The Rubik Cube and GP Temporal Sequence Learning: An Initial Study

Abstract

The 3 × 3 Rubik cube represents a potential benchmark for temporal sequence learning under a discrete application domain with multiple actions. Challenging aspects of the problem domain include the large state space and a requirement to learn invariances relative to the specific colours present the latter element of the domain making it difficult to evolve individuals that learn ‘macro-moves’ relative tomultiple cube configurations. An initial study is presented in thiswork to investigate the utility ofGenetic Programming capable of layered learning and problem decomposition. The resulting solutions are tested on 5,000 test cubes, of which specific individuals are able to solve up to 350 (7 percent) cube configurations and population wide behaviours are capable of solving up to 1,200 (24 percent) of the test cube configurations. It is noted that the design options for generic fitness functions are such that users are likely to face either reward functions that are very expensive to evaluate or functions that are very deceptive. Addressing this might well imply that domain knowledge is explicitly used to decompose the task to avoid these challenges. This would augment the described generic approach currently employed for Layered learning/ problem decomposition.