Real
This module contains operators defined to work with problems
whose dtype
s are real numbers (e.g. torch.float32
).
CosynePermutation (CopyingOperator)
¶
Representation of permutation operation on a SolutionBatch.
For each decision variable index, a permutation operation across all or a subset of solutions, is performed. The result is returned on a new SolutionBatch. The original SolutionBatch remains unmodified.
Reference:
F.Gomez, J.Schmidhuber, R.Miikkulainen (2008).
Accelerated Neural Evolution through Cooperatively Coevolved Synapses
Journal of Machine Learning Research 9, 937965
Source code in evotorch/operators/real.py
class CosynePermutation(CopyingOperator):
"""
Representation of permutation operation on a SolutionBatch.
For each decision variable index, a permutation operation across
all or a subset of solutions, is performed.
The result is returned on a new SolutionBatch.
The original SolutionBatch remains unmodified.
Reference:
F.Gomez, J.Schmidhuber, R.Miikkulainen (2008).
Accelerated Neural Evolution through Cooperatively Coevolved Synapses
Journal of Machine Learning Research 9, 937965
"""
def __init__(self, problem: Problem, obj_index: Optional[int] = None, *, permute_all: bool = False):
"""
`__init__(...)`: Initialize the CosynePermutation.
Args:
problem: The problem object to work on.
obj_index: The index of the objective according to which the
candidates for permutation will be selected.
Can be left as None if the problem is singleobjective,
or if `permute_all` is given as True (in which case there
will be no candidate selection as the entire population will
be subject to permutation).
permute_all: Whether or not to apply permutation on the entire
population, instead of using a selective permutation.
"""
if permute_all:
if obj_index is not None:
raise ValueError(
"When `permute_all` is given as True (which seems to be the case)"
" `obj_index` is expected as None,"
" because the operator is independent of any objective and any fitness in this mode."
" However, `permute_all` was found to be something other than None."
)
self._obj_index = None
else:
self._obj_index = problem.normalize_obj_index(obj_index)
super().__init__(problem)
self._permute_all = bool(permute_all)
@property
def obj_index(self) > Optional[int]:
"""Objective index according to which the operator will run.
If `permute_all` was given as True, objectives are irrelevant, in which case
`obj_index` is returned as None.
If `permute_all` was given as False, the relevant `obj_index` is provided
as an integer.
"""
return self._obj_index
@torch.no_grad()
def _do(self, batch: SolutionBatch) > SolutionBatch:
indata = batch._data
if not self._permute_all:
n = batch.solution_length
ranks = batch.utility(self._obj_index, ranking_method="centered")
# fitnesses = batch.evals[:, self._obj_index].clone().reshape(1)
# ranks = rank(
# fitnesses, ranking_method="centered", higher_is_better=(self.problem.senses[self.obj_index] == "max")
# )
prob_permute = (1  (ranks + 0.5).pow(1 / float(n))).unsqueeze(1).expand(len(batch), batch.solution_length)
else:
prob_permute = torch.ones_like(indata)
perm_mask = self.problem.make_uniform_shaped_like(prob_permute) <= prob_permute
perm_mask_sorted = torch.sort(perm_mask.to(torch.long), descending=True, dim=0)[0].to(
torch.bool
) # Sort permutations
perm_rand = self.problem.make_uniform_shaped_like(prob_permute)
perm_rand[torch.logical_not(perm_mask)] = 1.0
permutations = torch.argsort(perm_rand, dim=0) # Generate permutations
perm_sort = (
torch.arange(0, perm_mask.shape[0], device=indata.device).unsqueeze(1).repeat(1, perm_mask.shape[1])
)
perm_sort[torch.logical_not(perm_mask)] += perm_mask.shape[0] + 1
perm_sort = torch.sort(perm_sort, dim=0)[0] # Generate the origin of permutations
_, permutation_columns = torch.nonzero(perm_mask_sorted, as_tuple=True)
permutation_origin_indices = perm_sort[perm_mask_sorted]
permutation_target_indices = permutations[perm_mask_sorted]
newbatch = SolutionBatch(like=batch, empty=True)
newdata = newbatch._data
newdata[:] = indata[:]
newdata[permutation_origin_indices, permutation_columns] = newdata[
permutation_target_indices, permutation_columns
]
return newbatch
obj_index: Optional[int]
property
readonly
¶
Objective index according to which the operator will run.
If permute_all
was given as True, objectives are irrelevant, in which case
obj_index
is returned as None.
If permute_all
was given as False, the relevant obj_index
is provided
as an integer.
__init__(self, problem, obj_index=None, *, permute_all=False)
special
¶
__init__(...)
: Initialize the CosynePermutation.
Parameters:
Name  Type  Description  Default 

problem 
Problem 
The problem object to work on. 
required 
obj_index 
Optional[int] 
The index of the objective according to which the
candidates for permutation will be selected.
Can be left as None if the problem is singleobjective,
or if 
None 
permute_all 
bool 
Whether or not to apply permutation on the entire population, instead of using a selective permutation. 
False 
Source code in evotorch/operators/real.py
def __init__(self, problem: Problem, obj_index: Optional[int] = None, *, permute_all: bool = False):
"""
`__init__(...)`: Initialize the CosynePermutation.
