Data-driven multi-phase optimization for expensive black-box problems via enhanced niche identification and tabu subspace filtering

This paper presents a data-driven multi-phase optimization method for expensive black-box problems via enhanced niche identification and tabu subspace filtering (DMENTS). DMENTS conducts optimization across three phases: global, promising, and local, each corresponding to a search in the global design space, the promising subspace, and the local subspace, respectively. The promising subspace represents a potential region within the design space that enables more efficient search, avoiding ineffective exploration in less important areas. The local subspace, constructed from the current best sample, is used to further refine this sample. In each iteration of the three phases, new samples are obtained by optimizing acquisition functions. An enhanced niche identification technique is proposed to perform more accurate multistart optimization on acquisition functions for new sample generation. Moreover, to prevent invalid sampling in well-exploited regions, a tabu subspace filtering strategy is introduced to filter out candidate points located in well-exploited valleys, preventing them from being selected as new samples and reducing computational resource waste. Additionally, when the algorithm stagnates, a cluster-based global exploration method is invoked to escape from local valleys. We also extend DMENTS to solve problems with black-box constraints. The proposed algorithm is tested on 19 unconstrained and 10 constrained benchmark problems, demonstrating remarkable performance compared to other peer methods. Furthermore, the practicality of DMENTS is further validated through two real-world engineering applications, namely unmanned underwater vehicle (UUV) shape optimization and lightweight UUV hull design.