Optimizing Two-level Orthogonal Arrays for Estimating Main Effects and Pre-specified Two-factor Interactions

Abstract

In this work, we are interested in constructing D-optimal orthogonal arrays that allow joint estimation of main effects and some specified two-factor interactions. A hybrid algorithm that combines an enhanced stochastic evolutionary algorithm and a discrete particle swarm algorithm is proposed. We demonstrate the performance of the proposed algorithm by generating orthogonal arrays with different interaction set-ups, and then comparing with these designs obtained in the previous literatures. In addition to the numerical generating algorithm, we also study the upper bound of the determinant of the corresponding matrix for D-optimality based on our numerical results. Joint with Ray-Bing Chen (NCKU) and Chunfang Devon Lin (Queen’s University) Keywords: D-optimal designs, Hadamard matrices, orthogonal arrays, particle swarm optimization.