🤖 AI Summary
This work addresses the limitations of existing bi-objective optimization benchmark problems, which often suffer from distortion or uncontrolled complexity and lack test suites that are both realistic and theoretically tractable. To bridge this gap, the authors propose a construction method based on combinations of convex quadratic functions, enabling precise control over problem characteristics such as decision variable dimensionality, modality, and condition number. The resulting BONO-Bench suite comprises 20 problem classes with analytically traceable Pareto sets, controllable Pareto front shapes, and adjustable numbers of local optima. Notably, it is the first benchmark to unify theoretical solvability with flexible configuration of multidimensional attributes. The accompanying open-source Python package, bonobench, supports exact computation of hypervolume and R2 indicators, offering a high-fidelity, reproducible evaluation framework for multi-objective optimization algorithms.
📝 Abstract
The evaluation of heuristic optimizers on test problems, better known as benchmarking, is a cornerstone of research in multi-objective optimization. However, most test problems used in benchmarking numerical multi-objective black-box optimizers come from one of two flawed approaches: On the one hand, problems are constructed manually, which result in problems with well-understood optimal solutions, but unrealistic properties and biases. On the other hand, more realistic and complex single-objective problems are composited into multi-objective problems, but with a lack of control and understanding of problem properties. This paper proposes an extensive problem generation approach for bi-objective numerical optimization problems consisting of the combination of theoretically well-understood convex-quadratic functions into unimodal and multimodal landscapes with and without global structure. It supports configuration of test problem properties, such as the number of decision variables, local optima, Pareto front shape, plateaus in the objective space, or degree of conditioning, while maintaining theoretical tractability: The optimal front can be approximated to an arbitrary degree of precision regarding Pareto-compliant performance indicators such as the hypervolume or the exact R2 indicator. To demonstrate the generator’s capabilities, a test suite of 20 problem categories, called BONO-Bench, is created and subsequently used as a basis of an illustrative benchmark study. Finally, the general approach underlying our proposed generator, together with the associated test suite, is publicly released in the Python package bonobench to facilitate reproducible benchmarking.