Mode-Pursuing Sampling Method Using Discriminative Coordinate Perturbation for High-Dimensional Expensive Black-Box Optimization

Abstract

This article presents a novel mode-pursuing sampling method using discriminative coordinate perturbation (MPS-DCP) to further improve the convergence performance of solving high-dimensional, expensive, and black-box (HEB) problems. In MPS-DCP, a discriminative coordinate perturbation strategy is integrated into the original mode-pursuing sampling (MPS) framework for sequential sampling. During optimization, the importance of variables is defined by approximated global sensitivities, while the perturbation probabilities of variables are dynamically adjusted according to the number of optimization stalling iterations. Expensive points considering both optimality and space-filling property are selected from cheap points generated by perturbing the current best point, which balances between global exploration and local exploitation. The convergence property of MPS-DCP is theoretically analyzed. The performance of MPS-DCP is tested on several numerical benchmarks and compared with state-of-the-art metamodel-based design optimization methods for HEB problems. The results indicate that MPS-DCP generally outperforms the competitive methods regarding convergence and robustness performances. Finally, the proposed MPS-DCP is applied to a stepped cantilever beam design optimization problem and an all-electric satellite multidisciplinary design optimization (MDO) problem. The results demonstrate that MPS-DCP can find better feasible optima with the same or less computational cost than the competitive methods, which demonstrates its effectiveness and practicality in solving real-world engineering problems.