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.

翻译：参数控制已成功加速了进化算法的收敛过程。尽管针对单目标优化的算法行为已通过经验与理论研究得以阐明，但自适应性对多目标进化算法的影响仍鲜为人知。本研究贡献如下：(1) 对全局简单进化多目标算法（GSEMO）变体在经典问题（如OneMinMax、LOTZ、COCZ）上进行了广泛的实验分析；(2) 提出了一种具有自适应变异能力的新型GSEMO版本。为实现GSEMO的自适应性，我们借鉴了单目标优化中的三种自适应变异技术，并采用超体积、倒置世代距离等性能指标指导自适应过程。实验表明，基于单目标优化和超体积调整变异率可加速GSEMO收敛。此外，我们进一步提出了带自适应变异的GSEMO算法，该算法同时考虑单目标优化需求，并为每个解单独调整变异率。结果表明，所提方法在所有测试问题上均优于采用固定变异率的GSEMO。本研究为多目标进化算法提供了全面的基准测试，补充了现有理论运行时间分析。所提算法为未来实际应用中设计多目标进化算法解决了关键问题。