Using Well-Understood Single-Objective Functions in Multiobjective Black-Box Optimization Test Suites

• Published in: Evolutionary computation Vol. 30; no. 2; pp. 165 - 193
• Main Authors: Brockhoff, Dimo, Auger, Anne, Hansen, Nikolaus, Tušar, Tea
• Format: Journal Article
• Language: English
• 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)
• Subjects: algorithm comparison; Algorithms; benchmark suite generator; Benchmarks; Black boxes; Black-box optimization benchmarking; Computer Science; Continuity (mathematics); Machine Learning; Mathematical Software; multiobjective optimization; Multiple objective analysis; Neural and Evolutionary Computing; Numerical Analysis; Optimization; Pareto optimization; multiobjective optimization; algorithm comparison; benchmark suite generator; Black-box optimization benchmarking; benchmarking; optimization; numerical optimization; black-box optimization
• ISSN: 1530-9304; 1063-6560; 1530-9304
• DOI: 10.1162/evco_a_00298

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.