An Empirical Study of Perfect Potential Heuristics

Potential heuristics are weighted functions over state features of a planning task. A recent study defines the complexity of a task as the minimum required feature complexity for a potential heuristic that makes a search backtrack-free. This gives an indication of how complex potential heuristics need to be to achieve good results in satisficing planning. However, these results do not directly transfer to optimal planning. In this paper, we empirically study how complex potential heuristics must be to represent the perfect heuristic and how close to perfect heuristics can get with a limited number of features. We aim to identify the practical trade-offs between size, complexity and time for the quality of potential heuristics. Our results show that, even for simple planning tasks, finding perfect potential heuristics might be harder than expected

Abstraction Heuristics, Cost Partitioning and Network Flows

Cost partitioning is a well-known technique to make admissible heuristics for classical planning additive. The optimal cost partitioning of explicit-state abstraction heuristics can be computed in polynomial time with a linear program, but the size of the model is often prohibitive. We study this model from a dual perspective and develop several simplification rules to reduce its size. We use these rules to answer open questions about extensions of the state equation heuristic and their relation to cost partitioning

Higher-Dimensional Potential Heuristics for Optimal Classical Planning

Potential heuristics for state-space search are defined as weighted sums over simple state features. Atomic features consider the value of a single state variable in a factored state representation, while binary features consider joint assignments to two state variables. Previous work showed that the set of all admissible and consistent potential heuristics using atomic features can be characterized by a compact set of linear constraints. We generalize this result to binary features and prove a hardness result for features of higher dimension. Furthermore, we prove a tractability result based on the treewidth of a new graphical structure we call the context-dependency graph. Finally, we study the relationship of potential heuristics to transition cost partitioning. Experimental results show that binary potential heuristics are significantly more informative than the previously considered atomic ones

New perspectives on cost partitioning for optimal classical planning

Admissible heuristics are the main ingredient when solving classical planning tasks optimally with heuristic search. There are many such heuristics, and each has its own strengths and weaknesses. As higher admissible heuristic values are more accurate, the maximum over several admissible heuristics dominates each individual one. Operator cost partitioning is a well-known technique to combine admissible heuristics in a way that dominates their maximum and remains admissible. But are there better options to combine the heuristics? We make three main contributions towards this question: Extensions to the cost partitioning framework can produce higher estimates from the same set of heuristics. Cost partitioning traditionally uses non-negative cost functions. We prove that this restriction is not necessary, and that allowing negative values as well makes the framework more powerful: the resulting heuristic values can be exponentially higher, and unsolvability can be detected even if all component heuristics have a finite value. We also generalize operator cost partitioning to transition cost partitioning, which can differentiate between different contexts in which an operator is used. Operator-counting heuristics reason about the number of times each operator is used in a plan. Many existing heuristics can be expressed in this framework, which gives new theoretical insight into their relationship. Different operator-counting heuristics can be easily combined within the framework in a way that dominates their maximum. Potential heuristics compute a heuristic value as a weighted sum over state features and are a fast alternative to operator-counting heuristics. Admissible and consistent potential heuristics for certain feature sets can be described in a compact way which means that the best heuristic from this class can be extracted in polynomial time. Both operator-counting and potential heuristics are closely related to cost partitioning. They offer a new look on cost-partitioned heuristics and already sparked research beyond their use as classical planning heuristics

State-dependent Cost Partitionings for Cartesian Abstractions in Classical Planning

Abstraction heuristics are a popular method to guide optimal search algorithms in classical planning. Cost partitionings allow to sum heuristic estimates admissibly by distributing action costs among the heuristics. We introduce state-dependent cost partitionings which take context information of actions into account, and show that an optimal state-dependent cost partitioning dominates its state-independent counterpart. We demonstrate the potential of our idea with a state-dependent variant of the recently proposed saturated cost partitioning, and show that it has the potential to improve not only over its state-independent counterpart, but even over the optimal state-independent cost partitioning. Our empirical results give evidence that ignoring the context of actions in the computation of a cost partitioning leads to a significant loss of information

Mechanically Proving Guarantees of Generalized Heuristics: First Results and Ongoing Work

The goal of generalized planning is to find a solution that works for all tasks of a specific planning domain. Ideally, this solution is also efficient (i.e., polynomial) in all tasks. One possible approach is to learn such a solution from training examples and then prove that this generalizes for any given task. However, such proofs are usually pen-and-paper proofs written by a human. In our paper, we aim at automating these proofs so we can use a theorem prover to show that a solution generalizes for any task. Furthermore, we want to prove that this generalization works while still preserving efficiency. Our focus is on generalized potential heuristics encoding tiered measures of progress, which can be proven to lead to a find in a polynomial number of steps in all tasks of a domain. We show our ongoing work in this direction using the interactive theorem prover Isabelle/HOL. We illustrate the key aspects of our implementation using the Miconic domain and then discuss possible obstacles and challenges to fully automating this pipeline

Oversubscription Planning as Classical Planning with Multiple Cost Functions

The aim of classical planning is to minimize the summed cost of operators among those plans that achieve a fixed set of goals. Oversubscription planning (OSP), on the other hand, seeks to maximize the utility of the set of facts achieved by a plan, while keeping the cost of the plan at or below some specified bound. Here, we investigate the use of reformulations that yield planning problems with two separate cost functions, but no utilities, for solving OSP tasks. Such reformulations have also been proposed in the context of net-benefit planning, where the planner tries to maximize the difference between the utility achieved and the cost of the plan. One of our reformulations is adapted directly from that setting, while the other is novel. In both cases, they allow for easy adaptation of existing classical planning heuristics to the OSP problem within a simple branch and bound search. We validate our approach using state of the art admissible heuristics in this framework, and report our results

Planutils: Bringing Planning to the Masses

PLANUTILS is a general library for setting up Linux-based environments for developing, running, and evaluating planners. Over the last decades, the planning community has produced countless solvers for various planning formalisms, as well as many other tools to help the planning practitioner. From state-of-the-art planners, over validators, to parsing libraries, the planning ecosystem has grown quite large. In the demo, we highlight an effort that aims to unify this ecosystem and make it seamless for users to get started with what the ICAPS community has to offer

Optimal planning for delete-free tasks with incremental LM-cut

Optimal plans of delete-free planning tasks are interesting both in domains that have no delete effects and as the relaxation heuristic h+ in general planning. Many heuristics for optimal and satisficing planning approximate the h+ heuristic, which is well-informed and admissible but intractable to compute. In this work, branch-and-bound and IDA* search are used in a search space tailored to delete-free planning together with an incrementally computed version of the LM-cut heuristic. The resulting algorithm for optimal delete-free planning exceeds the performance of A* with the LM-cut heuristic in the state-of-the-art planner Fast Downward