{"type":"ScholarlyArticle","title":"An Archive Can Bring Provable Speed-ups in Multi-Objective Evolutionary Algorithms","authors":[{"name":"Chao Bian","slug":"chao-bian","given":"Chao","family":"Bian","affiliation":"National Key Laboratory for Novel Software Technology , Nanjing University , Nanjing 210023 , China School of Artificial Intelligence ,"},{"name":"Shengjie Ren","slug":"shengjie-ren","given":"Shengjie","family":"Ren","affiliation":"National Key Laboratory for Novel Software Technology , Nanjing University , Nanjing 210023 , China School of Artificial Intelligence ,"},{"name":"Miqing Li","slug":"miqing-li","given":"Miqing","family":"Li","affiliation":"School of Computer Science , University of Birmingham , Birmingham B15 2TT , U.K."},{"name":"Chao Qian","slug":"chao-qian","given":"Chao","family":"Qian","affiliation":"National Key Laboratory for Novel Software Technology , Nanjing University , Nanjing 210023 , China School of Artificial Intelligence ,; Nanjing University , Nanjing 210023 , China"}],"abstract":"In the area of multi-objective evolutionary algorithms (MOEAs), there is a trend of using an archive to store non-dominated solutions generated during the search. This is because 1) MOEAs may easily end up with the final population containing inferior solutions that are dominated by other solutions discarded during the search process and 2) the  population that has a commensurable size of the problem's Pareto front is often not practical. In this paper, we theoretically show, for the first time, that using an archive can guarantee speed-ups for MOEAs. Specifically, we prove that for two well-established MOEAs (NSGA-II and SMS-EMOA) on two commonly studied problems (OneMinMax and LeadingOnesTrailingZeroes), using an archive brings a polynomial acceleration on the expected running time. The reason is that with an archive, the size of the population can reduce to a small constant; there is no need for the population to keep all the Pareto optimal solutions found. This contrasts existing theoretical studies for MOEAs where a population with a commensurable size of the problem's Pareto front is needed. The findings in this paper not only provide a theoretical confirmation for an increasingly popular practice in the design of MOEAs, but can also be beneficial to the theory community towards studying more practical MOEAs.","doi":"10.24963/ijcai.2024/763","url":"https://ijcai.org/proceedings/2024/763","pdf":"https://ijcai.org/proceedings/2024/0763.pdf","markdown":"https://ijcai.org/proceedings/2024/763.md","bibtex":"https://ijcai.org/proceedings/2024/bibtex/763","volume":{"slug":"2024","title":"Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2024","url":"https://ijcai.org/proceedings/2024/","year":2024,"location":"Jeju, Korea","dates":"3-9 August 2024","editors":"Kate Larson","isbn":"978-1-956792-04-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2024"},"section":"Search","track":"Main Track","number":763,"pages":{"first":6905,"last":6913},"keywords":["Search: S: Evolutionary computation"],"videos":[],"references":[{"position":1,"raw":"[Beume et al., 2007] N. 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