Design and comparison of two evolutionary approaches for solving the Rubik's cube

Abstract

Solutions calculated by Evolutionary Algorithms have come to surpass exact methods for solving various problems. The Rubik's Cube multiobjective optimization problem is one such area. In this paper we design, benchmark and compare two different evolutionary approaches to solve the Rubik's Cube. One is based on the work of Michael Herdy using predefined swapping and flipping algorithms, the other adapting the Thistlethwaite Algorithm. The latter is based on group theory, transforming the problem of solving the Cube into four subproblems. We give detailed information about realizing those Evolutionary Algorithms regarding selection method, fitness function and mutation operators. Finally, both methods are benchmarked and compared to enable an interesting view of solution space size and exploration/exploitation in regard to the Rubik's Cube. © 2010 Springer-Verlag.