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Symbolic Numeric Planning with Patterns

Matteo Cardellini, Enrico Giunchiglia, Marco Maratea

TL;DR

The paper tackles linear numeric planning by introducing Symbolic Pattern Planning, a pattern-based encoding $Π^{\prec}$ that, for a fixed bound $n$, uses fewer variables and clauses than prior encodings and provably dominates both the rolled-up $Π^R$ and the ${R^2\exists}$ encoding. By enabling arbitrary action sequences and multiple executions without mutex overhead, the framework can solve planning problems with smaller bounds and offer a bridge between symbolic and search-based approaches. The authors provide formal domination results and implement the approach in the Patty planner, coupled with an ARPG-driven method to compute effective patterns, and demonstrate competitive performance on the 2023 IPC benchmarks relative to six other planners. These contributions offer a new starting point for symbolic planning, highlighting opportunities to extend pattern-driven encodings and pattern discovery to broaden applicability and scalability.

Abstract

In this paper, we propose a novel approach for solving linear numeric planning problems, called Symbolic Pattern Planning. Given a planning problem $Π$, a bound $n$ and a pattern -- defined as an arbitrary sequence of actions -- we encode the problem of finding a plan for $Π$ with bound $n$ as a formula with fewer variables and/or clauses than the state-of-the-art rolled-up and relaxed-relaxed-$\exists$ encodings. More importantly, we prove that for any given bound, it is never the case that the latter two encodings allow finding a valid plan while ours does not. On the experimental side, we consider 6 other planning systems -- including the ones which participated in this year's International Planning Competition (IPC) -- and we show that our planner Patty has remarkably good comparative performances on this year's IPC problems.

Symbolic Numeric Planning with Patterns

TL;DR

The paper tackles linear numeric planning by introducing Symbolic Pattern Planning, a pattern-based encoding that, for a fixed bound , uses fewer variables and clauses than prior encodings and provably dominates both the rolled-up and the encoding. By enabling arbitrary action sequences and multiple executions without mutex overhead, the framework can solve planning problems with smaller bounds and offer a bridge between symbolic and search-based approaches. The authors provide formal domination results and implement the approach in the Patty planner, coupled with an ARPG-driven method to compute effective patterns, and demonstrate competitive performance on the 2023 IPC benchmarks relative to six other planners. These contributions offer a new starting point for symbolic planning, highlighting opportunities to extend pattern-driven encodings and pattern discovery to broaden applicability and scalability.

Abstract

In this paper, we propose a novel approach for solving linear numeric planning problems, called Symbolic Pattern Planning. Given a planning problem , a bound and a pattern -- defined as an arbitrary sequence of actions -- we encode the problem of finding a plan for with bound as a formula with fewer variables and/or clauses than the state-of-the-art rolled-up and relaxed-relaxed- encodings. More importantly, we prove that for any given bound, it is never the case that the latter two encodings allow finding a valid plan while ours does not. On the experimental side, we consider 6 other planning systems -- including the ones which participated in this year's International Planning Competition (IPC) -- and we show that our planner Patty has remarkably good comparative performances on this year's IPC problems.
Paper Structure (8 sections, 2 theorems, 10 equations, 1 figure, 1 table)

This paper contains 8 sections, 2 theorems, 10 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Symbolic Planning With Patterns
  4. Symbolic Planning
  5. Rolled-up, Standard and $R^2\exists$ Encodings
  6. Pattern Encoding
  7. Implementation and Experimental Analysis
  8. Conclusions

Key Result

Theorem 1

Let $\Pi$ be a numeric planning problem. Let $<$ be a total order of actions. The rolled-up encoding $\Pi^R$, the $R^2\exists$$<$-encoding $\Pi^<$ and the standard encoding $\Pi^S$ of $\Pi$ are correct and complete. $\Pi^R$ and $\Pi^<$ dominate $\Pi^S$.

Figures (1)

  • Figure 1: Performance on the LineExchange domain.

Theorems & Definitions (5)

  • Example
  • Theorem 1
  • proof
  • Theorem 2
  • proof