Hypervolume

Hypervolume History Calculator

Abstract This package provides a utility to compute the hypervolume history of a multi-objective Optuna study. The hypervolume indicator measures the volume of the objective space dominated by the current Pareto front relative to a reference point, and tracking it over trials is a common way to evaluate the convergence of multi-objective optimizers. The implementation supports arbitrary numbers of objectives, mixed minimization/maximization directions, and constraint handling via Optuna’s constraint mechanism. For 2D and 3D cases, specialized efficient algorithms are used; for higher dimensions, the WFG algorithm is employed.

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.