Integer-valued Particle Swarm Optimization applied to Sudoku puzzles

In this paper we develop a variation of the particle swarm optimization (PSO) algorithm that is tailored to discrete optimization problems. We focus on solving Sudoku puzzles but the ideas can be extended to other problems with discrete solutions. We compare our PSO-based algorithm to the classic PSO and to a (mu+lambda) evolutionary strategy (ES) for 50 puzzles and find that the PSO algorithms do much worse than the ES. We then consider why PSO does not do well on this type of problem.