Args:
problem: The problem object to work on.
obj_index: The index of the objective according to which the
candidates for permutation will be selected.
Can be left as None if the problem is singleobjective,
or if `permute_all` is given as True (in which case there
will be no candidate selection as the entire population will
be subject to permutation).
permute_all: Whether or not to apply permutation on the entire
population, instead of using a selective permutation.
"""
if permute_all:
if obj_index is not None:
raise ValueError(
"When `permute_all` is given as True (which seems to be the case)"
" `obj_index` is expected as None,"
" because the operator is independent of any objective and any fitness in this mode."
" However, `permute_all` was found to be something other than None."
)
self._obj_index = None
else:
self._obj_index = problem.normalize_obj_index(obj_index)
super().__init__(problem)
self._permute_all = bool(permute_all)
GaussianMutation (CopyingOperator)
¶
Gaussian mutation operator.
Follows the algorithm description in:
Sean Luke, 2013, Essentials of Metaheuristics, Lulu, second edition
available for free at http://cs.gmu.edu/~sean/book/metaheuristics/
Source code in evotorch/operators/real.py
class GaussianMutation(CopyingOperator):
"""
Gaussian mutation operator.
Follows the algorithm description in:
Sean Luke, 2013, Essentials of Metaheuristics, Lulu, second edition
available for free at http://cs.gmu.edu/~sean/book/metaheuristics/
"""
def __init__(self, problem: Problem, *, stdev: float, mutation_probability: Optional[float] = None):
"""
`__init__(...)`: Initialize the GaussianMutation.
Args:
problem: The problem object to work with.
stdev: The standard deviation of the Gaussian noise to apply on
each decision variable.
mutation_probability: The probability of mutation, for each
decision variable.
If None, the value of this argument becomes 1.0, which means
that all of the decision variables will be affected by the
mutation. Defatuls to None
"""
super().__init__(problem)
self._mutation_probability = 1.0 if mutation_probability is None else float(mutation_probability)
self._stdev = float(stdev)
@torch.no_grad()
def _do(self, batch: SolutionBatch) > SolutionBatch:
result = deepcopy(batch)
data = result.access_values()
mutation_matrix = self.problem.make_uniform_shaped_like(data) <= self._mutation_probability
data[mutation_matrix] += self._stdev * self.problem.make_gaussian_shaped_like(data[mutation_matrix])
data[:] = self._respect_bounds(data)
return result
__init__(self, problem, *, stdev, mutation_probability=None)
special
¶
__init__(...)
: Initialize the GaussianMutation.
Parameters:
Name  Type  Description  Default 

problem 
Problem 
The problem object to work with. 
required 
stdev 
float 
The standard deviation of the Gaussian noise to apply on each decision variable. 
required 
mutation_probability 
Optional[float] 
The probability of mutation, for each decision variable. If None, the value of this argument becomes 1.0, which means that all of the decision variables will be affected by the mutation. Defatuls to None 
None 
Source code in evotorch/operators/real.py
def __init__(self, problem: Problem, *, stdev: float, mutation_probability: Optional[float] = None):
"""
`__init__(...)`: Initialize the GaussianMutation.
Args:
problem: The problem object to work with.
stdev: The standard deviation of the Gaussian noise to apply on
each decision variable.
mutation_probability: The probability of mutation, for each
decision variable.
If None, the value of this argument becomes 1.0, which means
that all of the decision variables will be affected by the
mutation. Defatuls to None
"""
super().__init__(problem)
self._mutation_probability = 1.0 if mutation_probability is None else float(mutation_probability)
self._stdev = float(stdev)
MultiPointCrossOver (CrossOver)
¶
Representation of a multipoint crossover operator.
When this operator is applied on a SolutionBatch, a tournament selection technique is used for selecting parent solutions from the batch, and then those parent solutions are mated via cutting from a random position and recombining. The result of these recombination operations is a new SolutionBatch, containing the children solutions. The original SolutionBatch stays unmodified.
This operator is a generalization over the standard crossover operators OnePointCrossOver and TwoPointCrossOver. In more details, instead of having one or two cutting points, this operator is configurable in terms of how many cutting points is desired. This generalized crossover implementation follows the procedure described in:
Sean Luke, 2013, Essentials of Metaheuristics, Lulu, second edition
available for free at http://cs.gmu.edu/~sean/book/metaheuristics/
Source code in evotorch/operators/real.py
class MultiPointCrossOver(CrossOver):
"""
Representation of a multipoint crossover operator.
When this operator is applied on a SolutionBatch, a tournament selection
technique is used for selecting parent solutions from the batch, and then
those parent solutions are mated via cutting from a random position and
recombining. The result of these recombination operations is a new
SolutionBatch, containing the children solutions. The original
SolutionBatch stays unmodified.
This operator is a generalization over the standard crossover operators
[OnePointCrossOver][evotorch.operators.real.OnePointCrossOver]
and [TwoPointCrossOver][evotorch.operators.real.TwoPointCrossOver].
In more details, instead of having one or two cutting points, this operator
is configurable in terms of how many cutting points is desired.
