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.
Ioannis
Refanidis
14-8-2001