Optimal retrieval in puzzle-based storage with heuristic search and tabulation

Puzzle-based storage (PBS) systems provide a space efficient solution for storage and retrieval of unit loads (e.g., cars, boxes) in the very land-expensive urban environment. In this work, we formulate a highly generic optimal retrieval problem, consisting of any number of loads to be retrieved, and an arbitrary number of I/O points and empty locations (escorts) on a two-dimensional lattice graph. We theoretically analyze the characteristics of the problem and propose a set of graph search algorithms to tackle the inherent complexities thereof. In contrast to existing work in the field, we investigate the runtime-memory tradeoff pertaining to our problem, highlighting the possible benefits and limitations of our heuristic search and tabulation techniques. Our results demonstrate that our algorithms are capable of optimally solving moderate-sized PBS problems using a limited amount of memory and in a reasonable amount of time.