Product geometric crossover for the Sudoku puzzle

Geometric crossover is a representation-independent definition of crossover based on the distance of the search space interpreted as a metric space. It generalizes the traditional crossover for binary strings and other important recombination operators for the most used representations. Using a distance tailored to the problem at hand, the abstract definition of crossover can be used to design new problem specific crossovers that embed problem knowledge in the search. In recent work, we have introduced the important notion of product geometric crossover that enables the construction of new geometric crossovers combining preexisting geometric crossovers in a simple way. In this paper, we use it to design an evolutionary algorithm to solve the Sudoku puzzle. The different types of constraints make Sudoku an interesting study case for crossover design. We conducted extensive experimental testing and found that, on medium and hard problems, the new geometric crossovers perform significantly better than hill-climbers and mutations alone.