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 Bézier Evolutionary Algorithm (MM-BezEA), which produces approximation sets that cover individual niches and exhibit inherent decision-space smoothness as they are parameterized by Bézier 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.

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Lecture Notes in Computer Science
17th International Conference on Parallel Problem Solving from Nature, PPSN 2022
Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands

Scholman, R.J, Bouter, P.A, Dickhoff, L.R.M, Alderliesten, T, & Bosman, P.A.N. (2022). Obtaining smoothly navigable approximation sets in bi-objective multi-modal optimization. In Proceedings of PPSN 2022 (pp. 247–262). doi:10.1007/978-3-031-14721-0_18