Potential Heuristics: Weakening Consistency Constraints

In classical planning, admissible potential heuristics are computed by solving linear programs (LPs) with constraints expressing consistency and goal-awareness of the heuristic. Potential heuristics can return negative estimates. So, given a potential heuristic h^P, the actual heuristic used in search is another heuristic defined as h^P_0+(s) = max(h^P(s),0) for every reachable state s. In this paper, we reformulate the LP constraints for consistency of h^P so that they ensure consistency of h^P_0+ instead. This leads to more informative heuristics with positive impact on the overall performance in exchange for a more time and memory demanding computation using mixed integer linear programs instead of LPs.