Operator cost partitioning is a well-known technique to make admissible heuristics additive by distributing the operator costs among individual heuristics. Planning tasks are usually defined with non-negative operator costs and therefore it appears natural to demand the same for the distributed costs. We argue that this requirement is not necessary and demonstrate the benefit of using general cost partitioning. We show that LP heuristics for operator-counting constraints are cost-partitioned heuristics and that the state equation heuristic computes a cost partitioning over atomic projections. We also introduce a new family of potential heuristics and show their relationship to general cost partitioning.

Many heuristics for cost-optimal planning are based on linear programming. We cover several interesting heuristics of this type by a common framework that fixes the objective function of the linear program. Within the framework, constraints from different heuristics can be combined in one heuristic estimate which dominates the maximum of the component heuristics. Different heuristics of the framework can be compared on the basis of their constraints. With this new method of analysis, we show dominance of the recent LP-based state-equation heuristic over optimal cost partitioning on single-variable abstractions.  We also show that the previously suggested extension of the state-equation heuristic to exploit safe variables cannot lead to an improved heuristic estimate. We experimentally evaluate the potential of the proposed framework on an extensive suite of benchmark tasks.

The standard PDDL language for classical planning uses several first-order features, such as schematic actions. Yet, most classical planners ground this first-order representation into a propositional one as a preprocessing step. While this simplifies the design of other parts of the planner, in several benchmarks the grounding process causes an exponential blowup that puts otherwise solvable tasks out of reach of the planners. In this work, we take a step towards planning with lifted representations. We tackle the successor generation task, a key operation in forward-search planning, directly on the lifted representation using well-known techniques from database theory. We show how computing the variable substitutions that make an action schema applicable in a given state is essentially a query evaluation problem. Interestingly, a large number of the action schemas in the standard benchmarks result in acyclic conjunctive queries, for which query evaluation is tractable. Our empirical results show that our approach is competitive with the standard (grounded) successor generation techniques in a few domains and outperforms them on benchmarks where grounding is challenging or infeasible.

Potential heuristics, recently introduced by Pommerening et al., characterize admissible and consistent heuristics for classical planning as a set of declarative constraints. Every feasible solution for these constraints defines an admissible heuristic, and we can obtain heuristics that optimize certain criteria such as informativeness by specifying suitable objective functions. The original paper only considered one such objective function: maximizing the heuristic value of the initial state. In this paper, we explore objectives that attempt to maximize heuristic estimates for all states (reachable and unreachable), maximize heuristic estimates for a sample of reachable states, maximize the number of detected dead ends, or minimize search effort. We also search for multiple heuristics with complementary strengths that can be combined to obtain even better heuristics.

Generalized planning aims at computing solutions that work for all instances of the same domain. In this paper, we show that several interesting planning domains possess compact generalized heuristics that can guide a greedy search in guaranteed polynomial time to the goal, and which work for any instance of the domain. These heuristics are weighted sums of state features that capture the number of objects satisfying a certain first-order logic property in any given state. These features have a meaningful interpretation and generalize naturally to the whole domain. Additionally, we present an approach based on mixed integer linear programming to compute such heuristics automatically from the observation of small training instances. We develop two variations of the approach that progressively refine the heuristic as new states are encountered. We illustrate the approach empirically on a number of standard domains, where we show that the generated heuristics will correctly generalize to all possible instances.