{"type":"ScholarlyArticle","title":"Maintaining Diversity Provably Helps in Evolutionary Multimodal Optimization","authors":[{"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":"Zhijia Qiu","slug":"zhijia-qiu","given":"Zhijia","family":"Qiu","affiliation":"National Key Laboratory for Novel Software Technology , Nanjing University , Nanjing 210023 , China School of Artificial Intelligence ,"},{"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":"Miqing Li","slug":"miqing-li","given":"Miqing","family":"Li","affiliation":"School of Computer Science , University of Birmingham , Birmingham B15 2TT , U.K.; Nanjing University , Nanjing 210023 , China"},{"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 ,"}],"abstract":"In the real world, there exist a class of optimization problems that multiple (local) optimal solutions in the solution space correspond to a single point in the objective space. In this paper, we theoretically show that for such multimodal problems, a simple method that considers the diversity of solutions in the solution space can benefit the search in evolutionary algorithms (EAs). Specifically, we prove that the proposed method, working with crossover, can help enhance the exploration, leading to polynomial or even exponential acceleration on the expected running time. This result is derived by rigorous running time analysis in both single-objective and multi-objective scenarios, including (mu+1)-GA solving the widely studied single-objective problem, Jump, and NSGA-II and SMS-EMOA (two well-established multi-objective EAs) solving the widely studied bi-objective problem, OneJumpZeroJump. Experiments are also conducted to validate the theoretical results. We hope that our results may encourage the exploration of diversity maintenance in the solution space for multi-objective optimization, where existing EAs usually only consider the diversity in the objective space and can easily be trapped in local optima.","doi":"10.24963/ijcai.2024/775","url":"https://ijcai.org/proceedings/2024/775","pdf":"https://ijcai.org/proceedings/2024/0775.pdf","markdown":"https://ijcai.org/proceedings/2024/775.md","bibtex":"https://ijcai.org/proceedings/2024/bibtex/775","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":775,"pages":{"first":7012,"last":7020},"keywords":["Search: S: Evolutionary computation"],"videos":[],"references":[{"position":1,"raw":"[Auger and Doerr, 2011] A. 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