An Evolutionary Approach for Solving the Rubik’s Cube Incorporating Exact Methods
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 work we present an evolutionary approach to solve the Rubik’s Cube with a low number of moves by building upon the classic Thistlethwaite’s approach. We provide a group theoretic analysis of the subproblem complexity induced by Thistlethwaite’s group transitions and design an Evolutionary Algorithm from the ground up including detailed derivation of our custom fitness functions. The implementation resulting from these observations is thoroughly tested for integrity and random scrambles, revealing performance that is competitive with exact methods without the need for pre-calculated lookup-tables.
Unable to display preview. Download preview PDF.
- 1.Borschbach, M., Grelle, C.: Empirical Benchmarks of a Genetic Algorithm Incorporating Human Strategies. Technical Report, University of Applied Sciences, Bergisch Gladbach (2009)Google Scholar
- 3.El-Sourani, N.: Design and Benchmark of different Evolutionary Approaches to Solve the Rubiks Cube as a Discrete Optimization Problem. Diploma Thesis, WWU Muenster, Germany (2009)Google Scholar
- 5.Frey, A., Singmaster, D.: Handbook of Cubic Math. Enslow, Hillside (1982)Google Scholar
- 6.Herdy, M., Patone, G.: Evolution Strategy in Action, 10 ES-Demonstrations. Technical Report, International Conference on Evolutionary Computation (1994)Google Scholar
- 7.Kociemba, H.: Cube Explorer, http://kociemba.org/Cube.htm
- 9.Reid, M.: Cube Lovers Mailing List, http://www.math.rwth-aachen.de/~Martin.Schoenert/Cube-Lovers/Index_by_Author.html
- 10.Rokicki, T.: Twenty-Five Moves Suffice for Rubik’s Cube, http://Cubezzz.homelinux.org/drupal/?q=node/view/121
- 12.Singmaster, D.: Notes on Rubik’s Magic Cube. Enslow, Hillside (1981)Google Scholar
- 13.Thistlethwaite, M.B.: The 45-52 Move Strategy. London CL VIII (1981)Google Scholar
- 14.Zitzler, E.: Evolutionary Algorithms for Multiobjective Optimization: Methods and Applications. Penn State (1999)Google Scholar