses, or scores, or costs, or losses), each solution can store extra evaluation data. If storage of such extra evaluation data is required, one can set this argument to an integer bigger than 0.

None
seed Optional[int]

Random seed to be used by the random number generator attached to the problem object. If left as None, no random number generator will be attached, and the global random number generator of PyTorch will be used instead.

None
num_actors Union[int, str]

Number of actors to create for parallelized evaluation of the solutions. Certain string values are also accepted. When given as "max" or as "num_cpus", the number of actors will be equal to the number of all available CPUs in the ray cluster. When given as "num_gpus", the number of actors will be equal to the number of all available GPUs in the ray cluster, and each actor will be assigned a GPU. There is also an option, "num_devices", which means that both the numbers of CPUs and GPUs will be analyzed, and new actors and GPUs for them will be allocated, in a one-to-one mapping manner, if possible. In more details, with num_actors="num_devices", if device is given as a GPU device, then it will be inferred that the user wishes to put everything (including the population) on a single GPU, and therefore there won't be any allocation of actors nor GPUs. With num_actors="num_devices" and with device set as "cpu" (or as left as None), if there are multiple CPUs and multiple GPUs, then n actors will be allocated where n is the minimum among the number of CPUs and the number of GPUs, so that there can be one-to-one mapping between CPUs and GPUs (i.e. such that each actor can be assigned an entire GPU). If num_actors is given as "num_gpus" or "num_devices", the argument num_gpus_per_actor must not be used, and the actor_config dictionary must not contain the key "num_gpus". If num_actors is given as something other than "num_gpus" or "num_devices", and if you wish to assign GPUs to each actor, then please see the argument num_gpus_per_actor.

None
actor_config Optional[dict]

A dictionary, representing the keyword arguments to be passed to the options(...) used when creating the ray actor objects. To be used for explicitly allocating resources per each actor. For example, for declaring that each actor is to use a GPU, one can pass actor_config=dict(num_gpus=1). Can also be given as None (which is the default), if no such options are to be passed.

None
num_gpus_per_actor Union[int, float, str]

Number of GPUs to be allocated by each remote actor. The default behavior is to NOT allocate any GPU at all (which is the default behavior of the ray library as well). When given as a number n, each actor will be given n GPUs (where n can be an integer, or can be a float for fractional allocation). When given as a string "max", then the available GPUs across the entire ray cluster (or within the local computer in the simplest cases) will be equally distributed among the actors. When given as a string "all", then each actor will have access to all the GPUs (this will be achieved by suppressing the environment variable CUDA_VISIBLE_DEVICES for each actor). When the problem is not distributed (i.e. when there are no actors), this argument is expected to be left as None.

None
num_subbatches Optional[int]

If num_subbatches is None (assuming that subbatch_size is also None), then, when evaluating a population, the population will be split into n pieces, n being the number of actors, and each actor will evaluate its assigned piece. If num_subbatches is an integer m, then the population will be split into m pieces, and actors will continually accept the next unevaluated piece as they finish their current tasks. The arguments num_subbatches and subbatch_size cannot be given values other than None at the same time. While using a distributed algorithm, this argument determines how many sub-batches will be generated, and therefore, how many gradients will be computed by the remote actors.

None
subbatch_size Optional[int]

If subbatch_size is None (assuming that num_subbatches is also None), then, when evaluating a population, the population will be split into n pieces, n being the number of actors, and each actor will evaluate its assigned piece. If subbatch_size is an integer m, then the population will be split into pieces of size m, and actors will continually accept the next unevaluated piece as they finish their current tasks. When there can be significant difference across the solutions in terms of computational requirements, specifying a subbatch_size can be beneficial, because, while one actor is busy with a subbatch containing computationally challenging solutions, other actors can accept more tasks and save time. The arguments num_subbatches and subbatch_size cannot be given values other than None at the same time. While using a distributed algorithm, this argument determines the size of a sub-batch (or sub-population) sampled by a remote actor for computing a gradient. In distributed mode, it is expected that the population size is divisible by subbatch_size.

None
store_solution_stats Optional[bool]

Whether or not the problem object should keep track of the best and worst solutions. Can also be left as None (which is the default behavior), in which case, it will store the best and worst solutions only when the first solution batch it encounters is on the cpu. This default behavior is to ensure that there is no transfer between the cpu and a foreign computation device (like the gpu) just for the sake of keeping the best and the worst solutions.

None
vectorized Optional[bool]

Set this to True if the provided fitness function is vectorized but is not decorated via @vectorized.

None
Source code in evotorch/core.py
def __init__(
    self,
    objective_sense: ObjectiveSense,
    objective_func: Optional[Callable] = None,
    *,
    initial_bounds: Optional[BoundsPairLike] = None,
    bounds: Optional[BoundsPairLike] = None,
    solution_length: Optional[int] = None,
    dtype: Optional[DType] = None,
    eval_dtype: Optional[DType] = None,
    device: Optional[Device] = None,
    eval_data_length: Optional[int] = None,
    seed: Optional[int] = None,
    num_actors: Optional[Union[int, str]] = None,
    actor_config: Optional[dict] = None,
    num_gpus_per_actor: Optional[Union[int, float, str]] = None,
    num_subbatches: Optional[int] = None,
    subbatch_size: Optional[int] = None,
    store_solution_stats: Optional[bool] = None,
    vectorized: Optional[bool] = None,
):
    """
    `__init__(...)`: Initialize the Problem object.

