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

Copyright © The British Computer Society 2013This is a pre-copyedited, author-produced PDF of an article accepted for publication in the Computer Journal following peer review. The version of record in Volume 57, Issue 3, pp. 469-479 is available online at: http://dx.doi.org/10.1093/comjnl/bxt130A 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