The Optimization of Space-Filling and Orthogonality for Latin Hypercube Design Using a Local Search-Based NSGA-II

作     者：Hu, Xiaoru Ma, Ping Li, Shuang Li, Wei Yang, Ming 

作者机构：Harbin Inst Technol Control & Simulat Ctr Harbin 150000 Peoples R China Natl Key Lab Modeling & Simulat Complex Syst Harbin 150000 Peoples R China 

出 版 物：《JOURNAL OF STATISTICAL THEORY AND PRACTICE》 (J. Stat. Theory Pract.)

年 卷 期：2025年第19卷第1期

页      面：1-26页

学科分类：07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：National Natural Science Foundation of China National Natural Science Foundation of China 

主　　题：Latin hypercube design Space-filling Orthogonality Multi-objective optimization 

摘      要：Latin hypercube design (LHD), as a stratified sampling method, is widely employed in the design of experiments. To improve the space-filling and orthogonality of LHD, this paper proposes an efficient multi-objective optimization method, denoted as local search-based non-dominated sorting genetic algorithm II (LSNSGA-II). Compared with the vanilla non-dominated sorting genetic algorithm II (NSGA-II), LSNSGA-II utilizes a full-factors-based simulated binary crossover operator and a local search strategy to enhance its search ability. Furthermore, a cyclic elimination strategy in the elitist selection phase is also adopted to augment the uniformity of the Pareto fronts. Comparative experiments were conducted against various LHDs with different dimensions and numbers of sampling points, and the results demonstrate that the proposed LSNSGA-II significantly outperforms other peer algorithms from the perspectives of Hypervolume metric and computational efficiency, particularly suitable for high-dimensional and low-sampling scenarios.