Towards Self-adaptive Mutation in Evolutionary Multi-Objective Algorithms

arXiv (Cornell University)

Abstract

Parameter control has succeeded in accelerating the convergence process of evolutionary algorithms. While empirical and theoretical studies have shed light on the behavior of algorithms for single-objective optimization, little is known about how self-adaptation influences multi-objective evolutionary algorithms. In this work, we contribute (1) extensive experimental analysis of the Global Simple Evolutionary Multi-objective Algorithm (GSEMO) variants on classic problems, such as OneMinMax, LOTZ, COCZ, and (2) a novel version of GSEMO with self-adaptive mutation. To enable self-adaptation in GSEMO, we explore three self-adaptive mutation techniques from single-objective optimization and use various performance metrics, such as hypervolume and inverted generational distance, to guide the adaptation. Our experiments show that adapting the mutation rate based on single-objective optimization and hypervolume can speed up the convergence of GSEMO. Moreover, we propose a GSEMO with self-adaptive mutation, which considers optimizing for single objectives and adjusts the mutation rate for each solution individually. Our results demonstrate that the proposed method outperforms the GSEMO with static mutation rates across all the tested problems. This work provides a comprehensive benchmarking study for MOEAs and complements existing theoretical runtime analysis. Our proposed algorithm addresses interesting issues for designing MOEAs for future practical applications.

Authors 5

1. Furong Ye Aachen

   Leiden University · University of Applied Sciences Leiden

   Affiliation as printed

   LIACS , Leiden University Leiden , Netherlands

2. Frank Neumann

   The University of Adelaide

   Affiliation as printed

   The University of Adelaide Adelaide , Australia Jacob de Nobel

3. Jacob de Nobel
4. Aneta Neumann

   The University of Adelaide

   Affiliation as printed

   The University of Adelaide Adelaide , Australia

5. Thomas Bäck