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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Main Authors: Kheiri, Ahmed, Özcan, Ender
Format: Article
Published: Oxford University Press 2014
Subjects:
Online Access:https://eprints.nottingham.ac.uk/32177/
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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.
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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/