BEACON: Continuous Bi-objective Benchmark problems with Explicit Adjustable COrrelatioN control

Samuel Tebbet, George De Ath, Tinkle Chugh

Abstract: This paper presents BEACON, a novel methodology for generating bi-objective benchmark problems with explicitly controlled correlations in continuous spaces. Although numerous benchmark problems exist, continuous benchmarks lack systematic mechanisms to control objective correlations, critical in real-world optimisation. Our approach utilises Gaussian Process samples approximated via Random Fourier Features and a Cholesky-based correlation transformation to generate problems with tunable correlation values ranging from perfectly negative to perfectly positive. Experiments with three popular multi-objective evolutionary algorithms (NSGA-II, SMS-EMOA, MOEA/D) across varying correlation levels and decision space dimensions reveal that algorithm performance depends on the interplay between correlation structure and dimensionality rather than either factor in isolation. Our framework bridges the gap between discrete benchmarks with correlation control and continuous benchmarks without it, enabling systematic study of correlation effects on optimisation dynamics and supporting the development of algorithms that can adapt to different correlation structures found in real-world problems.

External IDs:doi:10.1145/3712255.3734303