This is coarse-grained in that, for each variable, it either remembers all past values (red), or remembers only the most recent one (black). We herein introduce limited-memory state variables, that remember a subset of their most recent values. It turns out that planning is still PSPACE-complete even when the memory is large enough to store all but a single value. Nevertheless, limited memory can be used to substantially broaden a known tractable fragment of red-black planning, yielding better heuristic functions in some domains.

Several known heuristic functions can capture the input at different levels of precision, and support relaxation-refinement operations guaranteeing to converge to exact information in a finite number of steps. A natural idea is to use such refinement online, during search, yet this has barely been addressed. We do so here for local search, where relaxation refinement is particularly appealing: escape local minima not by search, but by removing them from the search surface. Thanks to convergence, such an escape is always possible. We design a family of hill-climbing algorithms along these lines. We show that these are complete, even when using helpful actions pruning. Using them with the partial delete relaxation heuristic hCFF, the best-performing variant outclasses FF's enforced hill-climbing, outperforms FF, outperforms dual-queue greedy best-first search with hFF, and in 6 IPC domains outperforms both LAMA and Mercury.

Heuristic search is one of the most successful approaches to classical planning, finding solution paths in large state spaces. A major focus has been the development of domain-independent heuristic functions. One recent method are partial delete relaxation heuristics, improving over the standard delete relaxation heuristic through imposing a set C of conjunctions to be treated as atomic. Practical methods for selecting C are based on counter-example guided abstraction refinement, where iteratively a relaxed plan is checked for conflicts and new atomic conjunctions are introduced to address these. However, in each refinement step, the choice of possible new conjunctions is huge. The literature so far offers merely one simple strategy to make that choice. Here we fill that gap, considering a sizable space of basic ranking strategies as well as combinations thereof. We furthermore devise ranking strategies for conjunction-forgetting, where the ranking pertains to the current conjunctions and thus statistics over their usefulness can be maintained. Our experiments show that ranking strategies do make a large difference in performance, and that our new strategies can be useful.

Recent work has shown how to improve delete relaxation heuristics by computing relaxed plans, i.e., the hFF heuristic, in a compiled planning task PiC which represents a given set C of fact conjunctions explicitly. While this compilation view of such partial delete relaxation is simple and elegant, its meaning with respect to the original planning task is opaque, and the size of PiC grows exponentially in |C|. We herein provide a direct characterization, without compilation, making explicit how the approach arises from a combination of the delete-relaxation with critical-path heuristics. Designing equations characterizing a novel view on h+ on the one hand, and a generalized version hC of hm on the other hand, we show that h+(PiC) can be characterized in terms of a combined hcplus equation. This naturally generalizes the standard delete-relaxation framework: understanding that framework as a relaxation over singleton facts as atomic subgoals, one can refine the relaxation by using the conjunctions C as atomic subgoals instead. Thanks to this explicit view, we identify the precise source of complexity in hFF(PiC), namely maximization of sets of supported atomic subgoals during relaxed plan extraction, which is easy for singleton-fact subgoals but is NP-complete in the general case. Approximating that problem greedily, we obtain a polynomial-time hCFF version of hFF(PiC), superseding the PiC compilation, and superseding the modified PiCce compilation which achieves the same complexity reduction but at an information loss. Experiments on IPC benchmarks show that these theoretical advantages can translate into empirical ones.

We propose a new integer-linear programming model for the delete relaxation in cost-optimal planning. While a straightforward IP for the delete relaxation is impractical, our enhanced model incorporates variable reduction techniques based on landmarks, relevance-based constraints, dominated action elimination, immediate action application, and inverse action constraints, resulting in an IP that can be used to directly solve delete-free planning problems. We show that our IP model is competitive with previous state-of-the-art solvers for delete-free problems. The LP-relaxation of the IP model is often a very good approximation to the IP, providing an approach to approximating the optimal value of the delete-free task that is complementary to the well-known LM-cut heuristic. We also show that constraints that partially consider delete effects can be added to our IP/LP models. We embed the new IP/LP models into a forward-search based planner, and show that the performance of the resulting planner on standard IPC benchmarks is comparable with the state-of-the-art for cost-optimal planning.

Supporting state-dependent action costs in planning admits a more compact representation of many tasks. We generalize the additive heuristic and compute it by embedding decision-diagram representations of action cost functions into the RPG. We give a theoretical evaluation and present an implementation of the generalized additive heuristic. This allows us to handle even the hardest instances of the combinatorial Academic Advising domain from the IPPC 2014.

Many recent planning heuristics are based on LP optimization. However, planning experts mostly use LP solvers as a black box and it is often not obvious to them which LP techniques would be most suitable for their specific applications.To foster the communication between the planning and the optimization community, this paper gives an easily accessible overview over these recent LP-based heuristics, namely the optimal cost partitioning heuristic for abstractions, the post-hoc optimization heuristic, a landmark heuristic, the state-equation heuristic, and a delete relaxation heuristic. All these heuristics fit the framework of so-called operator counting constraints, which we also present.

The currently dominant approach to domain-independent planning is planning as heuristic search, with most successful planning heuristics being based on solutions to delete-relaxed versions of planning problems, in which the negative effects of actions are ignored. We introduce a principled, flexible, and practical technique for augmenting delete-relaxed tasks with a limited amount of delete information, by introducing special fluents that explicitly represent conjunctions of fluents in the original planning task. Differently from previous work, conditional effects are used to limit the growth of the task to be linear in the number of such conjunctions, making its use for obtaining heuristic functions feasible. The resulting heuristics are empirically evaluated, and shown to be some- times much more informative than standard delete-relaxation heuristics.

We present a novel method for computing increasing lower bounds on the cost of solving planning problems, based on repeatedly solving and strengthening the delete relaxation of the problem. Strengthening is done by compiling select conjunctions into new atoms, similar to the P m * construction. Because it does not rely on search in the state space, this method does not suffer some of the weaknesses of admissible search algorithms and therefore is able to prove higher lower bounds for many problems that are too hard for optimal planners to solve, thus narrowing the gap between lower bound and cost of the best known plan, providing better assurances of plan quality.

When planning in an uncertain environment, one is often interested in finding a contingent plan that prescribes appropriate actions for all possible states that may be encountered during the execution of the plan. We consider the problem of finding strong cyclic plans for fully observable nondeterministic (FOND) planning problems. The algorithm we choose is LAO*, an informed explicit state search algorithm. We investigate the use of pattern database (PDB) heuristics to guide LAO* towards goal states. To obtain a fully domain-independent planning system, we use an automatic pattern selection procedure that performs local search in the space of pattern collections. The evaluation of our system on the FOND benchmarks of the Uncertainty Part of the International Planning Competition 2008 shows that our approach is competitive with symbolic regression search in terms of problem coverage, speed, and plan quality.