Multi-Objective Optimization

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. Class or Function Names MOEADSampler 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.

Multi-objective CMA-ES (MO-CMA-ES) Sampler

Abstract MoCmaSampler provides the implementation of the s-MO-CMA-ES algorithm. This algorithm extends (1+1)-CMA-ES to multi-objective optimization by introducing a selection strategy based on non-domination sorting and contributing hypervolume (S-metric). It inherits important properties of CMA-ES, invariance against order-preserving transformations of the fitness function value and rotation and translation of the search space. Class or Function Names MoCmaSampler(*, search_space: dict[str, BaseDistribution] | None = None, popsize: int | None = None, seed: int | None = None) search_space: A dictionary containing the search space that defines the parameter space.

PLMBO (Preference Learning Multi-Objective Bayesian Optimization)

Class or Function Names PLMBOSampler Installation pip install -r https://hub.optuna.org/samplers/plmbo/requirements.txt Example from __future__ import annotations import matplotlib.pyplot as plt import optuna import optunahub from optuna.distributions import FloatDistribution import numpy as np PLMBOSampler = optunahub.load_module( # type: ignore "samplers/plmbo", ).PLMBOSampler if __name__ == "__main__": f_sigma = 0.01 def obj_func1(x): return np.sin(x[0]) + x[1] def obj_func2(x): return -np.sin(x[0]) - x[1] + 0.1 def obs_obj_func(x): return np.array( [ obj_func1(x) + np.random.normal(0, f_sigma), obj_func2(x) + np.

Plot Hypervolume History for Multiple Studies

Class or Function Names plot_optimization_history 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 samplers = [ optuna.samplers.RandomSampler(), optuna.samplers.TPESampler(), optuna.samplers.NSGAIISampler(), ] studies = [] for sampler in samplers: study = optuna.create_study( sampler=sampler, study_name=f"{sampler.__class__.__name__}", directions=["minimize", "minimize"], ) study.

Plot Hypervolume History with Reference Point

Class or Function Names plot_hypervolume_history Example mod = optunahub.load_module("visualization/plot_hypervolume_history_with_rp") mod.plot_hypervolume_history(study, reference_point) See example.py for more details. The example of generated image is as follows.

Plot Pareto Front for Multiple Studies

Class or Function Names plot_pareto_front 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 samplers = [ optuna.samplers.RandomSampler(), optuna.samplers.TPESampler(), optuna.samplers.NSGAIISampler(), ] studies = [] for sampler in samplers: study = optuna.create_study( sampler=sampler, study_name=f"{sampler.__class__.__name__}", directions=["minimize", "minimize"], ) study.