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Constructing constrained-version of magic squares using selection hyper-heuristics

Kheiri, Ahmed; Özcan, Ender

Authors

Ahmed Kheiri A.Kheiri@exeter.ac.uk

Ender Özcan exo@cs.nott.ac.uk

Abstract

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.

Journal Article Type Article
Publication Date Mar 1, 2014
Journal The Computer Journal
Print ISSN 0010-4620
Electronic ISSN 1460-2067
Publisher Oxford University Press (OUP)
Peer Reviewed Peer Reviewed
Volume 57
Issue 3
Institution Citation Kheiri, A., & Özcan, E. (2014). Constructing constrained-version of magic squares using selection hyper-heuristics. Computer Journal, 57(3), doi:10.1093/comjnl/bxt130
DOI https://doi.org/10.1093/comjnl/bxt130
Keywords Computational design; Computational problem; Heuristic solutions; Hyper-heuristics; Hyperheuristic; late acceptance; Magic square; Square matrices, Heuristic methods, Number theory
Publisher URL http://comjnl.oxfordjournals.org/content/57/3/469
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf




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