Data-driven constrained optimization using dual-surrogate collaboration and subspace exploration

Real-world engineering optimization problems often involve expensive black-box constraints, making them challenging to solve. This paper proposes a two-stage data-driven constrained optimization algorithm, named DCO-DSS, which integrates dual-surrogate collaboration and subspace exploration. DCO-DSS adopts a two-stage framework, where the first stage focuses on exploring the feasible region and the second stage searches for the global optimum. Each stage of DCO-DSS consists of two parts: global search and local search. In the global search, the algorithm explores the global design space using global surrogates. In the local search, a subspace exploration strategy is employed, where local surrogates are constructed and utilized for sampling. To facilitate efficient sampling, different auxiliary optimization subproblems (AOSPs) are designed based on surrogates in each part of both stages. To maximize the information gain during sampling and enhance sampling robustness, a dual-surrogate collaboration mechanism is introduced. When using a designed AOSP for sampling, the mechanism uses radial basis function (RBF) and Kriging models to dynamically construct two AOSPs with identical structures but different surrogates. Specifically, the first AOSP uses the surrogates with the top-ranked approximation accuracy, while the second uses the second-ranked models. The effectiveness of DCO-DSS is validated through 17 mathematical and 7 engineering benchmarks, showing superior performance compared to three peer algorithms. Additional ablation studies are conducted to analyze the contributions of different components in DCO-DSS. Finally, the algorithm is applied to a real-world engineering problem, demonstrating its practical applicability and effectiveness.