    Args:
        objective_sense: A string, or a sequence of strings.
            For a single-objective problem, a single string
            ("min" or "max", for minimization or maximization)
            is enough.
            For a problem with `n` objectives, a sequence
            of strings (e.g. a list of strings) of length `n` is
            required, each string in the sequence being "min" or
            "max". This argument specifies the goal of the
            optimization.
        initial_bounds: In which interval will the values of a
            new solution will be initialized.
            Expected as a tuple, each element being either a
            scalar, or a vector of length `n`, `n` being the
            length of a solution.
            If a manual solution initialization is preferred
            (instead of an interval-based initialization),
            one can leave `initial_bounds` as None, and override
            the `_fill(...)` method in the inheriting subclass.
        bounds: Interval in which all the solutions must always
            reside.
            Expected as a tuple, each element being either a
            scalar, or a vector of length `n`, `n` being the
            length of a solution.
            This argument is optional, and can be left as None
            if one does not wish to declare hard bounds on the
            decision values of the problem.
            If `bounds` is specified, `initial_bounds` is missing,
            and `_fill(...)` is not overriden, then `bounds` will
            also serve as the `initial_bounds`.
        solution_length: Length of a solution.
            Required for all fixed-length numeric optimization
            problems.
            For variable-length problems (which might or might not
            be numeric), one is expected to leave `solution_length`
            as None, and declare `dtype` as `object`.
        dtype: dtype (data type) of the data stored by a solution.
            Can be given as a string (e.g. "float32"),
            or as a numpy dtype (e.g. `numpy.dtype("float32")`),
            or as a PyTorch dtype (e.g. `torch.float32`).
            Alternatively, if the problem is variable-length
            and/or non-numeric, one is expected to declare `dtype`
            as `object`.
        eval_dtype: dtype to be used for storing the evaluations
            (or fitnesses, or scores, or costs, or losses)
            of the solutions.
            Can be given as a string (e.g. "float32"),
            or as a numpy dtype (e.g. `numpy.dtype("float32")`),
            or as a PyTorch dtype (e.g. `torch.float32`).
            `eval_dtype` must always refer to a "float" data type,
            therefore, `object` is not accepted as a valid `eval_dtype`.
            If `eval_dtype` is not specified (i.e. left as None),
            then the following actions are taken to determine the
            `eval_dtype`:
            if `dtype` is "float16", `eval_dtype` becomes "float16";
            if `dtype` is "bfloat16", `eval_dtype` becomes "bfloat16";
            if `dtype` is "float32", `eval_dtype` becomes "float32";
            if `dtype` is "float64", `eval_dtype` becomes "float64";
            and for any other `dtype`, `eval_dtype` becomes "float32".
        device: Default device in which a new population will be
            generated. For non-numeric problems, this must be "cpu".
            For numeric problems, this can be any device supported
            by PyTorch (e.g. "cuda").
            Note that, if the number of actors of the problem is configured
            to be more than 1, `device` has to be "cpu" (or, equivalently,
            left as None).
        eval_data_length: In addition to evaluation results
            (which are (un)fitnesses, or scores, or costs, or losses),
            each solution can store extra evaluation data.
            If storage of such extra evaluation data is required,
            one can set this argument to an integer bigger than 0.
        seed: Random seed to be used by the random number generator
            attached to the problem object.
            If left as None, no random number generator will be
            attached, and the global random number generator of
            PyTorch will be used instead.
        num_actors: Number of actors to create for parallelized
            evaluation of the solutions.
            Certain string values are also accepted.
            When given as "max" or as "num_cpus", the number of actors
            will be equal to the number of all available CPUs in the ray
            cluster.
            When given as "num_gpus", the number of actors will be
            equal to the number of all available GPUs in the ray
            cluster, and each actor will be assigned a GPU.
            There is also an option, "num_devices", which means that
            both the numbers of CPUs and GPUs will be analyzed, and
            new actors and GPUs for them will be allocated,
            in a one-to-one mapping manner, if possible.
            In more details, with `num_actors="num_devices"`, if
            `device` is given as a GPU device, then it will be inferred
            that the user wishes to put everything (including the
            population) on a single GPU, and therefore there won't be
            any allocation of actors nor GPUs.
            With `num_actors="num_devices"` and with `device` set as
            "cpu" (or as left as None), if there are multiple CPUs
            and multiple GPUs, then `n` actors will be allocated
            where `n` is the minimum among the number of CPUs
            and the number of GPUs, so that there can be one-to-one
            mapping between CPUs and GPUs (i.e. such that each actor
            can be assigned an entire GPU).
            If `num_actors` is given as "num_gpus" or "num_devices",
            the argument `num_gpus_per_actor` must not be used,
            and the `actor_config` dictionary must not contain the
            key "num_gpus".
            If `num_actors` is given as something other than "num_gpus"
            or "num_devices", and if you wish to assign GPUs to each
            actor, then please see the argument `num_gpus_per_actor`.
        actor_config: A dictionary, representing the keyword arguments
            to be passed to the options(...) used when creating the
            ray actor objects. To be used for explicitly allocating
            resources per each actor.
            For example, for declaring that each actor is to use a GPU,
            one can pass `actor_config=dict(num_gpus=1)`.
            Can also be given as None (which is the default),
            if no such options are to be passed.
        num_gpus_per_actor: Number of GPUs to be allocated by each
            remote actor.
            The default behavior is to NOT allocate any GPU at all
            (which is the default behavior of the ray library as well).
            When given as a number `n`, each actor will be given
            `n` GPUs (where `n` can be an integer, or can be a `float`
            for fractional allocation).
            When given as a string "max", then the available GPUs
            across the entire ray cluster (or within the local computer
            in the simplest cases) will be equally distributed among
            the actors.
            When given as a string "all", then each actor will have
            access to all the GPUs (this will be achieved by suppressing
            the environment variable `CUDA_VISIBLE_DEVICES` for each
            actor).
            When the problem is not distributed (i.e. when there are
            no actors), this argument is expected to be left as None.
        num_subbatches: If `num_subbatches` is None (assuming that
            `subbatch_size` is also None), then, when evaluating a
            population, the population will be split into n pieces, `n`
            being the number of actors, and each actor will evaluate
            its assigned piece. If `num_subbatches` is an integer `m`,
            then the population will be split into `m` pieces,
            and actors will continually accept the next unevaluated
            piece as they finish their current tasks.
            The arguments `num_subbatches` and `subbatch_size` cannot
            be given values other than None at the same time.
            While using a distributed algorithm, this argument determines
            how many sub-batches will be generated, and therefore,
            how many gradients will be computed by the remote actors.
        subbatch_size: If `subbatch_size` is None (assuming that
            `num_subbatches` is also None), then, when evaluating a
            population, the population will be split into `n` pieces, `n`
            being the number of actors, and each actor will evaluate its
            assigned piece. If `subbatch_size` is an integer `m`,
            then the population will be split into pieces of size `m`,
            and actors will continually accept the next unevaluated
            piece as they finish their current tasks.
            When there can be significant difference across the solutions
            in terms of computational requirements, specifying a
            `subbatch_size` can be beneficial, because, while one
            actor is busy with a subbatch containing computationally
            challenging solutions, other actors can accept more
            tasks and save time.
            The arguments `num_subbatches` and `subbatch_size` cannot
            be given values other than None at the same time.
            While using a distributed algorithm, this argument determines
            the size of a sub-batch (or sub-population) sampled by a
            remote actor for computing a gradient.
            In distributed mode, it is expected that the population size
            is divisible by `subbatch_size`.
        store_solution_stats: Whether or not the problem object should
            keep track of the best and worst solutions.
            Can also be left as None (which is the default behavior),
            in which case, it will store the best and worst solutions
            only when the first solution batch it encounters is on the
            cpu. This default behavior is to ensure that there is no
            transfer between the cpu and a foreign computation device
            (like the gpu) just for the sake of keeping the best and
            the worst solutions.
        vectorized: Set this to True if the provided fitness function
            is vectorized but is not decorated via `@vectorized`.
    """

    # Set the dtype for the decision variables of the Problem
    if dtype is None:
        self._dtype = torch.float32
    elif is_dtype_object(dtype):
        self._dtype = object
    else:
        self._dtype = to_torch_dtype(dtype)

    _evolog.info(message_from(self, f"The `dtype` for the problem's decision variables is set as {self._dtype}"))

    # Set the dtype for the solution evaluations (i.e. fitnesses and evaluation data)
    if eval_dtype is not None:
        # If an `eval_dtype` is explicitly stated, then accept it as the `_eval_dtype` of the Problem
        self._eval_dtype = to_torch_dtype(eval_dtype)
    else:
        # This is the case where an `eval_dtype` is not explicitly stated by the user.
        # We need to choose a default.
        if self._dtype in (torch.float16, torch.bfloat16, torch.float64):
            # If the `dtype` of the problem is a non-32-bit float type (i.e. float16, bfloat16, float64)
            # then we use that as our `_eval_dtype` as well.
            self._eval_dtype = self._dtype
        else:
            # For any other `dtype`, we use float32 as our `_eval_dtype`.
            self._eval_dtype = torch.float32

