Algorithms

pymoode.algorithms

class pymoode.algorithms.DE(pop_size=100, variant='DE/rand/1/bin', CR=0.7, F=(0.5, 1.0), gamma=0.0001, de_repair='bounce-back', survival=<pymoode.survival.replacement.ImprovementReplacement object>, **kwargs)

Bases: DifferentialEvolution

Single-objective Differential Evolution proposed by Storn and Price (1997).

Storn, R. & Price, K., 1997. Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Optim., 11(4), pp. 341-359.

Parameters:
pop_sizeint, optional

Population size. Defaults to 100.

variantstr, optional

Differential evolution strategy. Must be a string in the format: “DE/selection/n/crossover”, in which, n in an integer of number of difference vectors, and crossover is either ‘bin’ or ‘exp’. Selection variants are:

  • ‘ranked’

  • ‘rand’

  • ‘best’

  • ‘current-to-best’

  • ‘current-to-best’

  • ‘current-to-rand’

  • ‘rand-to-best’

The selection strategy ‘ranked’ might be helpful to improve convergence speed without much harm to diversity. Defaults to ‘DE/rand/1/bin’.

CRfloat, optional

Crossover parameter. Defined in the range [0, 1] To reinforce mutation, use higher values. To control convergence speed, use lower values.

Fiterable of float or float, optional

Scale factor or mutation parameter. Defined in the range (0, 2] To reinforce exploration, use higher values; for exploitation, use lower values.

gammafloat, optional

Jitter deviation parameter. Should be in the range (0, 2). Defaults to 1e-4.

de_repairstr, optional

Repair of DE mutant vectors. Is either callable or one of:

  • ‘bounce-back’

  • ‘midway’

  • ‘rand-init’

  • ‘to-bounds’

If callable, has the form fun(X, Xb, xl, xu) in which X contains mutated vectors including violations, Xb contains reference vectors for repair in feasible space, xl is a 1d vector of lower bounds, and xu a 1d vector of upper bounds. Defaults to ‘bounce-back’.

genetic_mutation, optional

Pymoo’s genetic mutation operator after crossover. Defaults to NoMutation().

survivalSurvival, optional

Replacement survival operator. Defaults to ImprovementReplacement().

repairRepair, optional

Pymoo’s repair operator after mutation. Defaults to NoRepair().

class pymoode.algorithms.GDE3(pop_size=100, variant='DE/rand/1/bin', CR=0.5, F=None, gamma=0.0001, de_repair='bounce-back', survival=<pymoode.survival.rank_and_crowding.rnc.RankAndCrowding object>, **kwargs)

Bases: MODE

GDE3 is an extension of DE to multi-objective problems using a mixed type survival strategy. It is implemented in this version with the same constraint handling strategy of NSGA-II by default.

Derived algorithms GDE3-MNN and GDE3-2NN use by default survival RankAndCrowding with metrics ‘mnn’ and ‘2nn’.

For many-objective problems, try using NSDE-R, GDE3-MNN, or GDE3-2NN.

For Bi-objective problems, survival = RankAndCrowding(crowding_func=’pcd’) is very effective.

Kukkonen, S. & Lampinen, J., 2005. GDE3: The third evolution step of generalized differential evolution. 2005 IEEE congress on evolutionary computation, Volume 1, pp. 443-450.

Parameters:
pop_sizeint, optional

Population size. Defaults to 100.

variantstr, optional

Differential evolution strategy. Must be a string in the format: “DE/selection/n/crossover”, in which, n in an integer of number of difference vectors, and crossover is either ‘bin’ or ‘exp’. Selection variants are:

  • ‘ranked’

  • ‘rand’

  • ‘best’

  • ‘current-to-best’

  • ‘current-to-best’

  • ‘current-to-rand’

  • ‘rand-to-best’

The selection strategy ‘ranked’ might be helpful to improve convergence speed without much harm to diversity. Defaults to ‘DE/rand/1/bin’.

CRfloat, optional

Crossover parameter. Defined in the range [0, 1] To reinforce mutation, use higher values. To control convergence speed, use lower values.

