This paper studies novel subgoaling relaxations for automated planning with propositional and numeric state variables. Subgoaling relaxations address one source of complexity of the planning problem: the requirement to satisfy conditions simultaneously. The core idea is to relax this requirement by recursively decomposing conditions into atomic subgoals that are considered in isolation. Such relaxations are typically used for pruning, or as the basis for computing admissible or inadmissible heuristic estimates to guide optimal or satis_cing heuristic search planners. In the last decade or so, the subgoaling principle has underpinned the design of an abundance of relaxation-based heuristics whose formulations have greatly extended the reach of classical planning. This paper extends subgoaling relaxations to support numeric state variables and numeric conditions. We provide both theoretical and practical results, with the aim of reaching a good trade-o_ between accuracy and computation costs within a heuristic state-space search planner. Our experimental results validate the theoretical assumptions, and indicate that subgoaling substantially improves on the state of the art in optimal and satisficing numeric planning via forward state-space search.

The paper generalises the notion of landmarks for reasoning about planning problems involving propositional and numeric variables. Intuitively, numeric landmarks are regions in the metric space defined by the problem whose crossing is necessary for its resolution. The paper proposes a relaxationbased method for their automated extraction directly from the problem structure, and shows how to exploit them to infer what we call disjunctive and additive hybrid action landmarks. The justification of such a disjunctive representation results from the intertwined propositional and numeric structure of the problem. The paper exercises their use in two novel admissible LP-Based numeric heuristics, and reports experiments on cost-optimal numeric planning problems. Results show the heuristics are more informed and effective than previous work for problems involving a higher number of (sub)goals.

Hybrid PDDL+ models are amongst the most advanced models of systems and the resulting problems are notoriously difficult for planning engines to cope with. An additional limiting factor for the exploitation of PDDL+ approaches in real-world applications is the restricted number of domain-independent planning engines that can reason upon those models. With the aim of deepening the understanding of PDDL+ models, in this work we study a novel mapping between a time discretisation of PDDL+ and numeric planning as for PDDL2.1 (level 2). The proposed mapping not only clarifies the relationship between these two formalisms, but also enables the use of a wider pool of engines, thus fostering the use of hybrid planning in real-world applications. Our experimental analysis shows the usefulness of the proposed translation, and demonstrates the potential of the approach for improving the solvability of complex PDDL+ instances.

This paper describes a novel encoding for sequential numeric planning into the problem of determining the satisfiability of a logical theory T. We introduce a novel technique, orthogonal to existing work aiming at producing more succinct encodings that enables the theory solver to roll up an unbounded yet finite number of instances of an action into a single plan step, greatly reducing the horizon at which T models valid plans. The technique is then extended to deal with problems featuring disjunctive global constraints, in which the state space becomes a non-convex n dimensional polytope. In order to empirically evaluate the encoding, we build a planner, SPRINGROLL, around a state–of–the–art off– the–shelf SMT solver. Experiments on a diverse set of domains are finally reported, and results show the generality and efficiency of the approach.