        _evolog.info(
            message_from(
                self, f"`eval_dtype` (the dtype of the fitnesses and evaluation data) is set as {self._eval_dtype}"
            )
        )

    # Set the main device of the Problem object
    self._device = torch.device("cpu") if device is None else torch.device(device)
    _evolog.info(message_from(self, f"The `device` of the problem is set as {self._device}"))

    # Declare the internal variable that might store the random number generator
    self._generator: Optional[torch.Generator] = None

    # Set the seed of the Problem object, if a seed is provided
    self.manual_seed(seed)

    # Declare the internal variables that will store the bounds and the solution length
    self._initial_lower_bounds: Optional[torch.Tensor] = None
    self._initial_upper_bounds: Optional[torch.Tensor] = None
    self._lower_bounds: Optional[torch.Tensor] = None
    self._upper_bounds: Optional[torch.Tensor] = None
    self._solution_length: Optional[int] = None

    if self._dtype is object:
        # If dtype is given as `object`, then there are some runtime sanity checks to perform
        if bounds is not None or initial_bounds is not None:
            # With dtype as object, if bounds are given then we raise an error.
            # This is because the `object` dtype implies that the decision values are not necessarily numeric,
            # and therefore, we cannot have the guarantee of satisfying numeric bounds.
            raise ValueError(
                f"With dtype as {repr(dtype)}, expected to receive `initial_bounds` and/or `bounds` as None."
                f" However, one or both of them is/are set as value(s) other than None."
            )
        if solution_length is not None:
            # With dtype as object, if `solution_length` is provided, then we raise an error.
            # This is because the `object` dtype implies that the solutions can be expressed via various
            # containers, each with its own length, and therefore, a fixed solution length cannot be guaranteed.
            raise ValueError(
                f"With dtype as {repr(dtype)}, expected to receive `solution_length` as None."
                f" However, received `solution_length` as {repr(solution_length)}."
            )
        if str(self._device) != "cpu":
            # With dtype as object, if `device` is something other than "cpu", then we raise an error.
            # This is because the `object` dtype implies that the decision values are stored by an ObjectArray,
            # whose device is always "cpu".
            raise ValueError(
                f"With dtype as {repr(dtype)}, expected to receive `device` as 'cpu'."
                f" However, received `device` as {repr(device)}."
            )
    else:
        # If dtype is something other than `object`, then we need to make sure that we have a valid length for
        # solutions, and also properly store the given numeric bounds.

        if solution_length is None:
            # With a numeric dtype, if solution length is missing, then we raise an error.
            raise ValueError(
                f"Together with a numeric dtype ({repr(dtype)}),"
                f" expected to receive `solution_length` as an integer."
                f" However, `solution_length` is None."
            )
        else:
            # With a numeric dtype, if a solution length is provided, we make sure that it is integer.
            solution_length = int(solution_length)

        # Store the solution length
        self._solution_length = solution_length

        if (bounds is not None) or (initial_bounds is not None):
            # This is the case where we have a dtype other than `object`, and either `bounds` or `initial_bounds`
            # was provided.
            initbnd_tuple_name = "initial_bounds"
            bnd_tuple_name = "bounds"

            if (bounds is not None) and (initial_bounds is None):
                # With a numeric dtype, if strict bounds are given but initial bounds are not given, then we assume
                # that the strict bounds also serve as the initial bounds.
                # Therefore, we take clones of the strict bounds and use this clones as the initial bounds.
                initial_bounds = clone(bounds)
                initbnd_tuple_name = "bounds"

            # Below is an internal helper function for some common operations for the (strict) bounds
            # and for the initial bounds.
            def process_bounds(bounds_tuple: BoundsPairLike, tuple_name: str) -> BoundsPair:
                # This function receives the bounds_tuple (a tuple containing lower and upper bounds),
                # and the string name of the bounds argument ("bounds" or "initial_bounds").
                # What is returned is the bounds expressed as PyTorch tensors in the correct dtype and device.

                nonlocal solution_length

                # Extract the lower and upper bounds from the received bounds tuple.
                lb, ub = bounds_tuple

                # Make sure that the lower and upper bounds are expressed as tensors of correct dtype and device.
                lb = self.make_tensor(lb)
                ub = self.make_tensor(ub)

                for bound_array in (lb, ub):  # For each boundary tensor (lb and ub)
                    if bound_array.ndim not in (0, 1):
                        # If the boundary tensor is not as scalar and is not a 1-dimensional vector, then raise an
                        # error.
                        raise ValueError(
                            f"Lower and upper bounds are expected as scalars or as 1-dimensional vectors."
                            f" However, these given boundaries have incompatible shape:"
                            f" {bound_array} (of shape {bound_array.shape})."
                        )
                    if bound_array.ndim == 1:
                        if len(bound_array) != solution_length:
                            # In the case where the boundary tensor is a 1-dimensional vector, if this vector's length
                            # is not equal to the solution length, then we raise an error.
                            raise ValueError(
                                f"When boundaries are expressed as 1-dimensional vectors, their length are"
                                f" expected as the solution length of the Problem object."
                                f" However, while the problem's solution length is {solution_length},"
                                f" these given boundaries have incompatible length:"
                                f" {bound_array} (of length {len(bound_array)})."
                            )

                # Return the processed forms of the lower and upper boundary tensors.
                return lb, ub

            # Process the initial bounds with the help of the internal function `process_bounds(...)`
            init_lb, init_ub = process_bounds(initial_bounds, initbnd_tuple_name)

            # Store the processed initial bounds
            self._initial_lower_bounds = init_lb
            self._initial_upper_bounds = init_ub

            if bounds is not None:
                # If there are strict bounds, then process those bounds with the help of `process_bounds(...)`.
                lb, ub = process_bounds(bounds, bnd_tuple_name)
                # Store the processed bounds
                self._lower_bounds = lb
                self._upper_bounds = ub

    # Annotate the variable that will store the objective sense(s) of the problem
    self._objective_sense: ObjectiveSense

    # Below is an internal function which makes sure that a provided objective sense has a valid value
    # (where valid values are "min" or "max")
    def validate_sense(s: str):
        if s not in ("min", "max"):
            raise ValueError(
                f"Invalid objective sense: {repr(s)}."
                f"Instead, please provide the objective sense as 'min' or 'max'."
            )

    if not is_sequence(objective_sense):
        # If the provided objective sense is not a sequence, then convert it to a single-element list
        senses = [objective_sense]
        num_senses = 1
    else:
        # If the provided objective sense is a sequence, then take a list copy of it
        senses = list(objective_sense)
        num_senses = len(objective_sense)

        # Ensure that each provided objective sense is valid
        for sense in senses:
            validate_sense(sense)

        if num_senses == 0:
            # If the given sequence of objective senses is empty, then we raise an error.
            raise ValueError(
                "Encountered an empty sequence via `objective_sense`."
                " For a single-objective problem, please set `objective_sense` as 'min' or 'max'."
                " For a multi-objective problem, please set `objective_sense` as a sequence,"
                " each element being 'min' or 'max'."
            )

