An Efficient Constraint-Based Local Search for Maximizing Water Retention on Magic Squares

Abstract

Water retention on magic square is a very recently introduced variation of magic square problem which has attracted a lot of attention from the research community over the years. Different approaches have been used to tackle this highly combinatorial optimization problem. In this paper, we have proposed an improved constraint-based local search approach that remedies all the identified shortcomings of the state-of-the-art technique. Several new methods such as greediness reduction technique, incremental calculation of the objective function and solving cycling problem through similarity checking have been incorporated within the proposed local search approach. Experimental results show that our proposed algorithm performs better than the existing technique with regards to solution quality and execution time.