# Algorithms¶

pymoo.algorithms.so_genetic_algorithm.ga(pop_size=100, sampling=RandomSampling(), selection=TournamentSelection(func_comp=comp_by_cv_and_fitness), crossover=SimulatedBinaryCrossover(prob=0.9, eta=3), mutation=PolynomialMutation(prob=None, eta=5), eliminate_duplicates=True, n_offsprings=None, **kwargs)
Parameters
pop_sizeint

The population sized used by the algorithm.

sampling

The sampling process defines the initial set of solutions which are the starting point of the optimization algorithm. Here, you have three different options by passing

(i) A Sampling implementation which is an implementation of a random sampling method.

(ii) A Population object containing the variables to be evaluated initially OR already evaluated solutions (F needs to be set in this case).

(iii) Pass a two dimensional numpy.array with (n_individuals, n_var) which contains the variable space values for each individual.

selectionSelection

This object defines the mating selection to be used. In an evolutionary algorithm each generation parents need to be selected to produce new offsprings using different recombination and mutation operators. Different strategies for selecting parents are possible e.g. selecting them just randomly, only in the neighbourhood, using a tournament selection to introduce some seletion pressure, …

crossoverCrossover

The crossover has the purpose of create offsprings during the evolution. After the mating selection the parents are passed to the crossover operator which will dependent on the implementation create a different number of offsprings.

mutationMutation

Some genetic algorithms rely only on the mutation operation. However, it has shown that increases the performance to perform a mutation after creating the offsprings through crossover as well. Usually the mutation operator needs to be initialized with a probability to be executed. Having a high probability of mutation will most of the time increase the diversity in the population.

eliminate_duplicatesbool

The genetic algorithm implementation has a built in feature that eliminates duplicates after merging the parent and the offspring population. If there are duplicates with respect to the current population or in the offsprings itself they are removed and the mating process is repeated to fill up the offsprings until the desired number of unique offsprings is met.

n_offspringsint (default: None)

Number of offspring that are created through mating. By default n_offsprings=None which sets the number of offsprings equal to the population size. By setting n_offsprings=1 a, so called, steady-state version of an algorithm can be achieved.

Returns
gaAlgorithm

Returns an SingleObjectiveGeneticAlgorithm algorithm object.

pymoo.algorithms.so_de.de(pop_size=100, sampling=LatinHypercubeSampling(iterations=100, criterion="maxmin"), variant="DE/rand/1/bin", CR=0.5, F=0.3, dither="vector", jitter=False, **kwargs)
Parameters
pop_sizeint

The population sized used by the algorithm.

sampling

The sampling process defines the initial set of solutions which are the starting point of the optimization algorithm. Here, you have three different options by passing

(i) A Sampling implementation which is an implementation of a random sampling method.

(ii) A Population object containing the variables to be evaluated initially OR already evaluated solutions (F needs to be set in this case).

(iii) Pass a two dimensional numpy.array with (n_individuals, n_var) which contains the variable space values for each individual.

variant{DE/(rand|best)/1/(bin/exp)}

The different variants of DE to be used. DE/x/y/z where x how to select individuals to be pertubed, y the number of difference vector to be used and z the crossover type. One of the most common variant is DE/rand/1/bin.

Ffloat

The weight to be used during the crossover.

CRfloat

The probability the individual exchanges variable values from the donor vector.

dither{‘no’, ‘scalar’, ‘vector’}

One strategy to introduce adaptive weights (F) during one run. The option allows the same dither to be used in one iteration (‘scalar’) or a different one for each individual (‘vector).

jitterbool

Another strategy for adaptive weights (F). Here, only a very small value is added or substracted to the weight used for the crossover for each individual.

Returns
deAlgorithm

Returns an DifferentialEvolution algorithm object.

pymoo.algorithms.nsga2.nsga2(pop_size=100, sampling=RandomSampling(), selection=TournamentSelection(func_comp=binary_tournament), crossover=SimulatedBinaryCrossover(prob=0.9, eta=15), mutation=PolynomialMutation(prob=None, eta=20), eliminate_duplicates=True, n_offsprings=None, **kwargs)
Parameters
pop_sizeint

The population sized used by the algorithm.

sampling

The sampling process defines the initial set of solutions which are the starting point of the optimization algorithm. Here, you have three different options by passing

(i) A Sampling implementation which is an implementation of a random sampling method.