    # Store the objective senses
    self._senses: Iterable[str] = senses

    # Store the provided objective function (which can be None)
    self._objective_func: Optional[Callable] = objective_func

    # Declare the instance variable that will store whether or not the external fitness function is
    # vectorized, if such an external fitness function is given.
    self._vectorized: Optional[bool]

    # Store the information which indicates whether or not the given objective function is vectorized
    if self._objective_func is None:
        # This is the case where an external fitness function is not given.
        # In this case, we expect the keyword argument `vectorized` to be left as None.

        if vectorized is not None:
            # If the keyword argument `vectorized` is something other than None, then we raise an error
            # to let the user know.
            raise ValueError(
                f"This problem object received no external fitness function."
                f" When not using an external fitness function, the keyword argument `vectorized`"
                f" is expected to be left as None."
                f" However, the value of the keyword argument `vectorized` is {vectorized}."
            )

        # At this point, we know that we do not have an external fitness function.
        # The variable which is supposed to tell us whether or not the external fitness function is vectorized
        # is therefore irrelevant. We just set it as None.
        self._vectorized = None
    else:
        # This is the case where an external fitness function is given.

        if (
            hasattr(self._objective_func, "__evotorch_vectorized__")
            and self._objective_func.__evotorch_vectorized__
        ):
            # If the external fitness function has an attribute `__evotorch_vectorized__`, and the value of this
            # attribute evaluates to True, then this is an indication that the fitness function was decorated
            # with `@vectorized`.

            if vectorized is not None:
                # At this point, we know (or at least have the assumption) that the fitness function was decorated
                # with `@vectorized`. Any boolean value given via the keyword argument `vectorized` would therefore
                # be either redundant or conflicting.
                # Therefore, in this case, if the keyword argument `vectorized` is anything other than None, we
                # raise an error to inform the user.

                raise ValueError(
                    f"Received a fitness function that was decorated via @vectorized."
                    f" When using such a fitness function, the keyword argument `vectorized`"
                    f" is expected to be left as None."
                    f" However, the value of the keyword argument `vectorized` is {vectorized}."
                )

            # Since we know that our fitness function declares itself as vectorized, we set the instance variable
            # _vectorized as True.
            self._vectorized = True
        else:
            # This is the case in which the fitness function does not appear to be decorated via `@vectorized`.
            # In this case, if the keyword argument `vectorized` has a value that is equivalent to True,
            # then the value of `_vectorized` becomes True. On the other hand, if the keyword argument `vectorized`
            # was left as None or if it has a value that is equivalent to False, `_vectorized` becomes False.
            self._vectorized = bool(vectorized)

    # If the evaluation data length is explicitly stated, then convert it to an integer and store it.
    # Otherwise, store the evaluation data length as 0.
    self._eval_data_length = 0 if eval_data_length is None else int(eval_data_length)

    # Initialize the actor index.
    # If the problem is configured to be parallelized and the parallelization is triggered, then each remote
    # copy will have a different integer value for `_actor_index`.
    self._actor_index: Optional[int] = None

    # Initialize the variable that might store the list of actors as None.
    # If the problem is configured to be parallelized and the parallelization is triggered, then this variable
    # will store references to the remote actors (each remote actor storing its own copy of this Problem
    # instance).
    self._actors: Optional[list] = None

    # Initialize the variable that might store the ray ActorPool.
    # If the problem is configured to be parallelized and the parallelization is triggered, then this variable
    # will store the ray ActorPool that is generated out of the remote actors.
    self._actor_pool: Optional[ActorPool] = None

    # Store the ray actor configuration dictionary provided by the user (if any).
    # When (or if) the parallelization is triggered, each actor will be created with this given configuration.
    self._actor_config: Optional[dict] = None if actor_config is None else deepcopy(dict(actor_config))

    # If given, store the sub-batch size or number of sub-batches.
    # When the problem is parallelized, a sub-batch size determines the maximum size for a SolutionBatch
    # that will be sent to a remote actor for parallel solution evaluation.
    # Alternatively, num_subbatches determines into how many pieces will a SolutionBatch be split
    # for parallelization.
    # If both are None, then the main SolutionBatch will be split among the actors.
    if (num_subbatches is not None) and (subbatch_size is not None):
        raise ValueError(
            f"Encountered both `num_subbatches` and `subbatch_size` as values other than None."
            f" num_subbatches={num_subbatches}, subbatch_size={subbatch_size}."
            f" Having both of them as values other than None cannot be accepted."
        )
    self._num_subbatches: Optional[int] = None if num_subbatches is None else int(num_subbatches)
    self._subbatch_size: Optional[int] = None if subbatch_size is None else int(subbatch_size)

    # Initialize the additional states to be loaded by the remote actor as None.
    # If there are such additional states for remote actors, the inheriting class can fill this as a list
    # of dictionaries.
    self._remote_states: Optional[Iterable[dict]] = None

    # Initialize a temporary internal variable which stores the resources available in the ray cluster.
    # Most probably, we are interested in the resources "CPU" and "GPU".
    ray_resources: Optional[dict] = None

    # The following is an internal helper function which returns the amount of availability for a given
    # resource in the ray cluster.
    # If the requested resource is not available at all, None will be returned.
    def get_ray_resource(resource_name: str) -> Any:
        # Ensure that the ray cluster is initialized
        ensure_ray()
        nonlocal ray_resources
        if ray_resources is None:
            # If the ray resource information was not fetched, then fetch them and store them.
            ray_resources = ray.available_resources()
        # Return the information regarding the requested resource from the fetched resource information.
        # If it turns out that the requested resource is not available at all, the result will be None.
        return ray_resources.get(resource_name, None)

    # Annotate the variable that will store the number of actors (to be created when the parallelization
    # is triggered).
    self._num_actors: int

    if num_actors is None:
        # If the argument `num_actors` is left as None, then we set `_num_actors` as 0, which means that
        # there will be no parallelization.
        self._num_actors = 0
    elif isinstance(num_actors, str):
        # This is the case where `num_actors` has a string value
        if num_actors in ("max", "num_cpus"):
            # If the `num_actors` argument was given as "max" or as "num_cpus", then we first read how many CPUs
            # are available in the ray cluster, then convert it to integer (via computing its ceil value), and
            # finally set `_num_actors` as this integer.
            self._num_actors = math.ceil(get_ray_resource("CPU"))
        elif num_actors == "num_gpus":
            # If the `num_actors` argument was given as "num_gpus", then we first read how many GPUs are
            # available in the ray cluster.
            num_gpus = get_ray_resource("GPU")
            if num_gpus is None:
                # If there are no GPUs at all, then we raise an error
                raise ValueError(
                    "The argument `num_actors` was encountered as 'num_gpus'."
                    " However, there does not seem to be any GPU available."
                )
            if num_gpus < 1e-4:
                # If the number of available GPUs are 0 or close to 0, then we raise an error
                raise ValueError(
                    f"The argument `num_actors` was encountered as 'num_gpus'."
                    f" However, the number of available GPUs are either 0 or close to 0 (= {num_gpus})."
                )
            if (actor_config is not None) and ("num_gpus" in actor_config):
                # With `num_actors` argument given as "num_gpus", we will also allocate each GPU to an actor.
                # If `actor_config` contains an item with key "num_gpus", then that configuration item would
                # conflict with the GPU allocation we are about to do here.
                # So, we raise an error.
                raise ValueError(
                    "The argument `num_actors` was encountered as 'num_gpus'."
                    " With this configuration, the number of GPUs assigned to an actor is automatically determined."
                    " However, at the same time, the `actor_config` argument was received with the key 'num_gpus',"
                    " which causes a conflict."
                )
            if num_gpus_per_actor is not None:
                # With `num_actors` argument given as "num_gpus", we will also allocate each GPU to an actor.
                # If the argument `num_gpus_per_actor` is also stated, then such a configuration item would
                # conflict with the GPU allocation we are about to do here.
                # So, we raise an error.
                raise ValueError(
                    f"The argument `num_actors` was encountered as 'num_gpus'."
                    f" With this configuration, the number of GPUs assigned to an actor is automatically determined."
                    f" However, at the same time, the `num_gpus_per_actor` argument was received with a value other"
                    f" than None ({repr(num_gpus_per_actor)}), which causes a conflict."
                )
            # Set the number of actors as the ceiled integer counterpart of the number of available GPUs
            self._num_actors = math.ceil(num_gpus)
            # We assign a GPU for each actor (by overriding the value for the argument `num_gpus_per_actor`).
            num_gpus_per_actor = num_gpus / self._num_actors
        elif num_actors == "num_devices":
            # This is the case where `num_actors` has the string value "num_devices".

