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An integer programming model for obtaining cyclic quasi-difference matrices

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  • Martínez, Luis
  • Merino, María
  • Montoya, Juan Manuel

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.

Suggested Citation

  • Martínez, Luis & Merino, María & Montoya, Juan Manuel, 2023. "An integer programming model for obtaining cyclic quasi-difference matrices," Operations Research Perspectives, Elsevier, vol. 10(C).
    • Handle: RePEc:eee:oprepe:v:10:y:2023:i:c:s2214716022000318
    DOI: 10.1016/j.orp.2022.100260
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    References listed on IDEAS

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    1. Alberto Seeger & Mounir Torki, 2014. "Centers of sets with symmetry or cyclicity properties," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 716-738, July.
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