Portability and Explainability of Synthesized Formula-based Heuristics

Heuristic search is a key component of automated planning and pathfinding. It is guided by a heuristic function which estimates remaining solution cost. Traditionally heuristic functions for pathfinding have been human-designed or pre-computed for a specific search graph. The former tend to be compact, human-readable but generic. The latter offer better guidance but require per-graph pre-computation and have a substantial memory cost. We aim to retain compactness and readability of human-designed heuristics and increase their performance. We adopt the recently published approach of representing heuristic functions as algebraic formulae and automatically synthesizing them for video-game maps. Whereas published work merely randomly sampled the space of formula-based heuristic functions, we implement and evaluate a parameterized synthesis algorithm that unifies and generalizes the stochastic sampling, simulated annealing and a basic genetic algorithm. We tune the parameters for better synthesis performance and then, using maps from multiple video games, show that heuristics synthesized for maps from one game still outperform the baseline search (A* with weighted Manhattan distance) on maps from a different game. We analyze a frequently synthesized formula and explain how, despite having a higher error than the Manhattan distance, it takes advantage of the structure in video-game pathfinding problems and speeds up A*