Planning as heuristic search is one of the most successful approaches to classical planning but unfortunately, it does not extend trivially 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 the number of objects, the number of state variables, their domain size, or their initial and goal configuration. The generalization requirements of GP make it impractical to perform the state-space search that is usually implemented by heuristic planners. This paper adapts the planning as heuristic search paradigm to the generalization requirements of GP, and presents 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 a set of evaluation and heuristic functions for guiding a combinatorial search in our new GP solution space. 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. Lastly, the paper defines an upgraded version of our novel algorithm for GP called Best-First Generalized Planning (BFGP), that implements a best-first search in our pointer-based solution space, and that is guided by our evaluation/heuristic functions for GP.

翻译：将规划问题视为启发式搜索是经典规划领域最成功的方法之一，但遗憾的是，该方法无法直接推广至广义规划（GP）。广义规划旨在为给定领域中的一组经典规划实例计算算法解，即使这些实例在对象数量、状态变量数量、变量域大小或初始/目标配置上存在差异。GP的泛化要求使得传统启发式规划器实施的基于状态空间的搜索难以实用化。本文首次将"规划即启发式搜索"范式适配至GP的泛化需求，提出了第一种原生启发式搜索的GP方法。首先，本文引入了一个新的基于指针的GP解空间，该空间与GP问题中经典规划实例的数量及其规模（即对象数量、状态变量数量及其域大小）无关。其次，本文定义了一组评估函数与启发式函数，用于指导我们在新型GP解空间中的组合搜索。这些评估函数与启发式函数的计算无需预先对状态或动作进行实例化，因此，我们的GP-启发式搜索方法能够处理具有大数值域（如整数域）的大规模状态变量集。最后，本文提出了改进版的GP算法——最佳优先广义规划（BFGP），该算法在基于指针的解空间中执行最佳优先搜索，并由我们提出的GP评估/启发式函数引导搜索过程。