On Simulated Annealing Dedicated to Maximin Latin Hypercube Designs.

The goal of our research was to enhance local search heuristics used to construct Latin Hypercube Designs. First, we introduce the textit{1D-move} perturbation to improve the space exploration performed by these algorithms. Second, we propose a new evaluation function $psi_{p,sigma}$ specifically targeting the Maximin criterion. Exhaustive series of experiments with Simulated Annealing, which we used as a typically well-behaving local search heuristics, confirm that our goal was reached as the result we obtained surpasses the best scores reported in the literature. Furthermore, the $psi_{p,sigma}$ function seems very promising for a wide spectrum of optimization problems through the Maximin criterion.