A Novel Rubik's Cube Problem Solver by Combining Group Theory and Genetic Algorithm

Alireza Darbandi, Seyed Abolghasem Mirroshandel

Abstract: Rubik’s cube is one of the most challenging problems in the field of evolutionary algorithm and group theory. Several algorithms have been considered to solve this problem in recent years. The solution of Rubik’s cube is different from other search algorithms. Finding the goal state is the target of the normal search algorithms. However, in this problem, the start (origin) and goal (destination) states are known and the challenge is to provide a convenient and efficient method for finding the shortest path between origin and destination. Existing solutions can be divided into several categories. In the first category, by dividing problem into sub-problems, researchers have tried to simplify and solve the cube. Apart from the divide and conquer method, the second category by creating a similar concept to the lookup tables tries to reduce computational costs with dynamic programming. Last category focused on the evolutionary algorithms to solve the problem. Regarding the fact that Rubik’s cube is one of the models in the field of group theory, we have proposed a novel method for solving this problem by a combination of group theory and genetic algorithm. The main idea of the proposed algorithm is finding and removing repeated states by group theory, because there are several repeated individuals (states) in different generations of genetic algorithm. The experimental results show a huge sieve in individuals per generations. In these experiments, by a significant reduction in the populations size, the speed of finding solutions has been increased by more than $$64\%$$ 64%.