{"title":"在多目标黑盒优化测试套件中使用理解良好的单目标函数","authors":"Dimo Brockhoff;Anne Auger;Nikolaus Hansen;Tea Tušar","doi":"10.1162/evco_a_00298","DOIUrl":null,"url":null,"abstract":"Several test function suites are being used for numerical benchmarking of multiobjective optimization algorithms. While they have some desirable properties, such as well-understood Pareto sets and Pareto fronts of various shapes, most of the currently used functions possess characteristics that are arguably underrepresented in real-world problems such as separability, optima located exactly at the boundary constraints, and the existence of variables that solely control the distance between a solution and the Pareto front. Via the alternative construction of combining existing single-objective problems from the literature, we describe the bbob-biobj test suite with 55 bi-objective functions in continuous domain, and its extended version with 92 bi-objective functions (bbob-biobj-ext). Both test suites have been implemented in the COCO platform for black-box optimization benchmarking and various visualizations of the test functions are shown to reveal their properties. Besides providing details on the construction of these problems and presenting their (known) properties, this article also aims at giving the rationale behind our approach in terms of groups of functions with similar properties, objective space normalization, and problem instances. The latter allows us to easily compare the performance of deterministic and stochastic solvers, which is an often overlooked issue in benchmarking.","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":"30 2","pages":"165-193"},"PeriodicalIF":4.6000,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"22","resultStr":"{\"title\":\"Using Well-Understood Single-Objective Functions in Multiobjective Black-Box Optimization Test Suites\",\"authors\":\"Dimo Brockhoff;Anne Auger;Nikolaus Hansen;Tea Tušar\",\"doi\":\"10.1162/evco_a_00298\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Several test function suites are being used for numerical benchmarking of multiobjective optimization algorithms. While they have some desirable properties, such as well-understood Pareto sets and Pareto fronts of various shapes, most of the currently used functions possess characteristics that are arguably underrepresented in real-world problems such as separability, optima located exactly at the boundary constraints, and the existence of variables that solely control the distance between a solution and the Pareto front. Via the alternative construction of combining existing single-objective problems from the literature, we describe the bbob-biobj test suite with 55 bi-objective functions in continuous domain, and its extended version with 92 bi-objective functions (bbob-biobj-ext). Both test suites have been implemented in the COCO platform for black-box optimization benchmarking and various visualizations of the test functions are shown to reveal their properties. Besides providing details on the construction of these problems and presenting their (known) properties, this article also aims at giving the rationale behind our approach in terms of groups of functions with similar properties, objective space normalization, and problem instances. The latter allows us to easily compare the performance of deterministic and stochastic solvers, which is an often overlooked issue in benchmarking.\",\"PeriodicalId\":50470,\"journal\":{\"name\":\"Evolutionary Computation\",\"volume\":\"30 2\",\"pages\":\"165-193\"},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2022-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"22\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Evolutionary Computation\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://ieeexplore.ieee.org/document/9931088/\",\"RegionNum\":2,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Evolutionary Computation","FirstCategoryId":"94","ListUrlMain":"https://ieeexplore.ieee.org/document/9931088/","RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
Using Well-Understood Single-Objective Functions in Multiobjective Black-Box Optimization Test Suites
Several test function suites are being used for numerical benchmarking of multiobjective optimization algorithms. While they have some desirable properties, such as well-understood Pareto sets and Pareto fronts of various shapes, most of the currently used functions possess characteristics that are arguably underrepresented in real-world problems such as separability, optima located exactly at the boundary constraints, and the existence of variables that solely control the distance between a solution and the Pareto front. Via the alternative construction of combining existing single-objective problems from the literature, we describe the bbob-biobj test suite with 55 bi-objective functions in continuous domain, and its extended version with 92 bi-objective functions (bbob-biobj-ext). Both test suites have been implemented in the COCO platform for black-box optimization benchmarking and various visualizations of the test functions are shown to reveal their properties. Besides providing details on the construction of these problems and presenting their (known) properties, this article also aims at giving the rationale behind our approach in terms of groups of functions with similar properties, objective space normalization, and problem instances. The latter allows us to easily compare the performance of deterministic and stochastic solvers, which is an often overlooked issue in benchmarking.
期刊介绍:
Evolutionary Computation is a leading journal in its field. It provides an international forum for facilitating and enhancing the exchange of information among researchers involved in both the theoretical and practical aspects of computational systems drawing their inspiration from nature, with particular emphasis on evolutionary models of computation such as genetic algorithms, evolutionary strategies, classifier systems, evolutionary programming, and genetic programming. It welcomes articles from related fields such as swarm intelligence (e.g. Ant Colony Optimization and Particle Swarm Optimization), and other nature-inspired computation paradigms (e.g. Artificial Immune Systems). As well as publishing articles describing theoretical and/or experimental work, the journal also welcomes application-focused papers describing breakthrough results in an application domain or methodological papers where the specificities of the real-world problem led to significant algorithmic improvements that could possibly be generalized to other areas.