Obtaining Smoothly Navigable Approximation Sets in Bi-Objective Multi-Modal Optimization

TL;DR

This paper introduces MM-BezEA, a novel multi-modal multi-objective evolutionary algorithm that produces smooth, navigable approximation sets by parameterizing solutions with Bézier curves, improving decision-maker insight.

Contribution

The paper presents MM-BezEA, a new MMOEA that ensures smoothness in approximation sets by leveraging Bézier curves, enhancing solution interpretability over existing methods.

Findings

MM-BezEA outperforms existing algorithms in hypervolume on benchmark problems.

It produces smoother, more navigable solution sets.

The approach effectively covers all locally optimal approximation sets.

Abstract

Even if a Multi-modal Multi-Objective Evolutionary Algorithm (MMOEA) is designed to find solutions well spread over all locally optimal approximation sets of a Multi-modal Multi-objective Optimization Problem (MMOP), there is a risk that the found set of solutions is not smoothly navigable because the solutions belong to various niches, reducing the insight for decision makers. To tackle this issue, a new MMOEAs is proposed: the Multi-Modal B\'ezier Evolutionary Algorithm (MM-BezEA), which produces approximation sets that cover individual niches and exhibit inherent decision-space smoothness as they are parameterized by B\'ezier curves. MM-BezEA combines the concepts behind the recently introduced BezEA and MO-HillVallEA to find all locally optimal approximation sets. When benchmarked against the MMOEAs MO_Ring_PSO_SCD and MO-HillVallEA on MMOPs with linear Pareto sets, MM-BezEA was found to perform best in terms of best hypervolume.