Optimize Planning Heuristics to Rank, not to Estimate Cost-to-Goal

Figure 1: Problem instance where perfect heuristic is not strictly optimally efficient with GBFS. However, the path (A, C,D, E) has cost 10 instead of 11 . Then h is a perfect ranking for GBFS on Γ. Proof. We carry the proof by induction with respect to the number of expanded states. Let's now make the induction step and assume the theorem holds for the first A 0 B 1 C 1 D 2 A 1 1 9 9 1 Figure 2: Problem instance where optimally efficient heuristic does not exists for GBFS.