From Non-Negative to General Operator Cost Partitioning

Abstract

Operator cost partitioning is a well-known technique to make admissible heuristics additive by distributing the operator costs among individual heuristics. Planning tasks are usually defined with non-negative operator costs and therefore it appears natural to demand the same for the distributed costs. We argue that this requirement is not necessary and demonstrate the benefit of using general cost partitioning. We show that LP heuristics for operator-counting constraints are cost-partitioned heuristics and that the state equation heuristic computes a cost partitioning over atomic projections. We also introduce a new family of potential heuristics and show their relationship to general cost partitioning.

Higher-Dimensional Potential Heuristics for Optimal Classical Planning

“…Katz and Domshlak (2010) show how the optimal operator cost partitioning (OCP) can be computed in polynomial time for a large family of abstraction heuristics. Pommerening et al (2015) show that an admissible and consistent potential heuristic over all atomic features that achieves the maximal initial heuristic value corresponds to an OCP over atomic projection heuristics. Here, we extend this result to all potential heuristics that use the abstract states of a set of abstractions as features.…”

“…Potential heuristics (Pommerening et al 2015) are a family of declarative heuristic functions for state-space search. They fix the form of the heuristic to be a weighted sum over a set of features.…”

“…Previous work on admissible potential heuristics is limited to atomic features, which consider the value of a single state variable in a factored state representation. Pommerening et al (2015) show that admissible and consistent potential heuristics over atomic features can be characterized by a compact set of linear constraints. Seipp, Pommerening, and Helmert (2015) introduce several objective functions to select the best potential heuristic according to different criteria.…”

“…We consider SAS + planning tasks (Bäckström and Nebel 1995) in transition normal form (TNF) (Pommerening and Helmert 2015). A planning task is a tuple Π = V, O, s I , s with the following components.…”

“…We denote this set of variables by vars(o). Considering only tasks in TNF does not limit generality, since there is an efficient transformation from general SAS + tasks into equivalent tasks in TNF (Pommerening and Helmert 2015).…”