Relaxed Exists-Step Plans in Planning as SMT

Abstract

Planning Modulo Theories (PMT), inspired by Satisfiability Modulo Theories (SMT), allows the integration of arbitrary first order theories, such as linear arithmetic, with propositional planning. Under this setting, planning as SAT is generalized to planning as SMT. In this paper we introduce a new encoding for planning as SMT, which adheres to the relaxed relaxed ∃-step (R 2 ∃-step) semantics for parallel plans. We show the benefits of relaxing the requirements on the set of actions eligible to be executed at the same time, even though many redundant actions can be introduced. We also show how, by a MaxSMT based post-processing step, redundant actions can be efficiently removed, and provide experimental results showing the benefits of this approach.

The RANTANPLAN planner: system description

“…These consistency checks can be done in a reasonable time with an SMT solver, and the amount of parallelism achieved is significantly higher than with syntactic approaches. To illustrate the situations where our new notion of interference (thoroughly explained in Bofill et al ., 2016) is especially accurate, consider the following example. The Planes domain in Figure 2 consists in transporting people between cities using planes.…”

“…With respect to the parallelism, for now this encoding only supports the sequential plan semantics, as encoding parallelism using this encoding is not straightforward. This approach is currently under development, as we obtained encouraging preliminary experimental results (Bofill et al ., 2014).…”

Effective grounding for hybrid planning problems represented in PDDL+

“…Grounding before planning is not the only way to initiate the solving of planning problems, even though is the most commonly exploited approach. Plan space planners in particular (either based on SAT, such as Robinson et al ., 2008, SMT, like Bofill et al ., 2016; Bit-Monnot, 2018, or more direct exploration of the plan space Younes & Simmons, 2003) indeed were built with the idea of combining search and grounding into a constraint satisfaction approach. Albeit this idea does not keep the pace with state-of-the-art planners based on heuristic search (probably for the difficulty of exploiting heuristics), there seems to be a revived interest in this direction that tries to combine lifted reasoning with heuristic forward search planner altogether (Ridder & Fox, 2014; Corrêa et al ., 2020).…”

Symbolic Numeric Planning with Patterns

“…In this paper, we propose a novel symbolic approach for solving numeric planning problems, called symbolic pattern planning. Given a problem Π and a pattern ≺ -defined as a sequence of actions -we show how it is possible to generalize the state-of-the-art rolled-up encoding Π R proposed in (Scala et al 2016b) and the relaxed-relaxed-∃ (R 2 ∃) encoding Π R 2 ∃ proposed in (Bofill, Espasa, and Villaret 2017), and define a new encoding Π ≺ which provably dominates both Π R and Π R 2 ∃ : for any bound n, it is never the case that the latter two allow to find a valid plan for Π while ours does not. Further, our encoding produces formulas with fewer clauses than the rolled-up encoding and also with far fewer variables than the R 2 ∃ encoding, even when considering a fixed bound.…”