An evolutionary approach for solving the rubik's cube incorporating exact methods

Authors:
Nail El-Sourani;Sascha Hauke;Markus Borschbach
Affiliations:
Faculty of Computer Science, Chair of Optimized Systems, University of Applied Sciences, Bergisch Gladbach, Germany;Faculty of Computer Science, Chair of Optimized Systems, University of Applied Sciences, Bergisch Gladbach, Germany;Faculty of Computer Science, Chair of Optimized Systems, University of Applied Sciences, Bergisch Gladbach, Germany
Venue:
EvoApplicatons'10 Proceedings of the 2010 international conference on Applications of Evolutionary Computation - Volume Part I
Year:
2010

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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 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.