On the effects of locality in a permutation problem: The Sudoku Puzzle

We present an analysis of an application of Evolutionary Computation to the Sudoku Puzzle. In particular, we are interested in understanding the locality of the search operators employed, and the difficulty of the problem landscape. Treating the Sudoku puzzle as a permutation problem we analyse the locality of four permutation-based crossover operators, named One Cycle Crossover, Multi-Cycle Crossover, Partially Matched Crossover (PMX) and Uniform Swap Crossover. These were analysed using different crossover rates. Experimental evidence is found to support the hypothesis that PMX and Uniform Swap Crossover operators have better properties of locality relative to the other operators examined regardless of the crossover rates used. Fitness distance correlation, a well-known measure of hardness, is used to analyse problem difficulty and the results are consistent with the difficulty levels associated with the benchmark Sudoku puzzles analysed.