Constructing constrained-version of magic squares using selection hyper-heuristics
A square matrix of distinct numbers in which every row, column and both diagonals have the same total is referred to as a magic square. Constructing a magic square of a given order is considered a difficult computational problem, particularly when additional constraints are imposed. Hyper-heuristics...
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| Format: | Article |
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Oxford University Press
2014
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| Online Access: | https://eprints.nottingham.ac.uk/32177/ |
| _version_ | 1848794350268448768 |
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| author | Kheiri, Ahmed Özcan, Ender |
| author_facet | Kheiri, Ahmed Özcan, Ender |
| author_sort | Kheiri, Ahmed |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | A square matrix of distinct numbers in which every row, column and both diagonals have the same total is referred to as a magic square. Constructing a magic square of a given order is considered a difficult computational problem, particularly when additional constraints are imposed. Hyper-heuristics are emerging high-level search methodologies that explore the space of heuristics for solving a given problem. In this study, we present a range of effective selection hyper-heuristics mixing perturbative low-level heuristics for constructing the constrained version of magic squares. The results show that selection hyper-heuristics, even the non-learning ones deliver an outstanding performance, beating the best-known heuristic solution on average. |
| first_indexed | 2025-11-14T19:14:48Z |
| format | Article |
| id | nottingham-32177 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:14:48Z |
| publishDate | 2014 |
| publisher | Oxford University Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-321772020-05-04T16:42:31Z https://eprints.nottingham.ac.uk/32177/ Constructing constrained-version of magic squares using selection hyper-heuristics Kheiri, Ahmed Özcan, Ender A square matrix of distinct numbers in which every row, column and both diagonals have the same total is referred to as a magic square. Constructing a magic square of a given order is considered a difficult computational problem, particularly when additional constraints are imposed. Hyper-heuristics are emerging high-level search methodologies that explore the space of heuristics for solving a given problem. In this study, we present a range of effective selection hyper-heuristics mixing perturbative low-level heuristics for constructing the constrained version of magic squares. The results show that selection hyper-heuristics, even the non-learning ones deliver an outstanding performance, beating the best-known heuristic solution on average. Oxford University Press 2014-03-01 Article PeerReviewed Kheiri, Ahmed and Özcan, Ender (2014) Constructing constrained-version of magic squares using selection hyper-heuristics. The Computer Journal, 57 (3). pp. 469-479. ISSN 1460-2067 Computational design; Computational problem; Heuristic solutions; Hyper-heuristics; Hyperheuristic; late acceptance; Magic square; Square matrices Heuristic methods Number theory http://comjnl.oxfordjournals.org/content/57/3/469 doi:10.1093/comjnl/bxt130 doi:10.1093/comjnl/bxt130 |
| spellingShingle | Computational design; Computational problem; Heuristic solutions; Hyper-heuristics; Hyperheuristic; late acceptance; Magic square; Square matrices Heuristic methods Number theory Kheiri, Ahmed Özcan, Ender Constructing constrained-version of magic squares using selection hyper-heuristics |
| title | Constructing constrained-version of magic squares using selection hyper-heuristics |
| title_full | Constructing constrained-version of magic squares using selection hyper-heuristics |
| title_fullStr | Constructing constrained-version of magic squares using selection hyper-heuristics |
| title_full_unstemmed | Constructing constrained-version of magic squares using selection hyper-heuristics |
| title_short | Constructing constrained-version of magic squares using selection hyper-heuristics |
| title_sort | constructing constrained-version of magic squares using selection hyper-heuristics |
| topic | Computational design; Computational problem; Heuristic solutions; Hyper-heuristics; Hyperheuristic; late acceptance; Magic square; Square matrices Heuristic methods Number theory |
| url | https://eprints.nottingham.ac.uk/32177/ https://eprints.nottingham.ac.uk/32177/ https://eprints.nottingham.ac.uk/32177/ |