{"type":"ScholarlyArticle","title":"A Theoretical Perspective on Why Stochastic Population Update Needs an Archive in Evolutionary Multi-objective Optimization","authors":[{"name":"Shengjie Ren","slug":"shengjie-ren","given":"Shengjie","family":"Ren","affiliation":""},{"name":"Zimin Liang","slug":"zimin-liang","given":"Zimin","family":"Liang","affiliation":""},{"name":"Miqing Li","slug":"miqing-li","given":"Miqing","family":"Li","affiliation":""},{"name":"Chao Qian","slug":"chao-qian","given":"Chao","family":"Qian","affiliation":""}],"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 (μ+μ) update mode may be more suitable for SPU than the (μ+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.","doi":"10.24963/ijcai.2025/992","url":"https://ijcai.org/proceedings/2025/992","pdf":"https://ijcai.org/proceedings/2025/0992.pdf","markdown":"https://ijcai.org/proceedings/2025/992.md","bibtex":"https://ijcai.org/proceedings/2025/bibtex/992","volume":{"slug":"2025","title":"Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2025","url":"https://ijcai.org/proceedings/2025/","year":2025,"location":"Montreal, Canada","dates":"16-22 August 2025","editors":"James Kwok","isbn":"978-1-956792-06-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2025"},"section":"Search","track":"Main Track","number":992,"pages":{"first":8921,"last":8929},"keywords":["Search: S: Evolutionary computation"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}