Hui Wang , Dong Xiao , Shahryar Rahnamayan , Wei Li , Jia Zhao
{"title":"基于多指标的人工蜂群算法,用于具有不规则帕累托前沿的多目标优化","authors":"Hui Wang , Dong Xiao , Shahryar Rahnamayan , Wei Li , Jia Zhao","doi":"10.1016/j.eswa.2024.125613","DOIUrl":null,"url":null,"abstract":"<div><div>Artificial bee colony (ABC) algorithm has shown excellent performance over many single and multi-objective optimization problems (MOPs). However, ABC encounters some difficulties when solving many-objective optimization problems (MaOPs) with irregular Pareto fronts (PFs). The possible reasons include two aspects: (1) there are many non-dominated solutions in the population and the low selection pressure cannot move the population toward the PF; and (2) it is hard to maintain population diversity for PFs having irregular geometric structures. To address these issues, a new many-objective ABC variant based on multiple indicators (called MIMaOABC) is proposed in this paper. Firstly, a convergence indicator <span><math><msub><mrow><mi>I</mi></mrow><mrow><msub><mrow><mi>ɛ</mi></mrow><mrow><mo>+</mo></mrow></msub></mrow></msub></math></span> and a diversity indicator (<span><math><mrow><mi>D</mi><mi>i</mi><mi>v</mi></mrow></math></span>) based on parallel distance are utilized. A single indicator may have preferences and it easily causes the population to converge to a subregion of the PF. Then, a two-stage environmental selection method is designed based on the two indicators. In the first stage, the <span><math><msub><mrow><mi>I</mi></mrow><mrow><msub><mrow><mi>ɛ</mi></mrow><mrow><mo>+</mo></mrow></msub></mrow></msub></math></span> based environmental selection is used to improve the convergence. In the second stage, the <span><math><mrow><mi>D</mi><mi>i</mi><mi>v</mi></mrow></math></span> based environmental selection is employed to maintain diversity and handle irregular PFs. To balance exploration and exploitation during the search, multiple search strategies are used in different search stages, respectively. In the onlooker bee stage, solutions with good convergence are chosen for further search based on a new selection mechanism. In order to verify the performance of MIMaOABC, a set of well-known benchmark problems with degenerate, discontinuous, inverted, and regular PFs are tested. Performance of MIMaOABC is compared with eight state-of-the-art algorithms. Computational results shows that the proposed MIMaOABC is competitive in solving MaOPs with both irregular and regular PFs.</div></div>","PeriodicalId":50461,"journal":{"name":"Expert Systems with Applications","volume":"262 ","pages":"Article 125613"},"PeriodicalIF":7.5000,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Artificial bee colony algorithm based on multiple indicators for many-objective optimization with irregular Pareto fronts\",\"authors\":\"Hui Wang , Dong Xiao , Shahryar Rahnamayan , Wei Li , Jia Zhao\",\"doi\":\"10.1016/j.eswa.2024.125613\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Artificial bee colony (ABC) algorithm has shown excellent performance over many single and multi-objective optimization problems (MOPs). However, ABC encounters some difficulties when solving many-objective optimization problems (MaOPs) with irregular Pareto fronts (PFs). The possible reasons include two aspects: (1) there are many non-dominated solutions in the population and the low selection pressure cannot move the population toward the PF; and (2) it is hard to maintain population diversity for PFs having irregular geometric structures. To address these issues, a new many-objective ABC variant based on multiple indicators (called MIMaOABC) is proposed in this paper. Firstly, a convergence indicator <span><math><msub><mrow><mi>I</mi></mrow><mrow><msub><mrow><mi>ɛ</mi></mrow><mrow><mo>+</mo></mrow></msub></mrow></msub></math></span> and a diversity indicator (<span><math><mrow><mi>D</mi><mi>i</mi><mi>v</mi></mrow></math></span>) based on parallel distance are utilized. A single indicator may have preferences and it easily causes the population to converge to a subregion of the PF. Then, a two-stage environmental selection method is designed based on the two indicators. In the first stage, the <span><math><msub><mrow><mi>I</mi></mrow><mrow><msub><mrow><mi>ɛ</mi></mrow><mrow><mo>+</mo></mrow></msub></mrow></msub></math></span> based environmental selection is used to improve the convergence. In the second stage, the <span><math><mrow><mi>D</mi><mi>i</mi><mi>v</mi></mrow></math></span> based environmental selection is employed to maintain diversity and handle irregular PFs. To balance exploration and exploitation during the search, multiple search strategies are used in different search stages, respectively. In the onlooker bee stage, solutions with good convergence are chosen for further search based on a new selection mechanism. In order to verify the performance of MIMaOABC, a set of well-known benchmark problems with degenerate, discontinuous, inverted, and regular PFs are tested. Performance of MIMaOABC is compared with eight state-of-the-art algorithms. Computational results shows that the proposed MIMaOABC is competitive in solving MaOPs with both irregular and regular PFs.</div></div>\",\"PeriodicalId\":50461,\"journal\":{\"name\":\"Expert Systems with Applications\",\"volume\":\"262 \",\"pages\":\"Article 125613\"},\"PeriodicalIF\":7.5000,\"publicationDate\":\"2024-10-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Expert Systems with Applications\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0957417424024801\",\"RegionNum\":1,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Expert Systems with Applications","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0957417424024801","RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
Artificial bee colony algorithm based on multiple indicators for many-objective optimization with irregular Pareto fronts
Artificial bee colony (ABC) algorithm has shown excellent performance over many single and multi-objective optimization problems (MOPs). However, ABC encounters some difficulties when solving many-objective optimization problems (MaOPs) with irregular Pareto fronts (PFs). The possible reasons include two aspects: (1) there are many non-dominated solutions in the population and the low selection pressure cannot move the population toward the PF; and (2) it is hard to maintain population diversity for PFs having irregular geometric structures. To address these issues, a new many-objective ABC variant based on multiple indicators (called MIMaOABC) is proposed in this paper. Firstly, a convergence indicator and a diversity indicator () based on parallel distance are utilized. A single indicator may have preferences and it easily causes the population to converge to a subregion of the PF. Then, a two-stage environmental selection method is designed based on the two indicators. In the first stage, the based environmental selection is used to improve the convergence. In the second stage, the based environmental selection is employed to maintain diversity and handle irregular PFs. To balance exploration and exploitation during the search, multiple search strategies are used in different search stages, respectively. In the onlooker bee stage, solutions with good convergence are chosen for further search based on a new selection mechanism. In order to verify the performance of MIMaOABC, a set of well-known benchmark problems with degenerate, discontinuous, inverted, and regular PFs are tested. Performance of MIMaOABC is compared with eight state-of-the-art algorithms. Computational results shows that the proposed MIMaOABC is competitive in solving MaOPs with both irregular and regular PFs.
期刊介绍:
Expert Systems With Applications is an international journal dedicated to the exchange of information on expert and intelligent systems used globally in industry, government, and universities. The journal emphasizes original papers covering the design, development, testing, implementation, and management of these systems, offering practical guidelines. It spans various sectors such as finance, engineering, marketing, law, project management, information management, medicine, and more. The journal also welcomes papers on multi-agent systems, knowledge management, neural networks, knowledge discovery, data mining, and other related areas, excluding applications to military/defense systems.