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

Kheiri, Ahmed; Özcan, Ender

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.

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

• Journal Article Type: Article
• Publication Date: Mar 1, 2014
• Deposit Date: Mar 10, 2016
• Publicly Available Date: Mar 10, 2016
• 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
• 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
• Public URL: http://eprints.nottingham.ac.uk/id/eprint/32177
• 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.nottingham.ac.uk/end_user_agreement.pdf