Fiterable of float or float, optional

Scale factor or mutation parameter. Defined in the range (0, 2] To reinforce exploration, use higher values; for exploitation, use lower values.

gammafloat, optional

Jitter deviation parameter. Should be in the range (0, 2). Defaults to 1e-4.

de_repairstr, optional

Repair of DE mutant vectors. Is either callable or one of:

  • ‘bounce-back’

  • ‘midway’

  • ‘rand-init’

  • ‘to-bounds’

If callable, has the form fun(X, Xb, xl, xu) in which X contains mutated vectors including violations, Xb contains reference vectors for repair in feasible space, xl is a 1d vector of lower bounds, and xu a 1d vector of upper bounds. Defaults to ‘bounce-back’.

genetic_mutation, optional

Pymoo’s genetic mutation operator after crossover. Defaults to NoMutation().

repairRepair, optional

Pymoo’s repair operator after mutation. Defaults to NoRepair().

survivalSurvival, optional

Pymoo’s survival strategy. Defaults to RankAndCrowding() with crowding distances (‘cd’). In GDE3, the survival strategy is applied after a one-to-one comparison between child vector and corresponding parent when both are non-dominated by the other.

class pymoode.algorithms.NSDE(pop_size=100, variant='DE/rand/1/bin', CR=0.7, F=None, gamma=0.0001, de_repair='bounce-back', survival=<pymoode.survival.rank_and_crowding.rnc.RankAndCrowding object>, **kwargs)

Bases: MODE

NSDE is an algorithm that combines that combines NSGA-II sorting and survival strategies to DE mutation and crossover.

For many-objective problems, try using NSDE-R, GDE3-MNN, or GDE3-2NN.

For Bi-objective problems, survival = RankAndCrowding(crowding_func=’pcd’) is very effective.

Parameters:
pop_sizeint, optional

Population size. Defaults to 100.

samplingSampling, optional

Sampling strategy of pymoo. Defaults to LHS().

variantstr, optional

Differential evolution strategy. Must be a string in the format: “DE/selection/n/crossover”, in which, n in an integer of number of difference vectors, and crossover is either ‘bin’ or ‘exp’. Selection variants are:

  • “ranked’

  • ‘rand’

  • ‘best’

  • ‘current-to-best’

  • ‘current-to-best’

  • ‘current-to-rand’

  • ‘rand-to-best’

The selection strategy ‘ranked’ might be helpful to improve convergence speed without much harm to diversity. Defaults to ‘DE/rand/1/bin’.

CRfloat, optional

Crossover parameter. Defined in the range [0, 1] To reinforce mutation, use higher values. To control convergence speed, use lower values.

Fiterable of float or float, optional

Scale factor or mutation parameter. Defined in the range (0, 2] To reinforce exploration, use higher values; for exploitation, use lower values.

gammafloat, optional

Jitter deviation parameter. Should be in the range (0, 2). Defaults to 1e-4.

de_repairstr, optional

Repair of DE mutant vectors. Is either callable or one of:

  • ‘bounce-back’

  • ‘midway’

  • ‘rand-init’

  • ‘to-bounds’

If callable, has the form fun(X, Xb, xl, xu) in which X contains mutated vectors including violations, Xb contains reference vectors for repair in feasible space, xl is a 1d vector of lower bounds, and xu a 1d vector of upper bounds. Defaults to ‘bounce-back’.

genetic_mutation, optional

Pymoo’s genetic mutation operator after crossover. Defaults to NoMutation().

repairRepair, optional

Pymoo’s repair operator after mutation. Defaults to NoRepair().

survivalSurvival, optional

Pymoo’s survival strategy. Defaults to RankAndCrowding() with crowding distances (‘cd’). In GDE3, the survival strategy is applied after a one-to-one comparison between child vector and corresponding parent when both are non-dominated by the other.

class pymoode.algorithms.NSDER(ref_dirs, pop_size=100, variant='DE/rand/1/bin', CR=0.7, F=None, gamma=0.0001, **kwargs)

Bases: NSDE

NSDE-R is an extension of NSDE to many-objective problems (Reddy & Dulikravich, 2019) using NSGA-III survival.

    1. Reddy and G. S. Dulikravich, “Many-objective differential evolution optimization based on reference points: NSDE-R,” Struct. Multidisc. Optim., vol. 60, pp. 1455-1473, 2019.