(ii) A Population object containing the variables to be evaluated initially OR already evaluated solutions (F needs to be set in this case).

(iii) Pass a two dimensional numpy.array with (n_individuals, n_var) which contains the variable space values for each individual.

selectionSelection

This object defines the mating selection to be used. In an evolutionary algorithm each generation parents need to be selected to produce new offsprings using different recombination and mutation operators. Different strategies for selecting parents are possible e.g. selecting them just randomly, only in the neighbourhood, using a tournament selection to introduce some seletion pressure, …

crossoverCrossover

The crossover has the purpose of create offsprings during the evolution. After the mating selection the parents are passed to the crossover operator which will dependent on the implementation create a different number of offsprings.

mutationMutation

Some genetic algorithms rely only on the mutation operation. However, it has shown that increases the performance to perform a mutation after creating the offsprings through crossover as well. Usually the mutation operator needs to be initialized with a probability to be executed. Having a high probability of mutation will most of the time increase the diversity in the population.

eliminate_duplicatesbool

The genetic algorithm implementation has a built in feature that eliminates duplicates after merging the parent and the offspring population. If there are duplicates with respect to the current population or in the offsprings itself they are removed and the mating process is repeated to fill up the offsprings until the desired number of unique offsprings is met.

n_offspringsint (default: None)

Number of offspring that are created through mating. By default n_offsprings=None which sets the number of offsprings equal to the population size. By setting n_offsprings=1 a, so called, steady-state version of an algorithm can be achieved.

Returns
nsga2Algorithm

Returns an NSGA2 algorithm object.

pymoo.algorithms.rnsga2.rnsga2(ref_points, epsilon=0.001, normalization="front", weights=None, extreme_points_as_reference_points=False, **kwargs)
Parameters
ref_pointsnumpy.array

Reference Points (or also called Aspiration Points) as a numpy.array where each row represents a point and each column a variable (must be equal to the objective dimension of the problem)

epsilonfloat
weightsnp.array
normalization{‘no’, ‘front’, ‘ever’}
extreme_points_as_reference_pointsbool
Returns
rnsga2Algorithm

Returns an RNSGA2 algorithm object.

pymoo.algorithms.nsga3.nsga3(ref_dirs, pop_size=None, sampling=RandomSampling(), selection=TournamentSelection(func_comp=comp_by_cv_then_random), crossover=SimulatedBinaryCrossover(prob=1.0, eta=30), mutation=PolynomialMutation(prob=None, eta=20), eliminate_duplicates=True, n_offsprings=None, **kwargs)
Parameters
ref_dirsnumpy.array

The reference direction that should be used during the optimization. Each row represents a reference line and each column a variable.

pop_sizeint (default = None)

By default the population size is set to None which means that it will be equal to the number of reference line. However, if desired this can be overwritten by providing a positve number.

sampling

The sampling process defines the initial set of solutions which are the starting point of the optimization algorithm. Here, you have three different options by passing

(i) A Sampling implementation which is an implementation of a random sampling method.

(ii) A Population object containing the variables to be evaluated initially OR already evaluated solutions (F needs to be set in this case).

(iii) Pass a two dimensional numpy.array with (n_individuals, n_var) which contains the variable space values for each individual.

selectionSelection

This object defines the mating selection to be used. In an evolutionary algorithm each generation parents need to be selected to produce new offsprings using different recombination and mutation operators. Different strategies for selecting parents are possible e.g. selecting them just randomly, only in the neighbourhood, using a tournament selection to introduce some seletion pressure, …

crossoverCrossover

The crossover has the purpose of create offsprings during the evolution. After the mating selection the parents are passed to the crossover operator which will dependent on the implementation create a different number of offsprings.