            # With `num_actors` set as "num_devices", if there are any GPUs, the behavior is to assign a GPU
            # to each actor. If there are conflicting configurations regarding how many GPUs are to be assigned
            # to each actor, then we raise an error.
            if (actor_config is not None) and ("num_gpus" in actor_config):
                raise ValueError(
                    "The argument `num_actors` was encountered as 'num_devices'."
                    " With this configuration, the number of GPUs assigned to an actor is automatically determined."
                    " However, at the same time, the `actor_config` argument was received with the key 'num_gpus',"
                    " which causes a conflict."
                )
            if num_gpus_per_actor is not None:
                raise ValueError(
                    f"The argument `num_actors` was encountered as 'num_devices'."
                    f" With this configuration, the number of GPUs assigned to an actor is automatically determined."
                    f" However, at the same time, the `num_gpus_per_actor` argument was received with a value other"
                    f" than None ({repr(num_gpus_per_actor)}), which causes a conflict."
                )

            if self._device != torch.device("cpu"):
                # If the main device is not CPU, then the user most probably wishes to put all the
                # computations (both evaluations and the population) on the GPU, without allocating
                # any actor.
                # So, we set `_num_actors` as None, and overwrite `num_gpus_per_actor` with None.
                self._num_actors = None
                num_gpus_per_actor = None
            else:
                # If the device argument is "cpu" or left as None, then we assume that actor allocations
                # might be desired.

                # Read how many CPUs and GPUs are available in the ray cluster.
                num_cpus = get_ray_resource("CPU")
                num_gpus = get_ray_resource("GPU")

                # If we have multiple CPUs, then we continue with the actor allocation procedures.
                if (num_gpus is None) or (num_gpus < 1e-4):
                    # If there are no GPUs, then we set the number of actors as the number of CPUs, and we
                    # set the number of GPUs per actor as None (which means that there will be no GPU
                    # assignment)
                    self._num_actors = math.ceil(num_cpus)
                    num_gpus_per_actor = None
                else:
                    # If there are GPUs available, then we compute the minimum among the number of CPUs and
                    # GPUs, and this minimum value becomes the number of actors (so that there can be
                    # one-to-one mapping between actors and GPUs).
                    self._num_actors = math.ceil(min(num_cpus, num_gpus))

                    # We assign a GPU for each actor (by overriding the value for the argument
                    # `num_gpus_per_actor`).
                    if self._num_actors <= num_gpus:
                        num_gpus_per_actor = 1
                    else:
                        num_gpus_per_actor = num_gpus / self._num_actors
        else:
            # This is the case where `num_actors` is given as an unexpected string. We raise an error here.
            raise ValueError(
                f"Invalid string value for `num_actors`: {repr(num_actors)}."
                f" The acceptable string values for `num_actors` are 'max', 'num_cpus', 'num_gpus', 'num_devices'."
            )
    else:
        # This is the case where `num_actors` has a value which is not a string.
        # In this case, we make sure that the given value is an integer, and then use this integer as our
        # number of actors.
        self._num_actors = int(num_actors)

    if self._num_actors == 1:
        _evolog.info(
            message_from(
                self,
                (
                    "The number of actors that will be allocated for parallelized evaluation was encountered as 1."
                    " This number is automatically dropped to 0,"
                    " because having only 1 actor does not bring any benefit in terms of parallelization."
                ),
            )
        )
        # Creating a single actor does not bring any benefit of parallelization.
        # Therefore, at the end of all the computations above regarding the number of actors, if it turns out
        # that the target number of actors is 1, we reduce it to 0 (meaning that no actor will be initialized).
        self._num_actors = 0

        # Since we are to allocate no actor, the value of the argument `num_gpus_per_actor` is meaningless.
        # We therefore overwrite the value of that argument with None.
        num_gpus_per_actor = None

    _evolog.info(
        message_from(
            self, f"The number of actors that will be allocated for parallelized evaluation is {self._num_actors}"
        )
    )

    if (self._num_actors >= 2) and (self._device != torch.device("cpu")):
        detailed_error_msg = (
            f"The number of actors that will be allocated for parallelized evaluation is {self._num_actors}."
            " When the number of actors is at least 2,"
            ' the only supported value for the `device` argument is "cpu".'
            f" However, `device` was received as {self._device}."
            "\n\n---- Possible ways to fix the error: ----"
            "\n\n"
            "(1)"
            " If both the population and the fitness evaluation operations can fit into the same device,"
            f" try setting `device={self._device}` and `num_actors=0`."
            "\n\n"
            "(2)"
            " If you would like to use N number of GPUs in parallel for fitness evaluation (where N>1),"
            ' set `device="cpu"` (so that the main process will keep the population on the cpu), set'
            " `num_actors=N` and `num_gpus_per_actor=1` (to allocate an actor for each of the `N` GPUs),"
            " and then, decorate your fitness function using `evotorch.decorators.on_cuda`"
            " so that the fitness evaluation will be performed on the cuda device assigned to the actor."
            " The code for achieving this can look like this:"
            "\n\n"
            "    from evotorch import Problem\n"
            "    from evotorch.decorators import on_cuda, vectorized\n"
            "    import torch\n"
            "\n"
            "    @on_cuda\n"
            "    @vectorized\n"
            "    def f(x: torch.Tensor) -> torch.Tensor:\n"
            "        ...\n"
            "\n"
            '    problem = Problem("min", f, device="cpu", num_actors=N, num_gpus_per_actor=1)\n'
            "\n"
            "Or, it can look like this:\n"
            "\n"
            "    from evotorch import Problem, SolutionBatch\n"
            "    from evotorch.decorators import on_cuda\n"
            "    import torch\n"
            "\n"
            "    class MyProblem(Problem):\n"
            "        def __init__(self, ...):\n"
            "            super().__init__(\n"
            '                objective_sense="min", device="cpu", num_actors=N, num_gpus_per_actor=1, ...\n'
            "            )\n"
            "\n"
            "        @on_cuda\n"
            "        def _evaluate_batch(self, batch: SolutionBatch):\n"
            "            ...\n"
            "\n"
            "    problem = MyProblem(...)\n"
            "\n"
            "\n"
            "(3)"
            " Similarly to option (2), for when you wish to use N number of GPUs for fitness evaluation,"
            ' set `device="cpu"`, set `num_actors=N` and `num_gpus_per_actor=1`, then, within the evaluation'
            ' function, manually use the device `"cuda"` to accelerate the computation.'
            "\n\n"
            "--------------\n"
            "Note for cases (2) and (3): if you are on a computer or on a ray cluster with multiple GPUs, you"
            ' might prefer to set `num_actors` as the string "num_gpus" instead of an integer N,'
            " which will cause the number of available GPUs to be counted, and the number of actors to be"
            " configured as that count."
        )

        raise ValueError(detailed_error_msg)

