On Simulated Annealing Dedicated to Maximin Latin Hypercube Designs
This work addresses optimization problems in experimental design, particularly for Maximin criterion applications, but appears incremental as it builds on existing simulated annealing methods.
The researchers tackled the problem of constructing Latin Hypercube Designs by enhancing local search heuristics with a new perturbation method and evaluation function, resulting in scores that surpass the best reported in the literature.
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 $ψ_{p,σ}$ 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 $ψ_{p,σ}$ function seems very promising for a wide spectrum of optimization problems through the Maximin criterion.