This generalized crossover implementation follows the procedure described
in:
Sean Luke, 2013, Essentials of Metaheuristics, Lulu, second edition
available for free at http://cs.gmu.edu/~sean/book/metaheuristics/
"""
def __init__(
self,
problem: Problem,
*,
tournament_size: int,
obj_index: Optional[int] = None,
num_points: Optional[int] = None,
num_children: Optional[int] = None,
cross_over_rate: Optional[float] = None,
):
"""
`__init__(...)`: Initialize the MultiPointCrossOver.
Args:
problem: The problem object to work on.
tournament_size: What is the size (or length) of a tournament
when selecting a parent candidate from a population
obj_index: Objective index according to which the selection
will be done.
num_points: Number of cutting points for the crossover operator.
num_children: Optionally a number of children to produce by the
crossover operation.
Not to be used together with `cross_over_rate`.
If `num_children` and `cross_over_rate` are both None,
then the number of children is equal to the number
of solutions received.
cross_over_rate: Optionally expected as a real number between
0.0 and 1.0. Specifies the number of crossover operations
to perform. 1.0 means `1.0 * len(solution_batch)` amount of
cross overs will be performed, resulting in
`2.0 * len(solution_batch)` amount of children.
Not to be used together with `num_children`.
If `num_children` and `cross_over_rate` are both None,
then the number of children is equal to the number
of solutions received.
"""
super().__init__(
problem,
tournament_size=tournament_size,
obj_index=obj_index,
num_children=num_children,
cross_over_rate=cross_over_rate,
)
self._num_points = int(num_points)
if self._num_points < 1:
raise ValueError(
f"Invalid `num_points`: {self._num_points}."
f" Please provide a `num_points` which is greater than or equal to 1"
)
@torch.no_grad()
def _do_cross_over(self, parents1: torch.Tensor, parents2: torch.Tensor) > SolutionBatch:
# What we expect here is this:
#
# parents1 parents2
# ========== ==========
# parents1[0] parents2[0]
# parents1[1] parents2[1]
# ... ...
# parents1[N] parents2[N]
#
# where parents1 and parents2 are 2D tensors, each containing values of N solutions.
# For each row i, we will apply crossover on parents1[i] and parents2[i].
# From each crossover, we will obtain 2 children.
# This means, there are N pairings, and 2N children.
num_pairings = parents1.shape[0]
# num_children = num_pairings * 2
device = parents1[0].device
solution_length = len(parents1[0])
num_points = self._num_points
# For each pairing, generate all gene indices (i.e. [0, 1, 2, ...] for each pairing)
gene_indices = (
torch.arange(0, solution_length, device=device).unsqueeze(0).expand(num_pairings, solution_length)
)
if num_points == 1:
# For each pairing, generate a gene index at which the parent solutions will be cut and recombined
crossover_point = self.problem.make_randint((num_pairings, 1), n=(solution_length  1), device=device) + 1
# Make a mask for crossing over
# (False: take the value from one parent, True: take the value from the other parent).
# For gene indices less than crossover_point of that pairing, the mask takes the value 0.
# Otherwise, the mask takes the value 1.
crossover_mask = gene_indices >= crossover_point
else:
# For each pairing, generate gene indices at which the parent solutions will be cut and recombined
crossover_points = self.problem.make_randint(
(num_pairings, num_points), n=(solution_length + 1), device=device
)
# From `crossover_points`, extract each cutting point for each solution.
cutting_points = [crossover_points[:, i].reshape(1, 1) for i in range(num_points)]
# Initialize `crossover_mask` as a tensor filled with False.
crossover_mask = torch.zeros((num_pairings, solution_length), dtype=torch.bool, device=device)
# For each cutting point p, toggle the boolean values of `crossover_mask`
# for indices bigger than the index pointed to by p
for p in cutting_points:
crossover_mask ^= gene_indices >= p
# Using the mask, generate two children.
children1 = torch.where(crossover_mask, parents1, parents2)
children2 = torch.where(crossover_mask, parents2, parents1)
# Combine the children tensors in one big tensor
children = torch.cat([children1, children2], dim=0)
# Write the children solutions into a new SolutionBatch, and return the new batch
result = self._make_children_batch(children)
return result
__init__(self, problem, *, tournament_size, obj_index=None, num_points=None, num_children=None, cross_over_rate=None)
special
¶
__init__(...)
: Initialize the MultiPointCrossOver.
Parameters:
Name  Type  Description  Default 

problem 
Problem 
The problem object to work on. 
required 
tournament_size 
int 
What is the size (or length) of a tournament when selecting a parent candidate from a population 
required 
obj_index 
Optional[int] 
Objective index according to which the selection will be done. 
None 
num_points 
Optional[int] 
Number of cutting points for the crossover operator. 
None 
num_children 
Optional[int] 
Optionally a number of children to produce by the
crossover operation.
Not to be used together with 
None 
cross_over_rate 
Optional[float] 
Optionally expected as a real number between
0.0 and 1.0. Specifies the number of crossover operations
to perform. 1.0 means 
None 
Source code in evotorch/operators/real.py
def __init__(
self,
problem: Problem,
*,
tournament_size: int,
obj_index: Optional[int] = None,
num_points: Optional[int] = None,
num_children: Optional[int] = None,
cross_over_rate: Optional[float] = None,
):
"""
`__init__(...)`: Initialize the MultiPointCrossOver.
