Data-driven multi-phase constrained optimization based on multi-surrogate collaboration mechanism and space reduction strategy

Solving complex black-box constrained optimization problems (BCOPs) remains a challenge in the optimization field. This paper presents a data-driven multi-phase constrained optimization method using a multi-surrogate collaboration mechanism and space reduction strategies (DMSCSR) that can efficiently find the global optimum. The proposed method consists of three main phases: the global, transitional, and local phases. These phases are executed in the original design space and two subspaces, respectively. The global phase employs global surrogates for optimization and sampling, while the transitional phase uses a self-organizing map to create a subspace where local surrogates are constructed and optimized. The local phase utilizes the current best sample to construct another subspace, where a local search is performed. Additionally, a multi-surrogate collaboration mechanism is integrated into DMSCSR, enhancing the accuracy of the approximate optimization problems by leveraging multiple types of surrogates. To balance exploration and exploitation, DMSCSR adopts the optimal complex function–Voronoi method to generate additional samples. The effectiveness of DMSCSR is demonstrated on twenty-three mathematical and eight engineering benchmark problems. Compared with three state-of-the-art methods, DMSCSR exhibits superior performance. We also compare DMSCSR with its five variants to further investigate its properties. The results are analyzed, and the noticeable advantages of DMSCSR in solving BCOPs are further confirmed.