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arXiv · 2501.16735

A Theoretical Perspective on Why Stochastic Population Update Needs an Archive in Evolutionary Multi-objective Optimization

Shengjie Ren·Zimin Liang·Miqing Li·Chao Qian
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Abstract

Evolutionary algorithms (EAs) have been widely applied to multi-objective optimization due to their population-based nature. Population update, a key component in multi-objective EAs (MOEAs), is usually performed in a greedy, deterministic manner. However, recent studies have questioned this practice and shown that stochastic population update (SPU), which allows inferior solutions have a chance to be preserved, can help MOEAs jump out of local optima more easily. Nevertheless, SPU risks losing high-quality solutions, potentially requiring a large population. Intuitively, a possible solution to this issue is to introduce an archive that stores the best solutions ever found. In this paper, we theoretically show that using an archive allows a small population and may enhance the search performance of SPU-based MOEAs. We examine two classic algorithms, SMS-EMOA and NSGA-II, on the bi-objective problem OneJumpZeroJump, and prove that using an archive can reduce the expected running time upper bound (even exponentially). The comparison between SMS-EMOA and NSGA-II also suggests that the $(\mu+\mu)$ update mode may be more suitable for SPU than the $(\mu+1)$ update mode. We also validate our findings empirically. We hope this work may provide theoretical support to explore different ideas of designing algorithms in evolutionary multi-objective optimization.

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Shengjie Ren, Zimin Liang, Miqing Li, Chao Qian. 2025-01-28. A Theoretical Perspective on Why Stochastic Population Update Needs an Archive in Evolutionary Multi-objective Optimization. https://arxiv.org/abs/2501.16735

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