An integer programming model for obtaining cyclic quasi-difference matrices
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 o...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-01-01
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| Series: | Operations Research Perspectives |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2214716022000318 |
| _version_ | 1797801056420233216 |
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| author | Luis Martínez María Merino Juan Manuel Montoya |
| author_facet | Luis Martínez María Merino Juan Manuel Montoya |
| author_sort | Luis Martínez |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-13T04:44:36Z |
| format | Article |
| id | doaj.art-901c02f8e5a14e96bc4e9e34feeb8e36 |
| institution | Directory Open Access Journal |
| issn | 2214-7160 |
| language | English |
| last_indexed | 2024-03-13T04:44:36Z |
| publishDate | 2023-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Operations Research Perspectives |
| spelling | doaj.art-901c02f8e5a14e96bc4e9e34feeb8e362023-06-19T04:28:17ZengElsevierOperations Research Perspectives2214-71602023-01-0110100260An integer programming model for obtaining cyclic quasi-difference matricesLuis Martínez0María Merino1Juan Manuel Montoya2University of the Basque Country UPV/EHU, Department of Mathematics, 48080 Bilbao, Spain; Corresponding author.University of the Basque Country UPV/EHU, Department of Mathematics, 48080 Bilbao, Spain; Basque Center for Applied Mathematics (BCAM), Alameda Mazarredo 14, 48009 Bilbo, Bizkaia, SpainUniversity of the Basque Country UPV/EHU, Department of Mathematics, 48080 Bilbao, Spain; University of Pamplona, Faculty of Basic Sciences, Pamplona, ColombiaOrthogonal 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.http://www.sciencedirect.com/science/article/pii/S2214716022000318Integer programmingBimodal Local SearchOrthogonal arraysAutomorphism groupsQuasi-difference matrices |
| spellingShingle | Luis Martínez María Merino Juan Manuel Montoya An integer programming model for obtaining cyclic quasi-difference matrices Operations Research Perspectives Integer programming Bimodal Local Search Orthogonal arrays Automorphism groups Quasi-difference matrices |
| title | An integer programming model for obtaining cyclic quasi-difference matrices |
| title_full | An integer programming model for obtaining cyclic quasi-difference matrices |
| title_fullStr | An integer programming model for obtaining cyclic quasi-difference matrices |
| title_full_unstemmed | An integer programming model for obtaining cyclic quasi-difference matrices |
| title_short | An integer programming model for obtaining cyclic quasi-difference matrices |
| title_sort | integer programming model for obtaining cyclic quasi difference matrices |
| topic | Integer programming Bimodal Local Search Orthogonal arrays Automorphism groups Quasi-difference matrices |
| url | http://www.sciencedirect.com/science/article/pii/S2214716022000318 |
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