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Erscheinungsjahr: 
2023
Quellenangabe: 
[Journal:] Operations Research Perspectives [ISSN:] 2214-7160 [Volume:] 10 [Article No.:] 100260 [Year:] 2023 [Pages:] 1-6
Verlag: 
Elsevier, Amsterdam
Zusammenfassung: 
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.
Schlagwörter: 
Automorphism groups
Bimodal Local Search
Integer programming
Orthogonal arrays
Quasi-difference matrices
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