Multi-Objective Covariance Matrix Adaptation MAP-Annealing

• URL: http://arxiv.org/abs/2505.20712v1
• Date: Tue, 27 May 2025 04:39:28 GMT
• Title: Multi-Objective Covariance Matrix Adaptation MAP-Annealing
• Authors: Shihan Zhao, Stefanos Nikolaidis,
• Abstract summary: Quality-Diversity (QD) optimization is an emerging field that focuses on finding a set of behaviorally diverse and high-quality solutions.<n>Recent work on Multi-Objective Quality-Diversity (MOQD) extends QD optimization to simultaneously optimize multiple objective functions.<n>This opens up multi-objective applications for QD, such as generating a diverse set of game maps that maximize difficulty, realism, or other properties.
• Score: 7.103319934188755
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quality-Diversity (QD) optimization is an emerging field that focuses on finding a set of behaviorally diverse and high-quality solutions. While the quality is typically defined w.r.t. a single objective function, recent work on Multi-Objective Quality-Diversity (MOQD) extends QD optimization to simultaneously optimize multiple objective functions. This opens up multi-objective applications for QD, such as generating a diverse set of game maps that maximize difficulty, realism, or other properties. Existing MOQD algorithms use non-adaptive methods such as mutation and crossover to search for non-dominated solutions and construct an archive of Pareto Sets (PS). However, recent work in QD has demonstrated enhanced performance through the use of covariance-based evolution strategies for adaptive solution search. We propose bringing this insight into the MOQD problem, and introduce MO-CMA-MAE, a new MOQD algorithm that leverages Covariance Matrix Adaptation-Evolution Strategies (CMA-ES) to optimize the hypervolume associated with every PS within the archive. We test MO-CMA-MAE on three MOQD domains, and for generating maps of a co-operative video game, showing significant improvements in performance.

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