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

Abstract

Abstract Several test function suites are being used for numerical benchmarking of multiobjective optimization algorithms. While they have some desirable properties, like wellunderstood Pareto sets and Pareto fronts of various shapes, most of the currently used functions possess characteristics that are arguably under-represented 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 biobjective functions in continuous domain, and its extended version with 92 biobjective 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 paper 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.