Args:
problem: The problem object to work on.
tournament_size: What is the size (or length) of a tournament
when selecting a parent candidate from a population
obj_index: Objective index according to which the selection
will be done.
num_points: Number of cutting points for the crossover operator.
num_children: Optionally a number of children to produce by the
crossover operation.
Not to be used together with `cross_over_rate`.
If `num_children` and `cross_over_rate` are both None,
then the number of children is equal to the number
of solutions received.
cross_over_rate: Optionally expected as a real number between
0.0 and 1.0. Specifies the number of crossover operations
to perform. 1.0 means `1.0 * len(solution_batch)` amount of
cross overs will be performed, resulting in
`2.0 * len(solution_batch)` amount of children.
Not to be used together with `num_children`.
If `num_children` and `cross_over_rate` are both None,
then the number of children is equal to the number
of solutions received.
"""
super().__init__(
problem,
tournament_size=tournament_size,
obj_index=obj_index,
num_children=num_children,
cross_over_rate=cross_over_rate,
)
self._num_points = int(num_points)
if self._num_points < 1:
raise ValueError(
f"Invalid `num_points`: {self._num_points}."
f" Please provide a `num_points` which is greater than or equal to 1"
)
OnePointCrossOver (MultiPointCrossOver)
¶
Representation of a onepoint crossover operator.
When this operator is applied on a SolutionBatch, a tournament selection technique is used for selecting parent solutions from the batch, and then those parent solutions are mated via cutting from a random position and recombining. The result of these recombination operations is a new SolutionBatch, containing the children solutions. The original SolutionBatch stays unmodified.
Let us assume that the two of the parent solutions that were selected for the crossover operation are as follows:
For recombining parents a
and b
, a cutting point is first randomly
selected. In the case of this example, let us assume that the cutting
point was chosen as the point between the items with indices 2 and 3:
Considering this selected cutting point, the two children c
and d
will be constructed from a
and b
like this:
Note that the recombination procedure explained above is be done on all of the parents chosen from the given SolutionBatch, in a vectorized manner. For each chosen pair of parents, the cutting points will be sampled differently.
Source code in evotorch/operators/real.py
class OnePointCrossOver(MultiPointCrossOver):
"""
Representation of a onepoint crossover operator.
When this operator is applied on a SolutionBatch, a tournament selection
technique is used for selecting parent solutions from the batch, and then
those parent solutions are mated via cutting from a random position and
recombining. The result of these recombination operations is a new
SolutionBatch, containing the children solutions. The original
SolutionBatch stays unmodified.
Let us assume that the two of the parent solutions that were selected for
the crossover operation are as follows:
```
a: [ a0 , a1 , a2 , a3 , a4 , a5 ]
b: [ b0 , b1 , b2 , b3 , b4 , b5 ]
```
For recombining parents `a` and `b`, a cutting point is first randomly
selected. In the case of this example, let us assume that the cutting
point was chosen as the point between the items with indices 2 and 3:
```
a: [ a0 , a1 , a2  a3 , a4 , a5 ]
b: [ b0 , b1 , b2  b3 , b4 , b5 ]

^
Selected cutting point
```
Considering this selected cutting point, the two children `c` and `d`
will be constructed from `a` and `b` like this:
```
c: [ a0 , a1 , a2  b3 , b4 , b5 ]
d: [ b0 , b1 , b2  a3 , a4 , a5 ]
```
Note that the recombination procedure explained above is be done on all
of the parents chosen from the given SolutionBatch, in a vectorized manner.
For each chosen pair of parents, the cutting points will be sampled
differently.
"""
def __init__(
self,
problem: Problem,
*,
tournament_size: int,
obj_index: Optional[int] = None,
num_children: Optional[int] = None,
cross_over_rate: Optional[float] = None,
):
"""
`__init__(...)`: Initialize the OnePointCrossOver.
Args:
problem: The problem object to work on.
tournament_size: What is the size (or length) of a tournament
when selecting a parent candidate from a population
obj_index: Objective index according to which the selection
will be done.
num_children: Optionally a number of children to produce by the
crossover operation.
Not to be used together with `cross_over_rate`.
If `num_children` and `cross_over_rate` are both None,
then the number of children is equal to the number
of solutions received.
cross_over_rate: Optionally expected as a real number between
0.0 and 1.0. Specifies the number of crossover operations
to perform. 1.0 means `1.0 * len(solution_batch)` amount of
cross overs will be performed, resulting in
`2.0 * len(solution_batch)` amount of children.
Not to be used together with `num_children`.
If `num_children` and `cross_over_rate` are both None,
then the number of children is equal to the number
of solutions received.
"""
super().__init__(
problem,
tournament_size=tournament_size,
obj_index=obj_index,
num_points=1,
num_children=num_children,
cross_over_rate=cross_over_rate,
)
__init__(self, problem, *, tournament_size, obj_index=None, num_children=None, cross_over_rate=None)
special
¶
__init__(...)
: Initialize the OnePointCrossOver.
