Hybrid Optimation for Constructing Uniform Designs

Abstract

This work presents hybrid optimization methods based on the Threshold Accepting algorithm, Local Search Process, and Variable Neighborhood Search algorithm for the construction of uniform experimental designs. Optimization methods are among the most effective tools for solving complex combinatorial problems. Uniform experimental design is a type of space-filling design introduced in the 1980s by Fang and Wang, commonly used in computer experiments. It seeks to fill the unit cube as uniformly as possible with a fixed number of points. The search for uniform design is presented as a combinatorial problem where the number of possible solutions dramatically increases with the number of runs and factors, making computation time very expensive. The main objective in applying hybrid optimization is to diversify and intensify the search space in order to obtain an optimum close to the true one. Firstly, we introduce some theories of uniform designs, such as the uniform criterion or discrepancy, its requirements, and its relation to other criteria. Then, we describe hybrid optimization methods and their application in constructing uniform designs. Finally, through simulation examples, we compare the discrepancies and computational times of these methods.