Using Well-Understood Single-Objective Functions in Multiobjective Black-Box Optimization Test Suites
This work addresses the need for more realistic benchmarking in multiobjective black-box optimization, which is crucial for researchers and practitioners to accurately evaluate algorithm performance, though it is incremental as it builds on existing single-objective functions.
The paper tackles the issue of unrealistic properties in existing multiobjective optimization test suites by proposing a new approach that combines well-understood single-objective functions, resulting in the bbob-biobj and bbob-biobj-ext suites with 55 and 92 bi-objective functions, respectively, implemented in the COCO platform.
Several test function suites are being used for numerical benchmarking of multiobjective optimization algorithms. While they have some desirable properties, like well-understood 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. They mainly stem from the easier construction of such functions and result in improbable properties 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. Here, we propose an alternative way to constructing multiobjective problems-by combining existing single-objective problems from the literature. We describe in particular 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. Finally, we recommend a general procedure for creating test suites for an arbitrary number of objectives. Besides providing the formal function definitions 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.