Parameters:
Name  Type  Description  Default 

problem 
Problem 
The problem object to work on. 
required 
tournament_size 
int 
What is the size (or length) of a tournament when selecting a parent candidate from a population 
required 
obj_index 
Optional[int] 
Objective index according to which the selection will be done. 
None 
num_children 
Optional[int] 
Optionally a number of children to produce by the
crossover operation.
Not to be used together with 
None 
cross_over_rate 
Optional[float] 
Optionally expected as a real number between
0.0 and 1.0. Specifies the number of crossover operations
to perform. 1.0 means 
None 
Source code in evotorch/operators/real.py
def __init__(
self,
problem: Problem,
*,
tournament_size: int,
obj_index: Optional[int] = None,
num_children: Optional[int] = None,
cross_over_rate: Optional[float] = None,
):
"""
`__init__(...)`: Initialize the OnePointCrossOver.
Args:
problem: The problem object to work on.
tournament_size: What is the size (or length) of a tournament
when selecting a parent candidate from a population
obj_index: Objective index according to which the selection
will be done.
num_children: Optionally a number of children to produce by the
crossover operation.
Not to be used together with `cross_over_rate`.
If `num_children` and `cross_over_rate` are both None,
then the number of children is equal to the number
of solutions received.
cross_over_rate: Optionally expected as a real number between
0.0 and 1.0. Specifies the number of crossover operations
to perform. 1.0 means `1.0 * len(solution_batch)` amount of
cross overs will be performed, resulting in
`2.0 * len(solution_batch)` amount of children.
Not to be used together with `num_children`.
If `num_children` and `cross_over_rate` are both None,
then the number of children is equal to the number
of solutions received.
"""
super().__init__(
problem,
tournament_size=tournament_size,
obj_index=obj_index,
num_points=1,
num_children=num_children,
cross_over_rate=cross_over_rate,
)
PolynomialMutation (CopyingOperator)
¶
Representation of the polynomial mutation operator.
Follows the algorithm description in:
Kalyanmoy Deb, Santosh Tiwari (2008).
Omnioptimizer: A generic evolutionary algorithm for single
and multiobjective optimization
The operator ensures a nonzero probability of generating offspring in the entire search space by dividing the space into two regions and using independent probability distributions associated with each region. In contrast, the original polynomial mutation formulation may render the mutation ineffective when the decision variable approaches its boundary.
Source code in evotorch/operators/real.py
class PolynomialMutation(CopyingOperator):
"""
Representation of the polynomial mutation operator.
Follows the algorithm description in:
Kalyanmoy Deb, Santosh Tiwari (2008).
Omnioptimizer: A generic evolutionary algorithm for single
and multiobjective optimization
The operator ensures a nonzero probability of generating offspring in
the entire search space by dividing the space into two regions and using
independent probability distributions associated with each region.
In contrast, the original polynomial mutation formulation may render the
mutation ineffective when the decision variable approaches its boundary.
"""
def __init__(
self,
problem: Problem,
*,
eta: Optional[float] = None,
mutation_probability: Optional[float] = None,
):
"""
`__init__(...)`: Initialize the PolynomialMutation.
Args:
problem: The problem object to work with.
eta: The index for polynomial mutation; a large value gives a higher
probability for creating nearparent solutions, whereas a small
value allows distant solutions to be created.
If not specified, `eta` will be assumed as 20.0.
mutation_probability: The probability of mutation, for each decision
variable. If not specified, all variables will be mutated.
"""
super().__init__(problem)
if "float" not in str(problem.dtype):
raise ValueError(
f"This operator can be used only when `dtype` of the problem is float type"
f" (like, e.g. torch.float32, torch.float64, etc.)"
f" The dtype of the problem is {problem.dtype}."
)
if (self.problem.lower_bounds is None) or (self.problem.upper_bounds is None):
raise ValueError(
"The polynomial mutation operator can be used only when the problem object has"
" `lower_bounds` and `upper_bounds`."
" In the given problem object, at least one of them appears to be missing."
)
if torch.any(self.problem.lower_bounds > self.problem.upper_bounds):
raise ValueError("Some of the `lower_bounds` appear greater than their `upper_bounds`")
self._prob = None if mutation_probability is None else float(mutation_probability)
self._eta = 20.0 if eta is None else float(eta)
self._lb = self.problem.lower_bounds
self._ub = self.problem.upper_bounds
@torch.no_grad()
def _do(self, batch: SolutionBatch) > SolutionBatch:
# Take a copy of the original batch. Modifications will be done on this copy.
result = deepcopy(batch)
