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

Several test function suites are being used for numerical benchmarking of optimization algorithms. While they have some desirable, like well-understood Pareto sets and Pareto fronts of various, most of the currently used functions possess characteristics that are under-represented in real-world problems. They mainly stem from the construction of such functions and result in improbable properties such separability, optima located exactly at the boundary constraints, and the of variables that solely control the distance between a solution and Pareto front. Here, we propose an alternative way to constructing problems-by combining existing single-objective problems from literature. We describe in particular the bbob-biobj test suite with 55-objective functions in continuous domain, and its extended version with 92-objective functions (bbob-biobj-ext). Both test suites have been implemented the COCO platform for black-box optimization benchmarking. Finally, we a general procedure for creating test suites for an arbitrary number objectives. Besides providing the formal function definitions and presenting (known) properties, this paper also aims at giving the rationale behind approach in terms of groups of functions with similar properties, objective normalization, and problem instances. The latter allows us to easily the performance of deterministic and stochastic solvers, which is an overlooked issue in benchmarking.