用聚类优化代理模型，高效寻找复杂系统的全局最优解。
Surrogate-based Optimization via Clustering for Box-Constrained Problems
- 通过聚类定位未探索区域，单代理模型覆盖全空间
- 在低维和高维测试函数上均显著降低计算成本
- 适合高维复杂系统优化，尤其4维以上表现突出
大规模复杂系统（如多物理场黑箱模拟和工业系统）的全局优化至关重要但极具挑战。本文提出一种基于聚类的代理模型优化框架SBOC，适用于任意代理建模方法。每轮迭代中，它使用单一代理模型覆盖整个定义域，通过k-means聚类识别未探索区域，并在代理最优附近局部搜索，可能新增三个采样点。SBOC在52个不同维度与形态的解析测试函数上，对比16种先进算法进行验证。结果表明，其在多数测试函数中成功找到全局最小值，且计算开销远低于其他算法。在四维及以上变量的问题上表现尤为出色，在接近全局最优方面位列前六。总体而言，SBOC是针对盒约束系统全局优化的一种鲁棒、可靠且高效的算法。
原文摘要 · Abstract (English)
Global optimization of large-scale, complex systems such as multi-physics black-box simulations and real-world industrial systems is important but challenging. This work presents a novel Surrogate-Based Optimization framework based on Clustering, SBOC for global optimization of such systems, which can be used with any surrogate modeling technique. At each iteration, it uses a single surrogate model for the entire domain, employs k-means clustering to identify unexplored domain, and exploits a local region around the surrogate optimum to potentially add three new sample points in the domain. SBOC has been tested against sixteen promising benchmarking algorithms using 52 analytical test functions of varying input dimensionalities and shape profiles. It successfully identified a global minimum for most test functions with substantially lower computational effort than other algorithms. It worked especially well on test functions with four or more input variables. It was also among the top six algorithms in approaching a global minimum closely. Overall, SBOC is a robust, reliable, and efficient algorithm for global optimization of box-constrained systems.
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