Formula- and Memory-based Heuristics In Video-game Pathfinding

The performance of a heuristic search depends substantially on the quality of its heuristic functions. A preferred heuristic is accurate, fast to query, and takes little memory. Recent research has explored two routes for building highperformance heuristics. Memory-based heuristics use a precomputed database containing optimal distances between a set of pivot states and all other states in the search graph. More pivot states tend to increase heuristic accuracy while slowing down heuristic computation and increasing memory cost. Alternatively, formula-based heuristics produced via program synthesis capture information about the search graph in short, human-readable formulae. These formulae have negligible memory cost and are fast to query, but generally perform worse than a memory-based heuristic. This paper presents the first empirical comparison between the two approaches for pathfinding. We find that formulabased heuristics can yield better performance than memorybased heuristics with a small number of pivots while being still more compact. With more pivots memory-based heuristics yield better speed-ups but take orders of magnitude more memory. We then investigate the degradation of search performance as the map changes and find that the performance of formula-based heuristics degrades more gracefully than that of memory-based heuristics.