Generalized Planning as Heuristic Search

Abstract

Although heuristic search is one of the most successful approaches to classical planning, this planning paradigm does not apply straightforwardly to Generalized Planning (GP). Planning as heuristic search traditionally addresses the computation of sequential plans by searching in a grounded state-space. On the other hand, GP aims at computing algorithm-like plans that can branch and loop, and that generalize to a (possibly infinite) set of planning instances. This paper adapts the {\em planning as heuristic search} paradigm to the particularities of GP and presents the first native heuristic search approach to GP. First, the paper defines a novel GP solution space that is independent of the number of planning instances in a GP problem, and the size of these instances. Second, the paper defines several evaluation and heuristic functions, that do not require grounding, for guiding a combinatorial search in the GP solution space, making it possible to handle state variables with large numerical domains (e.g. integers). Lastly, the paper defines an algorithm for GP called Best-First Generalized Planning (BFGP), that implements a best-first search in the solution space guided by our evaluation/heuristic functions.