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When both Grounding and not Grounding are Bad -- A Partially Grounded Encoding of Planning into SAT (Extended Version)

João Filipe, Gregor Behnke

Abstract

Classical planning problems are typically defined using lifted first-order representations, which offer compactness and generality. While most planners ground these representations to simplify reasoning, this can cause an exponential blowup in size. Recent approaches instead operate directly on the lifted level to avoid full grounding. We explore a middle ground between fully lifted and fully grounded planning by introducing three SAT encodings that keep actions lifted while partially grounding predicates. Unlike previous SAT encodings, which scale quadratically with plan length, our approach scales linearly, enabling better performance on longer plans. Empirically, our best encoding outperforms the state of the art in length-optimal planning on hard-to-ground domains.

When both Grounding and not Grounding are Bad -- A Partially Grounded Encoding of Planning into SAT (Extended Version)

Abstract

Classical planning problems are typically defined using lifted first-order representations, which offer compactness and generality. While most planners ground these representations to simplify reasoning, this can cause an exponential blowup in size. Recent approaches instead operate directly on the lifted level to avoid full grounding. We explore a middle ground between fully lifted and fully grounded planning by introducing three SAT encodings that keep actions lifted while partially grounding predicates. Unlike previous SAT encodings, which scale quadratically with plan length, our approach scales linearly, enabling better performance on longer plans. Empirically, our best encoding outperforms the state of the art in length-optimal planning on hard-to-ground domains.
Paper Structure (19 sections, 15 equations, 3 figures, 2 tables)

This paper contains 19 sections, 15 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Lifted Planning
  4. Lifted Mutex Groups
  5. Boolean Satisfiability
  6. Related Work
  7. Lifted Representation of Actions
  8. Partial Grounding in Propositional Logic
  9. Encoding with Fully Grounded Facts
  10. Predicate Pruning
  11. Encoding with Partially Grounded Facts
  12. Binary Encoding of Objects
  13. Experimental Evaluation
  14. Results -- Optimal
  15. Results -- Satisficing
  16. ...and 4 more sections

Figures (3)

  • Figure 1: Comparison of formula size, variable number and coverage
  • Figure 2: Ration comparisons of number of variables/clauses with respect to a formula of length 1
  • Figure 3: Solve Time Scatter Plot

Theorems & Definitions (11)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Definition 5
  • Definition 6
  • Definition 7
  • Example 1
  • Example 2
  • Example 3
  • ...and 1 more