Counterexample-Guided Cartesian Abstraction Refinement

Abstract

Counterexample-guided abstraction refinement (CEGAR) is a method for incrementally computing abstractions of transition systems. We propose a CEGAR algorithm for computing abstraction heuristics for optimal classical planning. Starting from a coarse abstraction of the planning task, we iteratively compute an optimal abstract solution, check if and why it fails for the concrete planning task and refine the abstraction so that the same failure cannot occur in future iterations. A key ingredient of our approach is a novel class of abstractions for classical planning tasks that admits efficient and very fine-grained refinement. Our implementation performs tens of thousands of refinement steps in a few minutes and produces heuristics that are often significantly more accurate than pattern database heuristics of the same size.

A Comparison of Cost Partitioning Algorithms for Optimal Classical Planning

“…Experimentally, we report results for pattern databases that are derived systematically (Pommerening, Röger, and Helmert 2013) and by hill climbing (Haslum et al 2007), for Cartesian abstractions (Seipp and Helmert 2013), and for landmark heuristics (Karpas and Domshlak 2009), showing that earlier evidence for the strength of saturated cost partitioning for Cartesian abstractions (Seipp, Keller, and Helmert 2017) generalizes to all considered kinds of heuristics.…”

“…If h is an abstraction heuristic, the saturated cost of operator o is the maximum over h(s) − h(s ) for all abstract state transitions s → s induced by o. For explicit-state abstraction heuristics based on pattern databases or Cartesian abstraction (Ball, Podelski, and Rajamani 2001;Seipp and Helmert 2013), this can be computed at negligible overhead during the construction of the heuristic. The same is true for merge-and-shrink heuristics not using label reduction (Sievers, Wehrle, and Helmert 2014).…”

“…Next, we consider Cartesian abstractions (Seipp and Helmert 2013) of the landmark and goal task decompositions (Seipp and Helmert 2014). Table 3 holds the domainwise and total coverage numbers for h UCP , h OUCP , h GZOCP , h SCP and h OCP on Cartesian abstractions.…”

Counterexample-Guided Abstraction Refinement for Pattern Selection in Optimal Classical Planning

“…The second technique is saturated cost partitioning (SCP) (Seipp and Helmert 2013), which has been successfully used for Cartesian abstractions and PDB heuristics (Seipp, Keller, and Helmert 2017a). Like greedy zero-one cost partitioning, SCP greedily distributes the costs among the heuristics in a given order, but in a more intelligent way that avoids using up costs that do not contribute to the heuristic value.…”

Incremental Search for Counterexample-Guided Cartesian Abstraction Refinement

“…The most common method for solving optimal classical planning tasks is to use A * (Hart, Nilsson, and Raphael 1968) with an admissible heuristic (Pearl 1984). One way of obtaining such a heuristic is counterexample-guided abstraction refinement (CEGAR) for Cartesian abstractions (Clarke et al 2003;Seipp and Helmert 2013;2018). Algorithm 1 shows pseudo-code for the CEGAR algorithm.…”