{"title":"关于具有异质目标的双目标组合优化","authors":"","doi":"10.1016/j.ejor.2024.06.029","DOIUrl":null,"url":null,"abstract":"<div><p>The heterogeneity among objectives in multi-objective optimization can be viewed from several perspectives. In this paper, we are interested in the heterogeneity arising in the underlying landscape of the objective functions, in terms of multi-modality and search difficulty. Building on recent efforts leveraging the so-called single-objective NK-landscapes to model such a setting, we conduct a three-fold empirical analysis on the impact of objective heterogeneity on the landscape properties and search difficulty of bi-objective optimization problems. Firstly, for small problems, we propose two techniques based on studying the distribution of the solutions in the objective space. Secondly, for large problems, we investigate the ability of existing landscape features to capture the degree of heterogeneity among the two objectives. Thirdly, we study the behavior of two state-of-the-art multi-objective evolutionary algorithms, namely MOEA/D and NSGA-II, when faced with a range of problems with different degrees of heterogeneity. Although one algorithm is found to consistently outperform the other, the dynamics of both algorithms vary similarly with respect to objective heterogeneity. Our analysis suggests that novel approaches are needed to understand the fundamental properties of heterogeneous bi-objective optimization problems and to tackle them more effectively.</p></div>","PeriodicalId":55161,"journal":{"name":"European Journal of Operational Research","volume":null,"pages":null},"PeriodicalIF":6.0000,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On bi-objective combinatorial optimization with heterogeneous objectives\",\"authors\":\"\",\"doi\":\"10.1016/j.ejor.2024.06.029\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The heterogeneity among objectives in multi-objective optimization can be viewed from several perspectives. In this paper, we are interested in the heterogeneity arising in the underlying landscape of the objective functions, in terms of multi-modality and search difficulty. Building on recent efforts leveraging the so-called single-objective NK-landscapes to model such a setting, we conduct a three-fold empirical analysis on the impact of objective heterogeneity on the landscape properties and search difficulty of bi-objective optimization problems. Firstly, for small problems, we propose two techniques based on studying the distribution of the solutions in the objective space. Secondly, for large problems, we investigate the ability of existing landscape features to capture the degree of heterogeneity among the two objectives. Thirdly, we study the behavior of two state-of-the-art multi-objective evolutionary algorithms, namely MOEA/D and NSGA-II, when faced with a range of problems with different degrees of heterogeneity. Although one algorithm is found to consistently outperform the other, the dynamics of both algorithms vary similarly with respect to objective heterogeneity. Our analysis suggests that novel approaches are needed to understand the fundamental properties of heterogeneous bi-objective optimization problems and to tackle them more effectively.</p></div>\",\"PeriodicalId\":55161,\"journal\":{\"name\":\"European Journal of Operational Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":6.0000,\"publicationDate\":\"2024-06-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"European Journal of Operational Research\",\"FirstCategoryId\":\"91\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0377221724004776\",\"RegionNum\":2,\"RegionCategory\":\"管理学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"OPERATIONS RESEARCH & MANAGEMENT SCIENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"European Journal of Operational Research","FirstCategoryId":"91","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0377221724004776","RegionNum":2,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}
引用次数: 0
摘要
多目标优化中目标之间的异质性可以从多个角度来看待。在本文中,我们关注的是目标函数底层景观在多模式和搜索难度方面产生的异质性。最近,我们利用所谓的单目标 NK 景观来模拟这种情况,在此基础上,我们从三个方面对目标异质性对双目标优化问题的景观属性和搜索难度的影响进行了实证分析。首先,对于小问题,我们提出了两种基于研究目标空间解分布的技术。其次,对于大型问题,我们研究了现有景观特征捕捉两个目标之间异质性程度的能力。第三,我们研究了两种最先进的多目标进化算法(即 MOEA/D 和 NSGA-II)在面对一系列具有不同异质性的问题时的表现。虽然其中一种算法的性能始终优于另一种算法,但这两种算法的动态变化与目标异质性的变化类似。我们的分析表明,需要采用新方法来理解异构双目标优化问题的基本特性,并更有效地解决这些问题。
On bi-objective combinatorial optimization with heterogeneous objectives
The heterogeneity among objectives in multi-objective optimization can be viewed from several perspectives. In this paper, we are interested in the heterogeneity arising in the underlying landscape of the objective functions, in terms of multi-modality and search difficulty. Building on recent efforts leveraging the so-called single-objective NK-landscapes to model such a setting, we conduct a three-fold empirical analysis on the impact of objective heterogeneity on the landscape properties and search difficulty of bi-objective optimization problems. Firstly, for small problems, we propose two techniques based on studying the distribution of the solutions in the objective space. Secondly, for large problems, we investigate the ability of existing landscape features to capture the degree of heterogeneity among the two objectives. Thirdly, we study the behavior of two state-of-the-art multi-objective evolutionary algorithms, namely MOEA/D and NSGA-II, when faced with a range of problems with different degrees of heterogeneity. Although one algorithm is found to consistently outperform the other, the dynamics of both algorithms vary similarly with respect to objective heterogeneity. Our analysis suggests that novel approaches are needed to understand the fundamental properties of heterogeneous bi-objective optimization problems and to tackle them more effectively.
期刊介绍:
The European Journal of Operational Research (EJOR) publishes high quality, original papers that contribute to the methodology of operational research (OR) and to the practice of decision making.