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To overcome the severe dimensional scaling bottlenecks of deterministic DIRECT-type global optimization, the authors introduce X-DTC-GL for medium-scale black-box optimization tasks. The algorithm couples dynamic space-partitioning driven by local one-dimensional surrogate models with selective hill-climbing exploitation in promising hyper-rectangles. Evaluated across four benchmark suites, it improves solvability by ~12%, enhances solution quality by ~27%, and achieves the fastest convergence on up to ~40% of tested instances compared to existing DIRECT baselines.
Deterministic black-box optimization no longer hits a wall beyond low dimensions, unlocking 27% better solution quality and the fastest convergence on 40% of medium-scale benchmark problems.
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.
