Dual surrogate-based optimization for expensive black-box multimodal problems using Louvain-identified niches for automatic space reduction

This paper presents a dual surrogate-based optimization method for expensive black-box multimodal problems using Louvain-identified niches for automatic space reduction (DSLNSR). To accurately identify potential regions and improve search efficiency, a novel automatic space reduction strategy, based on niches identified using the Louvain method, is introduced. Kriging and radial basis function models are employed to approximate the black-box function, and the proposed space reduction strategy is then applied to construct two distinct search subspaces for the surrogates. Two search strategies are employed in DSLNSR. The first strategy combines the two constructed subspaces and conducts both exploration and exploitation within the merged subspace. The second strategy performs exploitation separately within each subspace generated by the two surrogate models, then merges the subspaces for further exploration. Multistart optimization is utilized to perform exploration and exploitation within these subspaces. DSLNSR alternates between these two search strategies for efficient sampling. When the algorithm stagnates, an effective global exploration strategy is invoked to explore sparsely sampled regions, helping the algorithm escape local valleys. The performance of DSLNSR is evaluated on 18 standard benchmark functions, and the results demonstrate its effectiveness and superior performance compared to five peer algorithms. Additionally, several properties of the proposed method are also analyzed. Furthermore, DSLNSR is tested on several complex high-dimensional multimodal functions, where the results indicate that it outperforms other published algorithms in solving such challenging problems. Finally, the practicality of DSLNSR is validated on a real-world engineering problem.