mutationMutation

Some genetic algorithms rely only on the mutation operation. However, it has shown that increases the performance to perform a mutation after creating the offsprings through crossover as well. Usually the mutation operator needs to be initialized with a probability to be executed. Having a high probability of mutation will most of the time increase the diversity in the population.

eliminate_duplicatesbool

The genetic algorithm implementation has a built in feature that eliminates duplicates after merging the parent and the offspring population. If there are duplicates with respect to the current population or in the offsprings itself they are removed and the mating process is repeated to fill up the offsprings until the desired number of unique offsprings is met.

n_offspringsint (default: None)

Number of offspring that are created through mating. By default n_offsprings=None which sets the number of offsprings equal to the population size. By setting n_offsprings=1 a, so called, steady-state version of an algorithm can be achieved.

Returns
nsga3Algorithm

Returns an NSGA3 algorithm object.

pymoo.algorithms.unsga3.unsga3(**kwargs)

This is an implementation of the Unified NSGA3 algorithm . The same options as for pymoo.algorithms.nsga3.nsga3 are available.

Returns
unsga3Algorithm

Returns an UNSGA3 algorithm object.

pymoo.algorithms.rnsga3.rnsga3(ref_points, pop_per_ref_point, mu=0.05, **kwargs)
Parameters
ref_pointsnumpy.array

Reference Points (or also called Aspiration Points) as a numpy.array where each row represents a point and each column a variable (must be equal to the objective dimension of the problem)

pop_per_ref_pointint

Size of the population used for each reference point.

mufloat

Defines the scaling of the reference lines used during survival selection. Increasing mu will result having solutions with a larger spread.

Other Parameters
——-
n_offspringsint (default: None)

Number of offspring that are created through mating. By default n_offsprings=None which sets the number of offsprings equal to the population size. By setting n_offsprings=1 a, so called, steady-state version of an algorithm can be achieved.

sampling

The sampling process defines the initial set of solutions which are the starting point of the optimization algorithm. Here, you have three different options by passing

(i) A Sampling implementation which is an implementation of a random sampling method.

(ii) A Population object containing the variables to be evaluated initially OR already evaluated solutions (F needs to be set in this case).

(iii) Pass a two dimensional numpy.array with (n_individuals, n_var) which contains the variable space values for each individual.

selectionSelection

This object defines the mating selection to be used. In an evolutionary algorithm each generation parents need to be selected to produce new offsprings using different recombination and mutation operators. Different strategies for selecting parents are possible e.g. selecting them just randomly, only in the neighbourhood, using a tournament selection to introduce some seletion pressure, …

crossoverCrossover

The crossover has the purpose of create offsprings during the evolution. After the mating selection the parents are passed to the crossover operator which will dependent on the implementation create a different number of offsprings.

mutationMutation

Some genetic algorithms rely only on the mutation operation. However, it has shown that increases the performance to perform a mutation after creating the offsprings through crossover as well. Usually the mutation operator needs to be initialized with a probability to be executed. Having a high probability of mutation will most of the time increase the diversity in the population.

eliminate_duplicatesbool

The genetic algorithm implementation has a built in feature that eliminates duplicates after merging the parent and the offspring population. If there are duplicates with respect to the current population or in the offsprings itself they are removed and the mating process is repeated to fill up the offsprings until the desired number of unique offsprings is met.

Returns
nsga3Algorithm

Returns an NSGA3 algorithm object.

pymoo.algorithms.moead.moead(ref_dirs, n_neighbors=15, decomposition='auto', prob_neighbor_mating=0.7, **kwargs)
Parameters
ref_dirsnumpy.array

The reference direction that should be used during the optimization. Each row represents a reference line and each column a variable.

decomposition{ ‘auto’, ‘tchebi’, ‘pbi’ }

The decomposition approach that should be used. If set to auto for two objectives tchebi and for more than two pbi will be used.

n_neighborsint

Number of neighboring reference lines to be used for selection.

prob_neighbor_matingfloat

Probability of selecting the parents in the neighborhood.

Returns
moeadMOEAD

Returns an MOEAD algorithm object.

Model

Factory