Parameters:
ref_dirsarray like

The reference directions that should be used during the optimization.

pop_sizeint, optional

Population size. Defaults to 100.

samplingSampling, optional

Sampling strategy of pymoo. Defaults to LHS().

variantstr, optional

Differential evolution strategy. Must be a string in the format: “DE/selection/n/crossover”, in which, n in an integer of number of difference vectors, and crossover is either ‘bin’ or ‘exp’. Selection variants are:

  • “ranked’

  • ‘rand’

  • ‘best’

  • ‘current-to-best’

  • ‘current-to-best’

  • ‘current-to-rand’

  • ‘rand-to-best’

The selection strategy ‘ranked’ might be helpful to improve convergence speed without much harm to diversity. Defaults to ‘DE/rand/1/bin’.

CRfloat, optional

Crossover parameter. Defined in the range [0, 1] To reinforce mutation, use higher values. To control convergence speed, use lower values.

Fiterable of float or float, optional

Scale factor or mutation parameter. Defined in the range (0, 2] To reinforce exploration, use higher values; for exploitation, use lower values.

gammafloat, optional

Jitter deviation parameter. Should be in the range (0, 2). Defaults to 1e-4.

de_repairstr, optional

Repair of DE mutant vectors. Is either callable or one of:

  • ‘bounce-back’

  • ‘midway’

  • ‘rand-init’

  • ‘to-bounds’

If callable, has the form fun(X, Xb, xl, xu) in which X contains mutated vectors including violations, Xb contains reference vectors for repair in feasible space, xl is a 1d vector of lower bounds, and xu a 1d vector of upper bounds. Defaults to ‘bounce-back’.

genetic_mutation, optional

Pymoo’s genetic mutation operator after crossover. Defaults to NoMutation().

repairRepair, optional

Pymoo’s repair operator after mutation. Defaults to NoRepair().

survivalSurvival, optional

Pymoo’s survival strategy. Defaults to ReferenceDirectionSurvival().

pymoode.algorithms.base

class pymoode.algorithms.base.evolutionary.EvolutionaryAlgorithm(pop_size: int | None = None, sampling: Sampling | None = None, mating: Mating | None = None, survival: Survival | None = None, n_offsprings: int | None = None, eliminate_duplicates: bool = True, repair: Repair | None = None, advance_after_initial_infill: bool = False, **kwargs)

Base class for Evolutionary Algorithms

Parameters:
pop_sizeint, optional

Population size, by default None

samplingSampling, optional

pymoo Sampling instance, by default None

matingInfillCriterion, optional

pymoo mating operator, by default None

survivalSurvival, optional

pymoo survival operator, by default None

n_offspringsint, optional

Number of offspring individuals created at each generation, by default None

eliminate_duplicatesDuplicateElimination | bool | None, optional

Eliminate duplicates in mating, by default True

repairRepair, optional

pymoo repair operator. In the algorithm level it should be called when sampling. It is recommended that mating operators also have some repair associated with. By default None

advance_after_initial_infillbool, optional

Either or not apply survival after initialization, by default False

Attributes:
n_gen

Methods

advance

ask

finalize

has_next

infill

next

result

run

setup

tell
class pymoode.algorithms.base.genetic.GeneticAlgorithm(pop_size=None, sampling=None, selection=None, crossover=None, mutation=None, survival=None, n_offsprings=None, eliminate_duplicates=True, repair=None, **kwargs)

Base class for Genetic Algorithms. A Mating operator is instantiated using selection, crossover, mutation, repair, and eliminate_duplicates arguments.

Parameters:
pop_sizeint, optional

Population size, by default None

samplingSampling, optional

pymoo Sampling instance, by default None

selectionSelection, optional

pymoo parent selection operator, by default None

crossoverCrossover, optional

pymoo crossover operator, by default None

genetic_mutation, optional

pymoo mutation operator, by default None

survivalSurvival, optional

pymoo survival operator, by default None

n_offspringsint, optional

Number of offspring individuals created at each generation, by default None

eliminate_duplicatesDuplicateElimination | bool | None, optional

Eliminate duplicates in mating, by default True

repairRepair, optional

pymoo repair operator which should be passed to Mating and self. By default None

advance_after_initial_infillbool, optional

Either or not apply survival after initialization, by default False

Attributes:
n_gen

Methods

advance

ask

finalize

has_next

infill

next

result

run

setup

tell