# Take the decision values tensor from within the newly made copy of the batch (`result`).
# Any modification done on this tensor will affect the `result` batch.
data = result.access_values()
# Take the population size
pop_size, solution_length = data.size()
if self._prob is None:
# If a probability of mutation is not given, then we prepare our mutation mask (`to_mutate`) as a tensor
# consisting only of `True`s.
to_mutate = torch.ones(data.shape, dtype=torch.bool, device=data.device)
else:
# If a probability of mutation is given, then we produce a boolean mask that probabilistically marks which
# decision variables will be affected by this mutation operation.
to_mutate = self.problem.make_uniform_shaped_like(data) < self._prob
# Obtain a flattened (1dimensional) tensor which addresses only the variables that are subject to mutation
# (i.e. variables that are not subject to mutation are filtered out).
selected = data[to_mutate]
# Obtain flattened (1dimensional) lower and upper bound tensors such that `lb[i]` and `ub[i]` specify the
# bounds for `selected[i]`.
lb = self._lb.expand(pop_size, solution_length)[to_mutate]
ub = self._ub.expand(pop_size, solution_length)[to_mutate]
# Apply the mutation procedure explained by Deb & Tiwari (2008).
delta_1 = (selected  lb) / (ub  lb)
delta_2 = (ub  selected) / (ub  lb)
r = self.problem.make_uniform(selected.size())
mask = r < 0.5
mask_not = torch.logical_not(mask)
mut_str = 1.0 / (self._eta + 1.0)
delta_q = torch.zeros_like(selected)
v = 2.0 * r + (1.0  2.0 * r) * (1.0  delta_1).pow(self._eta + 1.0)
d = v.pow(mut_str)  1.0
delta_q[mask] = d[mask]
v = 2.0 * (1.0  r) + 2.0 * (r  0.5) * (1.0  delta_2).pow(self._eta + 1.0)
d = 1.0  v.pow(mut_str)
delta_q[mask_not] = d[mask_not]
mutated = selected + delta_q * (ub  lb)
# Put the mutated decision values into the decision variables tensor stored within the `result` batch.
data[to_mutate] = mutated
# Prevent violations that could happen because of numerical errors.
data[:] = self._respect_bounds(data)
# Return the `result` batch.
return result
__init__(self, problem, *, eta=None, mutation_probability=None)
special
¶
__init__(...)
: Initialize the PolynomialMutation.
Parameters:
Name  Type  Description  Default 

problem 
Problem 
The problem object to work with. 
required 
eta 
Optional[float] 
The index for polynomial mutation; a large value gives a higher
probability for creating nearparent solutions, whereas a small
value allows distant solutions to be created.
If not specified, 
None 
mutation_probability 
Optional[float] 
The probability of mutation, for each decision variable. If not specified, all variables will be mutated. 
None 
Source code in evotorch/operators/real.py
def __init__(
self,
problem: Problem,
*,
eta: Optional[float] = None,
mutation_probability: Optional[float] = None,
):
"""
`__init__(...)`: Initialize the PolynomialMutation.
Args:
problem: The problem object to work with.
eta: The index for polynomial mutation; a large value gives a higher
probability for creating nearparent solutions, whereas a small
value allows distant solutions to be created.
If not specified, `eta` will be assumed as 20.0.
mutation_probability: The probability of mutation, for each decision
variable. If not specified, all variables will be mutated.
"""
super().__init__(problem)
if "float" not in str(problem.dtype):
raise ValueError(
f"This operator can be used only when `dtype` of the problem is float type"
f" (like, e.g. torch.float32, torch.float64, etc.)"
f" The dtype of the problem is {problem.dtype}."
)
if (self.problem.lower_bounds is None) or (self.problem.upper_bounds is None):
raise ValueError(
"The polynomial mutation operator can be used only when the problem object has"
" `lower_bounds` and `upper_bounds`."
" In the given problem object, at least one of them appears to be missing."
)
if torch.any(self.problem.lower_bounds > self.problem.upper_bounds):
raise ValueError("Some of the `lower_bounds` appear greater than their `upper_bounds`")
self._prob = None if mutation_probability is None else float(mutation_probability)
self._eta = 20.0 if eta is None else float(eta)
self._lb = self.problem.lower_bounds
self._ub = self.problem.upper_bounds
SimulatedBinaryCrossOver (CrossOver)
¶
Representation of a simulated binary crossover (SBX).
When this operator is applied on a SolutionBatch, a tournament selection technique is used for selecting parent solutions from the batch, and then those parent solutions are mated via SBX. The generated children solutions are given in a new SolutionBatch. The original SolutionBatch stays unmodified.
Reference:
Kalyanmoy Deb, HansGeorg Beyer (2001).
SelfAdaptive Genetic Algorithms with Simulated Binary Crossover.
Source code in evotorch/operators/real.py
class SimulatedBinaryCrossOver(CrossOver):
"""
Representation of a simulated binary crossover (SBX).
When this operator is applied on a SolutionBatch,
a tournament selection technique is used for selecting
parent solutions from the batch, and then those parent
solutions are mated via SBX. The generated children
solutions are given in a new SolutionBatch.
The original SolutionBatch stays unmodified.
Reference:
Kalyanmoy Deb, HansGeorg Beyer (2001).
SelfAdaptive Genetic Algorithms with Simulated Binary Crossover.
"""
def __init__(
self,
problem: Problem,
*,
tournament_size: int,
eta: float,
obj_index: Optional[int] = None,
num_children: Optional[int] = None,
cross_over_rate: Optional[float] = None,
):
"""
`__init__(...)`: Initialize the SimulatedBinaryCrossOver.
