Symbolic Top-k Planning

Abstract

The objective of top-k planning is to determine a set of k different plans with lowest cost for a given planning task. In practice, such a set of best plans can be preferred to a single best plan generated by ordinary optimal planners, as it allows the user to choose between different alternatives and thus take into account preferences that may be difficult to model. In this paper we show that, in general, the decision problem version of top-k planning is PSPACE-complete, as is the decision problem version of ordinary classical planning. This does not hold for polynomially bounded plans for which the decision problem turns out to be PP-hard, while the ordinary case is NP-hard. We present a novel approach to top-k planning, called sym-k, which is based on symbolic search, and prove that sym-k is sound and complete. Our empirical analysis shows that sym-k exceeds the current state of the art for both small and large k.

Translating Totally Ordered HTN Planning Problems to Classical Planning Problems Using Regular Approximation of Context-Free Languages

“…be realized using Top-k planners (see e.g. Speck, Mattmüller, and Nebel (2020)). However, the incompleteness is not a problem on the 2020 IPC benchmark set.…”

Core Challenge 2022: Solver and Graph Descriptions

“…We run a forward symbolic blind search [Torralba et al, 2017, Speck et al, 2020a using Binary Decision Diagrams [Bryant, 1986] as the underlying data structure. The symbolic planner we use is SymK [Speck et al, 2020b], which uses CUDD [Somenzi, 2015] as its decision diagram library. This algorithm is optimal, sound, and complete, i.e., if it reports a plan, this is a shortest plan, if it reports unsolvability, the task is indeed unsolvable, and given sufficient resources, it will eventually find a shortest plan.…”

“…We run a modified forward symbolic blind search based on an algorithm called SymK-LL [von Tschammer et al, 2022], implemented in the symbolic planner SymK [Speck et al, 2020b], which iteratively finds and generates all loopless plans of a given task. However, we have made the following two major adjustments to solve the problem of finding the longest loopless plan feasible.…”

Symbolic Search for Optimal Total-Order HTN Planning

“…// t has empty method 5 if x = x and I = ∅ then return true bolic planners (Torralba 2015;Speck, Mattmüller, and Nebel 2020): backwards search from the goal while using the constructed data structures as a heuristic. In classical planning, we have constructed the perfect heuristic h * making this search efficient.…”