  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).
