Isomorphic Solutions of the N-queens Problem - uddin, Sawal (Prosiding SNATIKA Vol 01 (2011), 2011)
The N-queens problem is a classic example in mathematics as well as computer science that receives many attentions from researchers for nearly two centuries. Despite its usefulness in teaching computational intelligence algorithms, another interesting features of the N-queens problem is the notion of isomorphism and transformation groups. Once a solution of the N-queens problem is found, the isomorphic solutions can be transformed easily by performing two kinds of permutations, i.e. rotation and reflection. In this paper, we proposed a two-stage approach to find the isomorphic solutions to the N-queens problem. In the first stage, a genetic algorithm is used to find a solution of the N-queens problem. In the second stage, the solution is transformed into seven isomorphic solutions. Using this approach, a complete solution for the N-queens problem can be obtained. The results obtained show how the complete isomorphic solutions of 5-, 6-, 7-, and 8-queens can be generated in a very short execution time. Â  Keyword: object-oriented approach, genetic algorithm, N-queens problem, isomorphism.