Merge-and-Shrink Abstraction

Abstract

RAZ NISSIM, Ben-Gurion University of the Negev, Israel Many areas of computer science require answering questions about reachability in compactly described discrete transition systems. Answering such questions effectively requires techniques to be able to do so without building the entire system. In particular, heuristic search uses lower-bounding ("admissible") heuristic functions to prune parts of the system known to not contain an optimal solution. A prominent technique for deriving such bounds is to consider abstract transition systems that aggregate groups of states into one. The key question is how to design and represent such abstractions. The most successful answer to this question are pattern databases, which aggregate states if and only if they agree on a subset of the state variables. Merge-and-shrink abstraction is a new paradigm that, as we show, allows to compactly represent a more general class of abstractions, strictly dominating pattern databases in theory. We identify the maximal class of transition systems, which we call factored transition systems, to which merge-and-shrink applies naturally, and we show that the well-known notion of bisimilarity can be adapted to this framework in a way that still guarantees perfect heuristic functions, while potentially reducing abstraction size exponentially. Applying these ideas to planning, one of the foundational subareas of artificial intelligence, we show that in some benchmarks this size reduction leads to the computation of perfect heuristic functions in polynomial time and that more approximate merge-and-shrink strategies yield heuristic functions competitive with the state of the art. ACM Reference Format:Malte Helmert, Patrik Haslum, Jörg Hoffmann, and Raz Nissim. 2014. Merge-and-shrink abstraction: A method for generating lower bounds in factored state spaces.

Extending Classical Planning with State Constraints: Heuristics and Search for Optimal Planning

“…The merge-andshrink abstraction heuristic, for which we have not implemented an analogue in the planner with state constraints, is much better informed than the projection abstraction (i.e., PDB heuristic) in this domain. This agrees with the outcome of other comparisons between these two types of abstraction heuristics on similar classical planning problems (Helmert et al, 2014).…”

“…Thus, optimal plan cost in the abstract space is a lower bound on optimal real plan cost. Ab-straction is the basis of planning heuristics such as merge-and-shrink (Helmert, Haslum, Hoffmann, & Nissim, 2014). A projection is an abstraction in which all but a designated subset of primary state variables are ignored.…”

Operator Mutexes and Symmetries for Simplifying Planning Tasks

“…We also tried the most promising Π 2 op pruning technique with the Fast Downward planner (Helmert 2006). We used A with the LM-Cut (lmc) heuristic (Helmert and Domshlak 2009), the merge-and-shrink (m&s) heuristic with SCC-DFP merge strategy and non-greedy bisimulation shrink strategy (Helmert et al 2014;Sievers, Wehrle, and Helmert 2016), and the potential (pot) heuristic optimized for all syntactic states (Seipp, Pommerening, and Helmert 2015). The time limit was set to 30 minutes for the whole planning process.…”

“…Theorem 6 shows how we can infer strong operator mutexes using any known method for computing abstractions of planning tasks, including pattern databases (Culberson and Schaeffer 1996;Edelkamp 2001), merge-and-shrink (Helmert et al 2014;Sievers, Wehrle, and Helmert 2014), or Cartesian abstractions (Seipp and Helmert 2018). Analyzing what abstraction methods are best suited to find op-mutexes is out of the scope of this work, so we will focus our evaluation only on projections to individual mutex groups.…”

Lifted Fact-Alternating Mutex Groups and Pruned Grounding of Classical Planning Problems

“…heuristics (Helmert et al 2014;Sievers, Wehrle, and Helmert 2014), pattern databases (Culberson and Schaeffer 1996;Edelkamp 2001), SAT-based planning (Rintanen, Heljanko, and Niemelä 2006), or computing upper bounds on plan lengths (Abdulaziz, Gretton, and Norrish 2017).…”