An integer programming model for obtaining cyclic quasi-difference matrices

Luis Martínez, María Merino and Juan Manuel Montoya

Operations Research Perspectives, 2023, vol. 10, issue C

Abstract: Orthogonal arrays are of great importance in mathematical sciences. This paper analyses a certain practical advantage of quasi-difference matrices over difference matrices to obtain orthogonal arrays with given parameters. We also study the existence of quasi-difference matrices over cyclic groups originating orthogonal arrays with t=2 and λ=1, proving their existence for some parameters sets. Moreover, we present an Integer Programming model to find such quasi-difference matrices and also a Bimodal Local Search algorithm to obtain them. We provide a conjecture related to the distributions of differences along rows and columns of arbitrary square matrices with entries in a cyclic group in positions outside the main diagonal which shows an intriguing symmetry, and we prove it when the matrix is a quasi-difference matrix.

Keywords: Integer programming; Bimodal Local Search; Orthogonal arrays; Automorphism groups; Quasi-difference matrices (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:oprepe:v:10:y:2023:i:c:s2214716022000318

DOI: 10.1016/j.orp.2022.100260

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