A practical DIRECT-type algorithm for medium-scale black-box global optimization

Abstract:The DIRECT algorithm is a deterministic global optimization method known for its versatility and balanced exploration-exploitation strategy. However, DIRECT-type algorithms are primarily effective for low-dimensional problems and often exhibit slow convergence as dimensionality increases, limiting their applicability to more complex optimization tasks. To address this limitation, this paper introduces X-DTC-GL, a novel DIRECT-type algorithm that incorporates dynamic partitioning and hybridization techniques. The dynamic partitioning approach adaptively refines the search space based on local one-dimensional surrogate models, enabling rapid subdivision of promising hyper-rectangles. The hybridization strategy selectively employs a hill-climbing method to exploit promising regions identified by the surrogate models. Extensive experiments on four diverse benchmark suites demonstrate that X-DTC-GL significantly outperforms existing DIRECT-type baselines, achieving improvements of ~12% in solvability and ~27% in solution quality. Performance-profile analyses indicate the fastest convergence on up to ~40% of instances, the best runtime performance on ~17% of problems, and competitive overall execution times. By improving performance within the partition-based framework, these advances strengthen the algorithm's competitiveness in state-of-the-art black-box optimization.

Machine Learning (cs.LG); Numerical Analysis (math.NA)

arXiv:2609.09796 [cs.LG]

(or arXiv:2609.09796v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.09796 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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