We describe and evaluate the algorithmic techniques that are used in the FF planning system. Like the HSP system, FF relies on forward state space search, using a heuristic that estimates goal distances by ignoring delete lists. Unlike HSP's heuristic, our method does not assume facts to be independent. We introduce a novel search strategy that combines Hill-climbing with systematic search, and we show how other powerful heuristic information can be extracted and used to prune the search space. FF was the most successful automatic planner at the recent AIPS-2000 planning competition. We review the results of the competition, give data for other benchmark domains, and investigate the reasons for the runtime performance of FF compared to HSP.

The formulation of planning as heuristic search with heuristics derived from problem representations has turned out to be a fruitful approach for classical planning. In this paper, we pursue a similar idea in the context planning with incomplete information. Planning with incomplete information can be formulated as a problem of search in belief space, where belief states can be either sets of states or more generally probability distribution over states. While the formulation (as the formulation of classical planning as heuristic search) is not particularly novel, the contribution of this paper is to make it explicit, to test it over a number of domains, and to extend it to tasks like planning with sensing where the standard search algorithms do not apply. The resulting planner appears to be competitive with the most recent conformant and contingent planners (e.g., cgp, sgp, and cmbp) while at the same time is more general as it can handle probabilistic actions and se...

hsp and hspr are two recent planners that search the state-space using an heuristic function extracted from Strips encodings. hsp does a forward search from the initial state recomputing the heuristic in every state, while hspr does a regression search from the goal computing a suitable representation of the heuristic only once. Both planners have shown good performance, often producing solutions that are competitive in time and number of actions with the solutions found by Graphplan and sat planners. hsp and hspr, however, are not optimal planners. This is because the heuristic function is not admissible and the search algorithms are not optimal. In this paper we address this problem. We formulate a new admissible heuristic for planning, use it to guide an ida search, and empirically evaluate the resulting optimal planner over a number of domains. The main contribution is the idea underlying the heuristic that yields not one but a whole family of polynomial and admissible heuristics that trade accuracy for e ciency. The formulation is general and sheds some light on the heuristics used in hsp and Graphplan, and their relation. It exploits the factored (Strips) representation of planning problems, mapping shortest-path problems in state-space into suitably dened shortest-path problems in atom-space. The formulation applies with little variation to sequential and parallel planning, and problems with di erent action costs.

Planning with numeric state variables has been a challenge for many years, and was a part of the 3rd International Planning Competition (IPC-3). Currently one of the most popular and successful algorithmic techniques in STRIPS planning is to guide search by a heuristic function, where the heuristic is based on relaxing the planning task by ignoring the delete lists of the available actions. We present a natural extension of "ignoring delete lists" to numeric state variables, preserving the relevant theoretical properties of the STRIPS relaxation under the condition that the numeric task at hand is "monotonic". We then identify a subset of the numeric IPC-3 competition language, "linear tasks", where monotonicity can be achieved by preprocessing. Based on that, we extend the algorithms used in the heuristic planning system FF to linear tasks. The resulting system Metric-FF is, according to the IPC-3 results which we discuss, one of the two currently most efficient numeric planners.

Most recent strides in scaling up planning have centered around two competing themes--disjunctive planners, exemplified by Graphplan, and heuristic state search planners, exemplified by UNPOP, HSP and HSP-r. In this paper, we present a novel approach for successfully harnessing the advantages of the two competing paradigms to develop planners that are significantly more powerful than either of the approaches. Specifically, we show that the polynomial-time planning graph structure that the Graphplan builds provides a rich substrate for deriving a family of highly effective heuristics for guiding state space search as well as CSP-style search. The main leverage provided by the planning graph structure is a systematic and graded way to take subgoal interactions into account in designing state space heuristics.

This paper challenges the prevailing pessimism about the scalability of partial order planning (POP) algorithms by presenting several novel heuristic control techniques that make them competitive with the state of the art plan synthesis algorithms. Our key insight is that the techniques responsible for the efficiency of the currently successful planners--viz., distance based heuristics, reachability analysis and disjunctive constraint handling--can also be adapted to dramatically improve the efficiency of the POP algorithm. We implement our ideas in a variant of UCPOP called REPOP # . Our empirical results show that in addition to dominating UCPOP, REPOP also convincingly outperforms Graphplan in several "parallel" domains. The plans generated by REPOP also tend to be better than those generated by Graphplan and state search planners in terms of execution flexibility. 1

Some recent works in conditional planning have proposed reachability heuristics to improve planner scalability, but many lack a formal description of the properties of their distance estimates. To place previous work in context and extend work on heuristics for conditional planning, we provide a formal basis for distance estimates between belief states. We give a definition for the distance between belief states that relies on aggregating underlying state distance measures. We give several techniques to aggregate state distances and their associated properties. Many existing heuristics exhibit a subset of the properties, but in order to provide a standardized comparison we present several generalizations of planning graph heuristics that are used in a single planner. We compliment our belief state distance estimate framework by also investigating efficient planning graph data structures that incorporate BDDs to compute the most effective heuristics. We developed two planners to serve as test-beds for our investigation. The first, CAltAlt, is a conformant regression planner that uses A * search. The second, POND, is a conditional progression planner that uses AO * search. We show the relative effectiveness of our heuristic techniques within these planners. We also compare the performance of these planners with several

Although the deep affinity between Graphplan's backward search, and the process of solving constraint satisfaction problems has been noted earlier, these relations have hither-to been primarily used to adapt CSP search techniques into the backward search phase of Graphplan. This paper describes GP-CSP, a system that does planning by automatically converting Graphplan's planning graph into a CSP encoding, and solving the CSP encoding using standard CSP solvers. Our comprehensive empirical evaluation of GP-CSP demonstrates that it is superior to both standard Graphplan and Blackbox system, which compiles planning graphs into SAT encodings. Our results show that CSP encodings outperform SAT encodings in terms of both space and time requirements. The space reduction is particularly important as it makes GP-CSP less susceptible to the memory blow-up associated with SAT compilation methods. Our work is inspired by the success of van Beek & Chen's CPLAN system. However, in contrast...

System, performing abductive reasoning within the framework of Abductive Logic Programming. It is based on a hybrid computational model that implements the abductive search in terms of two tightly coupled processes: a reduction process of the highlevel logical representation to a lower-level constraint store and a lower-level constraint solving process. A set of initial "proof of principle" experiments demonstrate the versatility of the approach stemming from its declarative representation of problems and the good underlying computational behaviour of the system. The approach offers a general methodology of declarative problem solving in AI where an incremental and modular refinement of the high-level representation with extra domain knowledge can improve and scale the computational performance of the framework.

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