Args:
problem: Problem object to work with.
tournament_size: What is the size (or length) of a tournament
when selecting a parent candidate from a population.
eta: The crowding index, expected as a float.
Bigger eta values result in children closer
to their parents.
obj_index: Objective index according to which the selection
will be done.
num_children: Optionally a number of children to produce by the
crossover operation.
Not to be used together with `cross_over_rate`.
If `num_children` and `cross_over_rate` are both None,
then the number of children is equal to the number
of solutions received.
cross_over_rate: Optionally expected as a real number between
0.0 and 1.0. Specifies the number of crossover operations
to perform. 1.0 means `1.0 * len(solution_batch)` amount of
cross overs will be performed, resulting in
`2.0 * len(solution_batch)` amount of children.
Not to be used together with `num_children`.
If `num_children` and `cross_over_rate` are both None,
then the number of children is equal to the number
of solutions received.
"""
super().__init__(
problem,
tournament_size=int(tournament_size),
obj_index=obj_index,
num_children=num_children,
cross_over_rate=cross_over_rate,
)
self._eta = float(eta)
def _do_cross_over(self, parents1: torch.Tensor, parents2: torch.Tensor) > SolutionBatch:
# Generate u_i values which determine the spread
u = self.problem.make_uniform_shaped_like(parents1)
# Compute beta_i values from u_i values as the actual spread per dimension
betas = (2 * u).pow(1.0 / (self._eta + 1.0)) # Compute all values for u_i < 0.5 first
betas[u > 0.5] = (1.0 / (2 * (1.0  u[u > 0.5]))).pow(
1.0 / (self._eta + 1.0)
) # Replace the values for u_i >= 0.5
children1 = 0.5 * (
(1 + betas) * parents1 + (1  betas) * parents2
) # Create the first set of children from the beta values
children2 = 0.5 * (
(1 + betas) * parents2 + (1  betas) * parents1
) # Create the second set of children as a mirror of the first set of children
# Combine the children tensors in one big tensor
children = torch.cat([children1, children2], dim=0)
# Respect the lower and upper bounds defined by the problem object
children = self._respect_bounds(children)
# Write the children solutions into a new SolutionBatch, and return the new batch
result = self._make_children_batch(children)
return result
__init__(self, problem, *, tournament_size, eta, obj_index=None, num_children=None, cross_over_rate=None)
special
¶
__init__(...)
: Initialize the SimulatedBinaryCrossOver.
Parameters:
Name  Type  Description  Default 

problem 
Problem 
Problem object to work with. 
required 
tournament_size 
int 
What is the size (or length) of a tournament when selecting a parent candidate from a population. 
required 
eta 
float 
The crowding index, expected as a float. Bigger eta values result in children closer to their parents. 
required 
obj_index 
Optional[int] 
Objective index according to which the selection will be done. 
None 
num_children 
Optional[int] 
Optionally a number of children to produce by the
crossover operation.
Not to be used together with 
None 
cross_over_rate 
Optional[float] 
Optionally expected as a real number between
0.0 and 1.0. Specifies the number of crossover operations
to perform. 1.0 means 
None 
Source code in evotorch/operators/real.py
def __init__(
self,
problem: Problem,
*,
tournament_size: int,
eta: float,
obj_index: Optional[int] = None,
num_children: Optional[int] = None,
cross_over_rate: Optional[float] = None,
):
"""
`__init__(...)`: Initialize the SimulatedBinaryCrossOver.
Args:
problem: Problem object to work with.
tournament_size: What is the size (or length) of a tournament
when selecting a parent candidate from a population.
eta: The crowding index, expected as a float.
Bigger eta values result in children closer
to their parents.
obj_index: Objective index according to which the selection
will be done.
num_children: Optionally a number of children to produce by the
crossover operation.
Not to be used together with `cross_over_rate`.
If `num_children` and `cross_over_rate` are both None,
then the number of children is equal to the number
of solutions received.
cross_over_rate: Optionally expected as a real number between
0.0 and 1.0. Specifies the number of crossover operations
to perform. 1.0 means `1.0 * len(solution_batch)` amount of
cross overs will be performed, resulting in
`2.0 * len(solution_batch)` amount of children.
Not to be used together with `num_children`.
If `num_children` and `cross_over_rate` are both None,
then the number of children is equal to the number
of solutions received.
"""
super().__init__(
problem,
tournament_size=int(tournament_size),
obj_index=obj_index,
num_children=num_children,
cross_over_rate=cross_over_rate,
)
self._eta = float(eta)
TwoPointCrossOver (MultiPointCrossOver)
¶
Representation of a twopoint crossover operator.
When this operator is applied on a SolutionBatch, a tournament selection technique is used for selecting parent solutions from the batch, and then those parent solutions are mated via cutting from a random position and recombining. The result of these recombination operations is a new SolutionBatch, containing the children solutions. The original SolutionBatch stays unmodified.
