Multi-Valued Partial Order Plans in Numeric Planning

TL;DR

This paper introduces multi-valued partial order plans as a compact, least-committing representation for numeric planning, analyzing their properties and optimization techniques to handle soft preconditions, addressing undecidability issues.

Contribution

It proposes multi-valued partial order plans for numeric planning and explores their properties and optimization, providing a new approach to manage undecidability.

Findings

Identified causes of undecidability in numeric planning

Developed a heuristic-based NP-complete fragment

Introduced optimization techniques for soft preconditions

Abstract

Many planning formalisms allow for mixing numeric with Boolean effects. However, most of these formalisms are undecidable. In this paper, we will analyze possible causes for this undecidability by studying the number of different occurrences of actions, an approach that proved useful for metric fluents before. We will start by reformulating a numeric planning problem known as restricted tasks as a search problem. We will then show how an NP-complete fragment of numeric planning can be found by using heuristics. To achieve this, we will develop the idea of multi-valued partial order plans, a least committing compact representation for (sequential and parallel) plans. Finally, we will study optimization techniques for this representation to incorporate soft preconditions.