On Solving the Rubik's Cube with Domain-Independent Planners Using Standard Representations

TL;DR

This paper introduces a standard PDDL representation for the Rubik's Cube, enabling the use of general-purpose planners and comparing their performance with specialized approaches, revealing trade-offs in plan optimality and problem-solving efficiency.

Contribution

It presents the first PDDL encoding of the Rubik's Cube, facilitating broader accessibility and comparison of planning methods for this complex puzzle.

Findings

DeepCubeA solves all problems but with 78.5% optimal plans.

Scorpion with SAS+ solves 61.50% of problems optimally.

FastDownward with PDDL solves 56.50% of problems, with 79.64% optimal plans.

Abstract

Rubik's Cube (RC) is a well-known and computationally challenging puzzle that has motivated AI researchers to explore efficient alternative representations and problem-solving methods. The ideal situation for planning here is that a problem be solved optimally and efficiently represented in a standard notation using a general-purpose solver and heuristics. The fastest solver today for RC is DeepCubeA with a custom representation, and another approach is with Scorpion planner with State-Action-Space+ (SAS+) representation. In this paper, we present the first RC representation in the popular PDDL language so that the domain becomes more accessible to PDDL planners, competitions, and knowledge engineering tools, and is more human-readable. We then bridge across existing approaches and compare performance. We find that in one comparable experiment, DeepCubeA (trained with 12 RC actions) solves all problems with varying complexities, albeit only 78.5% are optimal plans. For the same problem set, Scorpion with SAS+ representation and pattern database heuristics solves 61.50% problems optimally, while FastDownward with PDDL representation and FF heuristic solves 56.50% problems, out of which 79.64% of the plans generated were optimal. Our study provides valuable insights into the trade-offs between representational choice and plan optimality that can help researchers design future strategies for challenging domains combining general-purpose solving methods (planning, reinforcement learning), heuristics, and representations (standard or custom).