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1.    Introduction

So far, planning problems have been considered as a special kind of particularly difficult search problems (Newell & Simon, 1972) and many algorithms for decomposition, abstraction, least commitment etc. have been proposed to cope with them. In the early 90's, researchers were arguing that plan-space planning is more efficient than state-space planning (Barrett & Weld, 1994; McAllester & Rosenblitt, 1991; Minton, Bresina & Drummond, 1994; Penberthy & Weld, 1992). In the mid 90's, new algorithms appeared that achieved even better performance by transforming planning problems either into graph solving problems (Blum & Furst, 1995, 1997) or into satisfiability ones (Kautz & Selman, 1992, 1996, 1998). However, it has been shown that simple search strategies with the use of domain-dependent heuristics can solve large problems (Gupta & Nau, 1992; Korf & Taylor, 1996; Pearl, 1983; Slaney & Thiebaux, 1996).

In recent years, part of the planning community turned towards heuristic planning, adopting known search strategies and developing powerful domain-independent heuristics that achieve significant performance. The first planner was Unpop (McDermott 1996, 1999) and was followed by Asp (Bonet, Loerings & Geffner, 1997), Hsp (Bonet & Geffner, 1998), Hspr (Bonet & Geffner, 1999), Grt (Refanidis & Vlahavas, 1999b), Ff (Hoffmann & Nebel, 2000) and Altalt (Nigenda, Nguyen & Kambhampati, 2000). These domain independent heuristic planners search for solutions either in the state-space or in the regression space. Most of them use variations of a relatively simple idea as a guide: they estimate the distance between two states, based on estimates of the distances between each fact of the problem and one of the two states.

The above planners can primarily be classified based on the forward or backward direction, in which the heuristic is constructed and the state-space is traversed. We distinguish the following three categories:

§         Forward heuristic construction, forward search (Asp, Hsp, Ff).

§         Forward heuristic construction, backward search (Hspr, Altalt).

§         Backward heuristic construction, forward search (Unpop, Grt).

Generally, the forward direction seems to be more advantageous than the backward one, both when constructing the heuristic and when searching, because in the backward direction and in case of incomplete goal states, problems with invalid states and unreachable facts usually arise. However, using the forward direction for both tasks requires reconstructing the heuristic function for each visited state, spending in this way a significant portion of the processing time, while using opposite directions for both tasks allows constructing the heuristic once, in a pre-processing phase.

This paper presents the Grt planning system. It is the only domain independent heuristic planner that constructs the heuristic once, in a backward direction and in a pre-processing phase. Unpop, although it uses the same directions, reconstructs the heuristic from scratch for each visited state. Grt, in a pre-processing phase estimates the distance between each fact and the goals of the problem. During the search phase, these estimates are used in order to further estimate the distance between each visited state and the goals, guiding so the search process in a forward direction and on a best-first basis. Constructing the heuristic once offers the ability to evaluate states very quickly, while traversing the state-space in a forward direction allows the planner to avoid invalid states that arise in the regression space.

The paper substantially extends previous work (Refanidis & Vlahavas, 1999b, 1999c, 2000a and 2000b), in that it presents and proves the fundamental theory of the planner, along with many new techniques developed on it, it extensively tests the contribution of each technique to its overall performance and provides a thorough comparison to other planning systems.

The rest of the paper is organized as follows: Section 2 presents the data structures and the main algorithms of the planner. Section 3 discusses the difficulties that incomplete goal states cause to the backward direction of the construction of the heuristic and presents methods to cope with them. The same methods are also applied to identify and enrich poor domain representations.

Two approaches to reduce the problem's size are presented in Section 4. The first one deals with the identification and elimination of irrelevant objects and the second one concerns the adoption of a numerical representation of resources.

Section 5 deals with the problem of local optimal states and proposes a method to cope with them. Specifically, the XOR-constraints are introduced and used in order to decompose difficult problems into easier sub-problems that have to be solved sequentially. Section 6 presents the operation of Grt, Section 7 presents the related work and Section 8 presents performance results, which show that Grt is among the fastest domain-independent planners. Finally, Section 9 concludes the paper and poses future directions.

 

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Next: The GRT Heuristic Up: The GRT Planning System Previous: The GRT Planning System

Ioannis Refanidis

14-8-2001