MOEA/D sampler

Abstract

Sampler using MOEA/D algorithm. MOEA/D stands for “Multi-Objective Evolutionary Algorithm based on Decomposition.

This sampler is specialized for multiobjective optimization. The objective function is internally decomposed into multiple single-objective subproblems to perform optimization.

It may not work well with multi-threading. Check results carefully.

APIs

• MOEADSampler(*, population_size = 100, n_neighbors = None, scalar_aggregation_func = "tchebycheff", mutation = None, mutation_prob = None, crossover = None, crossover_prob = 0.9, seed = None
  • n_neighbors: The number of the weight vectors in the neighborhood of each weight vector. The larger this value, the more weight is applied to the exploration.
    • If None, population_size // 10 is used
  • scalar_aggregation_func: The scalar aggregation function to use. The default is tchebycheff. Other options is weight_sum.
  • mutation: Mutation to be applied when creating child individual.
    • If None, UniformMutation is selected. For categorical variables, it is always UniformMutation.
  • crossover: Crossover to be applied when creating child individual.
    • If None, UniformCrossover(swapping_prob=0.5) is selected.
• The other arguments are the same as for Optuna’s NSGA-II.
• Supported mutation methods are listed below
  • UniformMutation()
    • This is a mutation method that uses a Uniform distribution for the distribution of the generated individuals.
  • PolynomialMutation(eta=20)
    • This is a mutation method that uses a Polynomial distribution for the distribution of the generated individuals.
    • eta: Argument for the width of the distribution. The larger the value, the narrower the distribution. A value eta ∈ [20, 100] is adequate in most problems
  • GaussianMutation(sigma_factor=1/30)
    • This is a mutation method that uses a Gaussian distribution for the distribution of the generated individuals.
    • sigma_factor: It is a factor that is multiplied by the sigma of the Gaussian distribution. When the sigma_factor is 1.0, the sigma is the difference between the maximum and minimum of the search range for the target variable.

Installation

pip install scipy

or

pip install -r https://hub.optuna.org/samplers/moead/requirements.txt

Example

import optuna
import optunahub

def objective(trial: optuna.Trial) -> tuple[float, float]:
    x = trial.suggest_float("x", 0, 5)
    y = trial.suggest_float("y", 0, 3)

    v0 = 4 * x**2 + 4 * y**2
    v1 = (x - 5) ** 2 + (y - 5) ** 2
    return v0, v1


mod = optunahub.load_module("samplers/moead")
sampler = mod.MOEADSampler(
    population_size=100,
    scalar_aggregation_func="tchebycheff",
    n_neighbors=20,
    mutation=mod.PolynomialMutation(eta=20)
)
study = optuna.create_study(sampler=sampler, directions=["minimize", "minimize"])
study.optimize(objective, n_trials=1000)

Others

For more information, check out Optuna’s Medium article

Reference

Q. Zhang and H. Li, “MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition,” in IEEE Transactions on Evolutionary Computation, vol. 11, no. 6, pp. 712-731, Dec. 2007, doi: 10.1109/TEVC.2007.892759.