On Simulated Annealing Dedicated to Maximin Latin Hypercube Designs

TL;DR

This paper introduces a new perturbation and evaluation function for simulated annealing to improve the construction of Maximin Latin Hypercube Designs, achieving superior results over existing methods.

Contribution

It proposes a novel 1D-move perturbation and a new evaluation function specifically for Maximin criteria, enhancing local search heuristics for Latin Hypercube Designs.

Findings

Surpassed best scores in literature for Latin Hypercube Designs

New evaluation function shows promise for various Maximin optimization problems

Enhanced exploration capabilities with 1D-move perturbation

Abstract

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.