Let us assume that the two of the parent solutions that were selected for the crossover operation are as follows:
For recombining parents a
and b
, two cutting points are first randomly
selected. In the case of this example, let us assume that the cutting
point were chosen as the point between the items with indices 1 and 2,
and between 3 and 4:
a: [ a0 , a1  a2 , a3  a4 , a5 ]
b: [ b0 , b1  b2 , b3  b4 , b5 ]
 
^ ^
First Second
cutting cutting
point point
Given these two cutting points, the two children c
and d
will be
constructed from a
and b
like this:
Note that the recombination procedure explained above is be done on all of the parents chosen from the given SolutionBatch, in a vectorized manner. For each chosen pair of parents, the cutting points will be sampled differently.
Source code in evotorch/operators/real.py
class TwoPointCrossOver(MultiPointCrossOver):
"""
Representation of a twopoint crossover operator.
When this operator is applied on a SolutionBatch, a tournament selection
technique is used for selecting parent solutions from the batch, and then
those parent solutions are mated via cutting from a random position and
recombining. The result of these recombination operations is a new
SolutionBatch, containing the children solutions. The original
SolutionBatch stays unmodified.
Let us assume that the two of the parent solutions that were selected for
the crossover operation are as follows:
```
a: [ a0 , a1 , a2 , a3 , a4 , a5 ]
b: [ b0 , b1 , b2 , b3 , b4 , b5 ]
```
For recombining parents `a` and `b`, two cutting points are first randomly
selected. In the case of this example, let us assume that the cutting
point were chosen as the point between the items with indices 1 and 2,
and between 3 and 4:
```
a: [ a0 , a1  a2 , a3  a4 , a5 ]
b: [ b0 , b1  b2 , b3  b4 , b5 ]
 
^ ^
First Second
cutting cutting
point point
```
Given these two cutting points, the two children `c` and `d` will be
constructed from `a` and `b` like this:
```
c: [ a0 , a1  b2 , b3  a4 , a5 ]
d: [ b0 , b1  a2 , a3  b4 , b5 ]
```
Note that the recombination procedure explained above is be done on all
of the parents chosen from the given SolutionBatch, in a vectorized manner.
For each chosen pair of parents, the cutting points will be sampled
differently.
"""
def __init__(
self,
problem: Problem,
*,
tournament_size: int,
obj_index: Optional[int] = None,
num_children: Optional[int] = None,
cross_over_rate: Optional[float] = None,
):
"""
`__init__(...)`: Initialize the TwoPointCrossOver.
Args:
problem: The problem object to work on.
tournament_size: What is the size (or length) of a tournament
when selecting a parent candidate from a population
obj_index: Objective index according to which the selection
will be done.
num_children: Optionally a number of children to produce by the
crossover operation.
Not to be used together with `cross_over_rate`.
If `num_children` and `cross_over_rate` are both None,
then the number of children is equal to the number
of solutions received.
cross_over_rate: Optionally expected as a real number between
0.0 and 1.0. Specifies the number of crossover operations
to perform. 1.0 means `1.0 * len(solution_batch)` amount of
cross overs will be performed, resulting in
`2.0 * len(solution_batch)` amount of children.
Not to be used together with `num_children`.
If `num_children` and `cross_over_rate` are both None,
then the number of children is equal to the number
of solutions received.
"""
super().__init__(
problem,
tournament_size=tournament_size,
obj_index=obj_index,
num_points=2,
num_children=num_children,
cross_over_rate=cross_over_rate,
)
__init__(self, problem, *, tournament_size, obj_index=None, num_children=None, cross_over_rate=None)
special
¶
__init__(...)
: Initialize the TwoPointCrossOver.
Parameters:
Name  Type  Description  Default 

problem 
Problem 
The problem object to work on. 
required 
tournament_size 
int 
What is the size (or length) of a tournament when selecting a parent candidate from a population 
required 
obj_index 
Optional[int] 
Objective index according to which the selection will be done. 
None 
num_children 
Optional[int] 
Optionally a number of children to produce by the
crossover operation.
Not to be used together with 
None 
cross_over_rate 
Optional[float] 
Optionally expected as a real number between
0.0 and 1.0. Specifies the number of crossover operations
to perform. 1.0 means 
None 
Source code in evotorch/operators/real.py
def __init__(
self,
problem: Problem,
*,
tournament_size: int,
obj_index: Optional[int] = None,
num_children: Optional[int] = None,
cross_over_rate: Optional[float] = None,
):
"""
`__init__(...)`: Initialize the TwoPointCrossOver.
Args:
problem: The problem object to work on.
tournament_size: What is the size (or length) of a tournament
when selecting a parent candidate from a population
obj_index: Objective index according to which the selection
will be done.
num_children: Optionally a number of children to produce by the
crossover operation.
Not to be used together with `cross_over_rate`.
If `num_children` and `cross_over_rate` are both None,
then the number of children is equal to the number
of solutions received.
cross_over_rate: Optionally expected as a real number between
0.0 and 1.0. Specifies the number of crossover operations
to perform. 1.0 means `1.0 * len(solution_batch)` amount of
cross overs will be performed, resulting in
`2.0 * len(solution_batch)` amount of children.
Not to be used together with `num_children`.
If `num_children` and `cross_over_rate` are both None,
then the number of children is equal to the number
of solutions received.
"""
super().__init__(
problem,
tournament_size=tournament_size,
obj_index=obj_index,
num_points=2,
num_children=num_children,
cross_over_rate=cross_over_rate,
)