    # Annotate the variable which will determine how many GPUs are to be assigned to each actor.
    self._num_gpus_per_actor: Optional[Union[str, int, float]]

    if (actor_config is not None) and ("num_gpus" in actor_config) and (num_gpus_per_actor is not None):
        # If `actor_config` dictionary has the item "num_gpus" and also `num_gpus_per_actor` is not None,
        # then there is a conflicting (or redundant) configuration. We raise an error here.
        raise ValueError(
            'The `actor_config` dictionary contains the key "num_gpus".'
            " At the same time, `num_gpus_per_actor` has a value other than None."
            " These two configurations are conflicting."
            " Please specify the number of GPUs per actor either via the `actor_config` dictionary,"
            " or via the `num_gpus_per_actor` argument, but not via both."
        )

    if num_gpus_per_actor is None:
        # If the argument `num_gpus_per_actor` is not specified, then we set the attribute
        # `_num_gpus_per_actor` as None, which means that no GPUs will be assigned to the actors.
        self._num_gpus_per_actor = None
    elif isinstance(num_gpus_per_actor, str):
        # This is the case where `num_gpus_per_actor` is given as a string.
        if num_gpus_per_actor == "max":
            # This is the case where `num_gpus_per_actor` is given as "max".
            num_gpus = get_ray_resource("GPU")
            if num_gpus is None:
                # With `num_gpus_per_actor` as "max", if there is no GPU available, then we set the attribute
                # `_num_gpus_per_actor` as None, which means there will be no GPU assignment to the actors.
                self._num_gpus_per_actor = None
            else:
                # With `num_gpus_per_actor` as "max", if there are GPUs available, then the available GPUs will
                # be shared among the actors.
                self._num_gpus_per_actor = num_gpus / self._num_actors
        elif num_gpus_per_actor == "all":
            # When `num_gpus_per_actor` is "all", we also set the attribute `_num_gpus_per_actor` as "all".
            # When a remote actor is initialized, the remote actor will see that the Problem instance has its
            # `_num_gpus_per_actor` set as "all", and it will remove the environment variable named
            # "CUDA_VISIBLE_DEVICES" in its own environment.
            # With "CUDA_VISIBLE_DEVICES" removed, an actor will see all the GPUs available in its own
            # environment.
            self._num_gpus_per_actor = "all"
        else:
            # This is the case where `num_gpus_per_actor` argument has an unexpected string value.
            # We raise an error.
            raise ValueError(
                f"Invalid string value for `num_gpus_per_actor`: {repr(num_gpus_per_actor)}."
                f' Acceptable string values for `num_gpus_per_actor` are: "max", "all".'
            )
    elif isinstance(num_gpus_per_actor, int):
        # When the argument `num_gpus_per_actor` is set as an integer we just set the attribute
        # `_num_gpus_per_actor` as this integer.
        self._num_gpus_per_actor = num_gpus_per_actor
    else:
        # For anything else, we assume that `num_gpus_per_actor` is an object that is convertible to float.
        # Therefore, we convert it to float and store it in the attribute `_num_gpus_per_actor`.
        # Also, remember that, when `num_actors` is given as "num_gpus" or as "num_devices",
        # the code above overrides the value for the argument `num_gpus_per_actor`, which means,
        # this is the case that is activated when `num_actors` is "num_gpus" or "num_devices".
        self._num_gpus_per_actor = float(num_gpus_per_actor)

    if self._num_actors > 0:
        _evolog.info(
            message_from(self, f"Number of GPUs that will be allocated per actor is {self._num_gpus_per_actor}")
        )

    # Initialize the Hook instances (and the related status dictionary for the `_after_eval_hook`)
    self._before_eval_hook: Hook = Hook()
    self._after_eval_hook: Hook = Hook()
    self._after_eval_status: dict = {}
    self._remote_hook: Hook = Hook()
    self._before_grad_hook: Hook = Hook()
    self._after_grad_hook: Hook = Hook()

    # Initialize various stats regarding the solutions encountered by this Problem instance.
    self._store_solution_stats = None if store_solution_stats is None else bool(store_solution_stats)
    self._best: Optional[list] = None
    self._worst: Optional[list] = None
    self._best_evals: Optional[torch.Tensor] = None
    self._worst_evals: Optional[torch.Tensor] = None

    # Initialize the boolean attribute which indicates whether or not this Problem instance (which can be
    # the main instance or a remote instance on an actor) is "prepared" via the `_prepare` method.
    self._prepared: bool = False

all_remote_envs(self)

Get an accessor which is used for running a method on all remote reinforcement learning environments.

This method can only be used on parallelized Problem objects which have their get_env() methods defined. For example, one can use this feature on a parallelized GymProblem.

As an example, let us consider a parallelized GymProblem object named my_problem. Given that my_problem has n remote actors, a method f() can be executed on all remote reinforcement learning environments as follows:

results = my_problem.all_remote_envs().f()

The variable results is a list of length n, the i-th item of the list belonging to the method f's result from the i-th actor.

Returns:

Type Description
AllRemoteEnvs

A method accessor for all the remote reinforcement learning environments.

Source code in evotorch/core.py
def all_remote_envs(self) -> AllRemoteEnvs:
    """
    Get an accessor which is used for running a method
    on all remote reinforcement learning environments.

    This method can only be used on parallelized Problem
    objects which have their `get_env()` methods defined.
    For example, one can use this feature on a parallelized
    GymProblem.

    As an example, let us consider a parallelized GymProblem
    object named `my_problem`. Given that `my_problem` has
    `n` remote actors, a method `f()` can be executed
    on all remote reinforcement learning environments as
    follows:

        results = my_problem.all_remote_envs().f()

    The variable `results` is a list of length `n`, the i-th
    item of the list belonging to the method f's result
    from the i-th actor.

    Returns:
        A method accessor for all the remote reinforcement
        learning environments.
    """
    self._parallelize()
    if self.is_remote:
        raise RuntimeError(
            "The method `all_remote_envs()` can only be used on the main (i.e. non-remote)"
            " Problem instance."
            " However, this Problem instance is on a remote actor."
        )
    return AllRemoteEnvs(self._actors)

all_remote_problems(self)

Get an accessor which is used for running a method on all remote clones of this Problem object.

