A Bit-Parallel Tabu Search Algorithm for Finding Es2-Optimal and Minimax-Optimal Supersaturated Designs
We prove the equivalence of two-symbol supersaturated designs (SSDs) with N (even) rows, m columns, and smax=4t+i, where i∈0,2 and t∈ℤ≥0 and resolvable incomplete block designs (RIBDs) whose any two blocks intersect in at most N+4t+i/4 points. Using this equivalence, we formulate the search for two-...
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Wiley
2023-01-01
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| Series: | Computational and Mathematical Methods |
| Online Access: | http://dx.doi.org/10.1155/2023/9431476 |
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| author | Luis B. Morales Dursun A. Bulutoglu |
| author_facet | Luis B. Morales Dursun A. Bulutoglu |
| author_sort | Luis B. Morales |
| collection | DOAJ |
| description | We prove the equivalence of two-symbol supersaturated designs (SSDs) with N (even) rows, m columns, and smax=4t+i, where i∈0,2 and t∈ℤ≥0 and resolvable incomplete block designs (RIBDs) whose any two blocks intersect in at most N+4t+i/4 points. Using this equivalence, we formulate the search for two-symbol Es2-optimal and minimax-optimal SSDs with smax∈2,4,6 as a search for RIBDs whose blocks intersect accordingly. This allows developing a bit-parallel tabu search (TS) algorithm. The TS algorithm found Es2-optimal and minimax-optimal SSDs achieving the sharpest known Es2 lower bound with smax∈2,4,6 of sizes N,m=16,25, (16, 26), (16, 27), (18, 23), (18, 24), (18, 25), (18, 26), (18, 27), (18, 28), (18, 29), (20, 21), (22, 22), (22, 23), (24, 24), and (24, 25). In each of these cases, no such SSD could previously be found. |
| format | Article |
| id | doaj-art-c988b721ee904a2a9c0fc0d9356b890d |
| institution | Kabale University |
| issn | 2577-7408 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
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| series | Computational and Mathematical Methods |
| spelling | doaj-art-c988b721ee904a2a9c0fc0d9356b890d2025-02-03T06:45:01ZengWileyComputational and Mathematical Methods2577-74082023-01-01202310.1155/2023/9431476A Bit-Parallel Tabu Search Algorithm for Finding Es2-Optimal and Minimax-Optimal Supersaturated DesignsLuis B. Morales0Dursun A. Bulutoglu1Unidad AcadAir Force Institute of TechnologyWe prove the equivalence of two-symbol supersaturated designs (SSDs) with N (even) rows, m columns, and smax=4t+i, where i∈0,2 and t∈ℤ≥0 and resolvable incomplete block designs (RIBDs) whose any two blocks intersect in at most N+4t+i/4 points. Using this equivalence, we formulate the search for two-symbol Es2-optimal and minimax-optimal SSDs with smax∈2,4,6 as a search for RIBDs whose blocks intersect accordingly. This allows developing a bit-parallel tabu search (TS) algorithm. The TS algorithm found Es2-optimal and minimax-optimal SSDs achieving the sharpest known Es2 lower bound with smax∈2,4,6 of sizes N,m=16,25, (16, 26), (16, 27), (18, 23), (18, 24), (18, 25), (18, 26), (18, 27), (18, 28), (18, 29), (20, 21), (22, 22), (22, 23), (24, 24), and (24, 25). In each of these cases, no such SSD could previously be found.http://dx.doi.org/10.1155/2023/9431476 |
| spellingShingle | Luis B. Morales Dursun A. Bulutoglu A Bit-Parallel Tabu Search Algorithm for Finding Es2-Optimal and Minimax-Optimal Supersaturated Designs Computational and Mathematical Methods |
| title | A Bit-Parallel Tabu Search Algorithm for Finding Es2-Optimal and Minimax-Optimal Supersaturated Designs |
| title_full | A Bit-Parallel Tabu Search Algorithm for Finding Es2-Optimal and Minimax-Optimal Supersaturated Designs |
| title_fullStr | A Bit-Parallel Tabu Search Algorithm for Finding Es2-Optimal and Minimax-Optimal Supersaturated Designs |
| title_full_unstemmed | A Bit-Parallel Tabu Search Algorithm for Finding Es2-Optimal and Minimax-Optimal Supersaturated Designs |
| title_short | A Bit-Parallel Tabu Search Algorithm for Finding Es2-Optimal and Minimax-Optimal Supersaturated Designs |
| title_sort | bit parallel tabu search algorithm for finding es2 optimal and minimax optimal supersaturated designs |
| url | http://dx.doi.org/10.1155/2023/9431476 |
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