A multi-objective approach to maximin and near-orthogonal Latin hypercube designs using good lattice points and genetic algorithms

Latin hypercube design (LHD), a prominent topic in computer experiments, aims to provide design points with optimal space-filling properties and minimal correlation coefficients. However, few articles consider both aspects simultaneously. This paper proposes a practical optimization model that maximizes the minimum inter-point distance and minimizes the maximum absolute column correlation. To reduce computational cost, a search space with good space-filling properties is constructed using good lattice point (GLP) sets and transformations. An improved genetic algorithm is then developed to search this space with a correlation-feasible initialization, and the complete GLP-based optimization procedure is called NOGA. The resulting design is optimal within the constructed GLP-based candidate set. The method allows users to adjust the tradeoff between space-filling and orthogonality via two weight parameters. Numerical comparisons with state-of-the-art methods and simulation studies on the Borehole and OTL circuit functions demonstrate that NOGA produces designs that are highly competitive in both criteria while remaining computationally feasible for moderate to large problem sizes.