For example, given a Problem object named my_problem, also assuming that this Problem object is parallelized, and therefore has n remote actors, a method f() can be executed on all the remote instances as follows:

results = my_problem.all_remote_problems().f()

The variable results is a list of length n, the i-th item of the list belonging to the method f's result from the i-th actor.

Returns:

Type Description
AllRemoteProblems

A method accessor for all the remote Problem objects.

Source code in evotorch/core.py
def all_remote_problems(self) -> AllRemoteProblems:
    """
    Get an accessor which is used for running a method
    on all remote clones of this Problem object.

    For example, given a Problem object named `my_problem`,
    also assuming that this Problem object is parallelized,
    and therefore has `n` remote actors, a method `f()`
    can be executed on all the remote instances as follows:

        results = my_problem.all_remote_problems().f()

    The variable `results` is a list of length `n`, the i-th
    item of the list belonging to the method f's result
    from the i-th actor.

    Returns:
        A method accessor for all the remote Problem objects.
    """
    self._parallelize()
    if self.is_remote:
        raise RuntimeError(
            "The method `all_remote_problems()` can only be used on the main (i.e. non-remote)"
            " Problem instance."
            " However, this Problem instance is on a remote actor."
        )
    return AllRemoteProblems(self._actors)

compare_solutions(self, a, b, obj_index=None)

Compare two solutions. It is assumed that both solutions are already evaluated.

Parameters:

Name Type Description Default
a Solution

The first solution.

required
b Solution

The second solution.

required
obj_index Optional[int]

The objective index according to which the comparison will be made. Can be left as None if the problem is single-objective.

None

Returns:

Type Description
float

A positive number if a is better; a negative number if b is better; 0 if there is a tie.

Source code in evotorch/core.py
def compare_solutions(self, a: "Solution", b: "Solution", obj_index: Optional[int] = None) -> float:
    """
    Compare two solutions.
    It is assumed that both solutions are already evaluated.

    Args:
        a: The first solution.
        b: The second solution.
        obj_index: The objective index according to which the comparison
            will be made.
            Can be left as None if the problem is single-objective.
    Returns:
        A positive number if `a` is better;
        a negative number if `b` is better;
        0 if there is a tie.
    """
    senses = self.senses
    obj_index = self.normalize_obj_index(obj_index)
    sense = senses[obj_index]

    def score(s: Solution):
        return s.evals[obj_index]

    if sense == "max":
        return score(a) - score(b)
    elif sense == "min":
        return score(b) - score(a)
    else:
        raise ValueError("Unrecognized sense: " + repr(sense))

ensure_numeric(self)

Ensure that the problem has a numeric dtype.

Exceptions:

Type Description
ValueError

if the problem has a non-numeric dtype.

Source code in evotorch/core.py
def ensure_numeric(self):
    """
    Ensure that the problem has a numeric dtype.

    Raises:
        ValueError: if the problem has a non-numeric dtype.
    """
    if is_dtype_object(self.dtype):
        raise ValueError("Expected a problem with numeric dtype, but the dtype is object.")

ensure_single_objective(self)

Ensure that the problem has only one objective.

Exceptions:

Type Description
ValueError

if the problem is multi-objective.

Source code in evotorch/core.py
def ensure_single_objective(self):
    """
    Ensure that the problem has only one objective.

    Raises:
        ValueError: if the problem is multi-objective.
    """
    n = len(self.senses)
    if n > 1:
        raise ValueError(f"Expected a single-objective problem, but this problem has {n} objectives.")

ensure_unbounded(self)

Ensure that the problem has no strict lower and upper bounds.

Exceptions:

Type Description
ValueError

if the problem has strict lower and upper bounds.

Source code in evotorch/core.py
def ensure_unbounded(self):
    """
    Ensure that the problem has no strict lower and upper bounds.

    Raises:
        ValueError: if the problem has strict lower and upper bounds.
    """
    if not (self.lower_bounds is None and self.upper_bounds is None):
        raise ValueError("Expected an unbounded problem, but this problem has lower and/or upper bounds.")

evaluate(self, x)

Evaluate the given Solution or SolutionBatch.

Parameters:

Name Type Description Default
x Union[SolutionBatch, Solution]

The SolutionBatch to be evaluated.

required
Source code in evotorch/core.py
def evaluate(self, x: Union["SolutionBatch", "Solution"]):
    """
    Evaluate the given Solution or SolutionBatch.

    Args:
        x: The SolutionBatch to be evaluated.
    """

    if isinstance(x, Solution):
        batch = x.to_batch()
    elif isinstance(x, SolutionBatch):
        batch = x
    else:
        raise TypeError(
            f"The method `evaluate(...)` expected a Solution or a SolutionBatch as its argument."
            f" However, the received object is {repr(x)}, which is of type {repr(type(x))}."
        )

    self._parallelize()

    if self.is_main:
        self.before_eval_hook(batch)

    must_sync_after = self._sync_before()

    self._start_preparations()

    self._evaluate_all(batch)

    if must_sync_after:
        self._sync_after()

    if self.is_main:
        self._after_eval_status = {}

        best_and_worst = self._get_best_and_worst(batch)
        if best_and_worst is not None:
            self._after_eval_status.update(best_and_worst)

        self._after_eval_status.update(self.after_eval_hook.accumulate_dict(batch))

generate_batch(self, popsize=None, *, empty=False, center=None, stdev=None, symmetric=False)

Generate a new SolutionBatch.

Parameters:

Name Type Description Default
popsize Optional[int]

Number of solutions that will be contained in the new batch.

None
empty bool

Set this as True if you would like to receive the solutions un-initialized.

False
center Union[float, Iterable[float], torch.Tensor]

Center point of the Gaussian distribution from which the decision values will be sampled, as a scalar or as a 1-dimensional vector. Can also be left as None. If center is None and stdev is None, all the decision values will be sampled from the interval specified by initial_bounds (or by bounds if initial_bounds was not specified). If center is None and stdev is not None, a center point will be sampled from within the interval specified by initial_bounds or bounds, and the decision values will be sampled from a Gaussian distribution around this center point.

None
stdev Union[float, Iterable[float], torch.Tensor]

Can be None (default) if the SolutionBatch is to contain decision values sampled from the interval specified by initial_bounds (or by bounds if initial_bounds was not provided during the initialization phase). Alternatively, a scalar or a 1-dimensional vector specifying the standard deviation of the Gaussian distribution from which the decision values will be sampled.

None
symmetric bool

To be used only when stdev is not None. If symmetric is True, decision values will be sampled from the Gaussian distribution in a symmetric (i.e. antithetic) manner. Otherwise, the decision values will be sampled in the non-antithetic manner.

False
Source code in evotorch/core.py
def generate_batch(
    self,
    popsize: Optional[int] = None,
    *,
    empty: bool = False,
    center: Optional[RealOrVector] = None,
    stdev: Optional[RealOrVector] = None,
    symmetric: bool = False,
) -> "SolutionBatch":
    """
    Generate a new SolutionBatch.

