Generalized planning as heuristic search: A new planning search-space that leverages pointers over objects

Planning as heuristic search is one of the most successful approaches to classical planning but unfortunately, it does not trivially extend to Generalized Planning (GP); GP aims to compute algorithmic solutions that are valid for a set of classical planning instances from a given domain, even if these instances differ in their number of objects, the initial and goal configuration of these objects and hence, in the number (and possible values) of the state variables. State-space search, as it is implemented by heuristic planners, becomes then impractical for GP. In this paper we adapt the planning as heuristic search paradigm to the generalization requirements of GP, and present the first native heuristic search approach to GP. First, the paper introduces a new pointer-based solution space for GP that is independent of the number of classical planning instances in a GP problem and the size of those instances (i.e. the number of objects, state variables and their domain sizes). Second, the paper defines an upgraded version of our GP algorithm, called Best-First Generalized Planning (BFGP), that implements a best-first search in our pointer-based solution space for GP. Lastly, the paper defines a set of evaluation and heuristic functions for BFGP that assess the structural complexity of the candidate GP solutions, as well as their fitness to a given input set of classical planning instances. The computation of these evaluation and heuristic functions does not require grounding states or actions in advance. Therefore our GP as heuristic search approach can handle large sets of state variables with large numerical domains, e.g. integers.