An analysis of Harmony Search for solving Sudoku puzzles

Abstract

The Harmony Search metaheuristic has been used to solve many different optimization problems. Several papers examined its effectiveness for solving Sudoku puzzles. Another paper claims that it is ineffective for solving Sudoku puzzles and further that the method itself lacks novelty compared to other evolutionary algorithms. Our paper analyzes the search process in harmony search when applied to a specific Sudoku puzzle examined in earlier research. The basic harmony search procedure is re-implemented and tested to evaluate its performance and verify its applicability to the specific example. We found that the while the criticisms of the method for this problem are valid, that the performance can be improved with a rather simple modification. First, we propose a new objective function for the search procedure. This proposed objective function facilitates the search method to find a proper solution. Second, the modified version of the harmony search, where harmony search is combined with local search is introduced and analyzed for its contribution of ‘improvisation’ in harmony search procedure by comparing the performance of local search and the modified search. For a specific problem, the modified version of harmony search generates a unique solution with new objective function in favorable time. Then extended experiments were performed for various Sudoku problems. We find that while the modified search procedure produces solutions more quickly, that it suffers the same issue that the original method has in that it sometimes fails to find a feasible solution.