    Args:
        popsize: Number of solutions that will be contained in the new
            batch.
        empty: Set this as True if you would like to receive the solutions
            un-initialized.
        center: Center point of the Gaussian distribution from which
            the decision values will be sampled, as a scalar or as a
            1-dimensional vector.
            Can also be left as None.
            If `center` is None and `stdev` is None, all the decision
            values will be sampled from the interval specified by
            `initial_bounds` (or by `bounds` if `initial_bounds` was not
            specified).
            If `center` is None and `stdev` is not None, a center point
            will be sampled from within the interval specified by
            `initial_bounds` or `bounds`, and the decision values will be
            sampled from a Gaussian distribution around this center point.
        stdev: Can be None (default) if the SolutionBatch is to contain
            decision values sampled from the interval specified by
            `initial_bounds` (or by `bounds` if `initial_bounds` was not
            provided during the initialization phase).
            Alternatively, a scalar or a 1-dimensional vector specifying
            the standard deviation of the Gaussian distribution from which
            the decision values will be sampled.
        symmetric: To be used only when `stdev` is not None.
            If `symmetric` is True, decision values will be sampled from
            the Gaussian distribution in a symmetric (i.e. antithetic)
            manner.
            Otherwise, the decision values will be sampled in the
            non-antithetic manner.
    """
    if (center is None) and (stdev is None):
        if symmetric:
            raise ValueError(
                f"The argument `symmetric` can be set as True only when `center` and `stdev` are provided."
                f" Although `center` and `stdev` are None, `symmetric` was received as {symmetric}."
            )
        return SolutionBatch(self, popsize, empty=empty, device=self.device)
    elif (center is not None) and (stdev is not None):
        if empty:
            raise ValueError(
                f"When `center` and `stdev` are provided, the argument `empty` must be False."
                f" However, the received value for `empty` is {empty}."
            )
        result = SolutionBatch(self, popsize, device=self.device, empty=True)
        self.make_gaussian(out=result.access_values(), center=center, stdev=stdev, symmetric=symmetric)
        return result
    else:
        raise ValueError(
            f"The arguments `center` and `stdev` were expected to be None or non-None at the same time."
            f" Received `center`: {center}."
            f" Received `stdev`: {stdev}."
        )

generate_values(self, num_solutions)

Generate decision values.

This function returns a tensor containing the decision values for n new solutions, n being the integer passed as the num_rows argument.

For numeric problems, this function generates the decision values which respect initial_bounds (or bounds, if initial_bounds was not provided). If this type of initialization is not desired, one can override this function and define a manual initialization scheme in the inheriting subclass.

For non-numeric problems, it is expected that the inheriting subclass will override the method _fill(...).

Parameters:

Name Type Description Default
num_solutions int

For how many solutions will new decision values be generated.

required

Returns:

Type Description
Union[torch.Tensor, evotorch.tools.objectarray.ObjectArray]

A PyTorch tensor for numeric problems, an ObjectArray for non-numeric problems.

Source code in evotorch/core.py
def generate_values(self, num_solutions: int) -> Union[torch.Tensor, ObjectArray]:
    """
    Generate decision values.

    This function returns a tensor containing the decision values
    for `n` new solutions, `n` being the integer passed as the `num_rows`
    argument.

    For numeric problems, this function generates the decision values
    which respect `initial_bounds` (or `bounds`, if `initial_bounds`
    was not provided).
    If this type of initialization is not desired, one can override
    this function and define a manual initialization scheme in the
    inheriting subclass.

    For non-numeric problems, it is expected that the inheriting subclass
    will override the method `_fill(...)`.

    Args:
        num_solutions: For how many solutions will new decision values be
            generated.
    Returns:
        A PyTorch tensor for numeric problems, an ObjectArray for
        non-numeric problems.
    """
    result = self.make_empty(num_solutions=num_solutions)
    self._fill(result)
    return result

get_obj_order_descending(self)

When sorting the solutions from best to worst according to each objective i, is the ordering descending?

Source code in evotorch/core.py
def get_obj_order_descending(self) -> Iterable[bool]:
    """When sorting the solutions from best to worst according to each objective i, is the ordering descending?"""
    result = []
    for s in self.senses:
        if s == "min":
            result.append(False)
        elif s == "max":
            result.append(True)
        else:
            raise ValueError(f"Invalid sense: {repr(s)}")
    return result

is_better(self, a, b, obj_index=None)

Check whether or not the first solution is better. It is assumed that both solutions are already evaluated.

Parameters:

Name Type Description Default
a Solution

The first solution.

required
b Solution

The second solution.

required
obj_index Optional[int]

The objective index according to which the comparison will be made. Can be left as None if the problem is single-objective.

None

Returns:

Type Description
bool

True if a is better; False otherwise.

Source code in evotorch/core.py
def is_better(self, a: "Solution", b: "Solution", obj_index: Optional[int] = None) -> bool:
    """
    Check whether or not the first solution is better.
    It is assumed that both solutions are already evaluated.

    Args:
        a: The first solution.
        b: The second solution.
        obj_index: The objective index according to which the comparison
            will be made.
            Can be left as None if the problem is single-objective.
    Returns:
        True if `a` is better; False otherwise.
    """
    return self.compare_solutions(a, b, obj_index) > 0

is_on_cpu(self)

Whether or not the Problem object has its device set as "cpu".

Source code in evotorch/core.py
def is_on_cpu(self) -> bool:
    """
    Whether or not the Problem object has its device set as "cpu".
    """
    return str(self.device) == "cpu"

is_worse(self, a, b, obj_index=None)

Check whether or not the first solution is worse. It is assumed that both solutions are already evaluated.

Parameters:

Name Type Description Default
a Solution

The first solution.

required
b Solution

The second solution.

required
obj_index Optional[int]

The objective index according to which the comparison will be made. Can be left as None if the problem is single-objective.

None

Returns:

Type Description
bool

True if a is worse; False otherwise.

Source code in evotorch/core.py
def is_worse(self, a: "Solution", b: "Solution", obj_index: Optional[int] = None) -> bool:
    """
    Check whether or not the first solution is worse.
    It is assumed that both solutions are already evaluated.

    Args:
        a: The first solution.
        b: The second solution.
        obj_index: The objective index according to which the comparison
            will be made.
            Can be left as None if the problem is single-objective.
    Returns:
        True if `a` is worse; False otherwise.
    """
    return self.compare_solutions(a, b, obj_index) < 0

kill_actors(self)

Kill all the remote actors used by the Problem instance.

One might use this method to release the resources used by the remote actors.

Source code in evotorch/core.py
def kill_actors(self):
    """
    Kill all the remote actors used by the Problem instance.

    One might use this method to release the resources used by the
    remote actors.
    """
    if not self.is_main:
        raise RuntimeError(
            "The method `kill_actors()` can only be used on the main (i.e. non-remote)"
            " Problem instance."
            " However, this Problem instance is on a remote actor."
        )
    for actor in self._actors:
        ray.kill(actor)
    self._actors = None
    self._actor_pool = None

manual_seed(self, seed=None)

Provide a manual seed for the Problem object.

If the given seed is None, then the Problem object will remove its own stored generator, and start using the global generator of PyTorch instead. If the given seed is an integer, then the Problem object will instantiate its own generator with the given seed.

Parameters:

Name Type Description Default
seed Optional[int]

None for using the global PyTorch generator; an integer for instantiating a new PyTorch generator with this given integer seed, specific to this Problem object.

None
Source code in evotorch/core.py
def manual_seed(self, seed: Optional[int] = None