一种用于中等规模黑箱全局优化的实用DIRECT型算法
A practical DIRECT-type algorithm for medium-scale black-box global optimization
- Vilnius University Institute of Data Science and Digital Technologies（维尔纽斯大学数据科学与数字技术研究所）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对DIRECT型算法在高维优化中收敛慢的问题，提出结合动态划分与混合技术的X-DTC-GL算法，在基准测试中可解性提升约12%，解质量提升约27%。
AI中文摘要：
DIRECT算法是一种确定性全局优化方法，以其通用性和均衡的探索-开发策略而闻名。然而，DIRECT型算法主要适用于低维问题，并且随着维度的增加往往表现出收敛速度缓慢的问题，限制了其在更复杂优化任务中的适用性。为解决这一局限性，本文提出了X-DTC-GL，一种结合动态划分和混合技术的新型DIRECT型算法。动态划分方法基于局部一维代理模型自适应地细化搜索空间，能够快速细分有前景的超矩形。混合策略选择性地采用爬山方法，以利用代理模型识别出的有前景区域。在四个不同基准套件上的大量实验表明，X-DTC-GL显著优于现有的DIRECT型基线算法，在可解性上提高了约12%，在解质量上提高了约27%。性能剖面分析显示，在多达约40%的实例上收敛速度最快，在约17%的问题上运行时间性能最佳，并且总体执行时间具有竞争力。通过在基于划分的框架内提升性能，这些进展增强了该算法在先进黑箱优化中的竞争力。
英文摘要：
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.
