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

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.