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...

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Bibliographic Details
Published inEvolutionary computation Vol. 30; no. 2; pp. 165 - 193
Main Authors Brockhoff, Dimo, Auger, Anne, Hansen, Nikolaus, Tušar, Tea
Format Journal Article
LanguageEnglish
Published One Rogers Street, Cambridge, MA 02142-1209, USA MIT Press 01.06.2022
MIT Press Journals, The
Massachusetts Institute of Technology Press (MIT Press)
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ISSN1530-9304
1063-6560
1530-9304
DOI10.1162/evco_a_00298

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Summary: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 test suite with 55 bi-objective functions in continuous domain, and its extended version with 92 bi-objective functions ( ). Both test suites have been implemented in the 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.
Bibliography:2022
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ISSN:1530-9304
1063-6560
1530-9304
DOI:10.1162/evco_a_00298