In this paper we presented the Grt planning system, a heuristic state-space
planner, which constructs its heuristic in a domain-independent way. The
fundamental difference between Grt
and other heuristic state-space planners is that Grt constructs its heuristic once, in a pre-processing phase
and in a backward direction, using regression from the goals. Grt attempts to track the positive and
negative interactions that occur between the problem facts when trying to
achieve them, in order to produce better estimates.
Grt employs
several new techniques that improve its efficiency. These are the automated
identification of incomplete goal states, the identification and enrichment of
inadequate domain representations, the elimination of irrelevant objects and
the adoption of a numerical representation of resources. Finally, a
knowledge-based method that uses domain axioms in the form of XOR-constraints,
in order to decompose difficult problems into easier sub-problems that have to
be solved sequentially, has adopted.
The paper presented
extensive comparative results in a large number of domains. In the comparisons,
besides Grt, four of the most
powerful domain independent planners took part. The results showed that no
planner clearly outperforms all the others.
Concerning solution
time, in most of the domains Grt
and Ff were the fastest planners.
The explanation behind this observation lies in that these planners construct
their heuristic either once (in the case of Grt),
or a few times only (in the case of Ff).
For example, in the elevator domain, where delete effects do not exist
and Ff constructs a relaxed
planning graph only once, it is extremely fast. On the contrary, in the gripper
and the puzzle domains, where Ff
needs to reconstruct the relaxed planning graphs, its efficiency decreases
drastically with respect to the Grt's
one.
Hsp-2 was not
faster than the other planners in any domain, being always outperformed by Ff. This was expected, since the two
planners use the forward direction both for the construction of their heuristics
and for traversing the state-space, however Ff
constructs its heuristic less times than Hsp-2.
Our impression is that the Ff
heuristic is also more informative and more accurate than the one of Hsp-2. Concerning Altalt, although it constructs its
heuristic once, it did not manage to be faster than the others in any domain
and this is (we believe) due to the problems that arise from the backward
direction in which it traverses the state-space. So, this is an indication that
in the case where opposite directions are used for the heuristic construction
and the search phase, as Grt, Altalt and Hspr do, it is preferable to use the backward direction for
the heuristic construction and the forward direction for the search phase. This
is why the problems that arise when constructing the heuristic backwards may be
confronted more easily than the problems that arise when traversing the
state-space backwards.
Domain analysis
techniques, which occur in pre-processing phase, also play an important role. Stan, which is primarily based on these
techniques, had many variations in its performance. In transportation domains,
like the logistics and the elevator ones, where Stan exploits specialized heuristics,
it was among the fastest planners. In the gripper domain, where Stan exploits its symmetry analysis,
its performance was also excellent. In other domains, as for example the freecell
or the blocks, it was not competitive due to its Graphplan basic architecture, which is not considered a fast
technology any more.
Ff also employed
a domain analysis technique concerning goal ordering, which played an important
role in the blocks problems. It would be very interesting to see the adaptation
and the impact of this technique to other planners as well. As far as we know, Hsp-2 and Altalt are not using any domain analysis technique. Grt exploited only the domain
enrichment technique in the elevator domain, however this technique is
an integral part of its heuristic mechanism, in order to overcome some problems
that arise from the backward heuristic construction.
An interesting
observation concerns the performance of Grt
in the bigger problems of the logistics, freecell, gripper
and puzzle domains, where Grt
exhibited better performance than in the smaller problems of the same domains,
compared to the other planners. We believe that this is due to the fact that Grt constructs its heuristic once,
while the repeated construction of the heuristics for the other planners is an
inhibitory factor in the bigger problems.
The conclusions drawn
above ignore a significant factor, which is the specific implementation, i.e.
the approaches adopted by the various planners for "trivial" tasks,
such as the computation of all the ground facts and actions of a problem or the
computation of the applicable actions to a given state, the optimization of the
code and of course potential "bugs". For example, in order to find
the applicable actions to a state, Grt
uses constraint satisfaction techniques to progressively instantiate the action
schemas for each state, whereas most of the other planners exploit connectivity
graphs between the facts of a problem and the pre-instantiated actions. Our
experiments with Grt have shown
that a significant portion of the processing time is spent in the determination
of the applicable actions to a state. This is the reason why we have developed
a parallel version of Grt, named
PGRT (Vrakas et. al., 1999; 2000), which makes use of this observation and has
been proved very efficient in all domains. However, it is in our future plans
to develop a connectivity graph also in Grt
and to compare it to the existent approach.
Differences that are
due to the code optimization or potential "bugs" cannot be easily
detected, but we believe that all the planners, both the oldest and the newest
ones are well-optimized programs. In the future we would like to see
theoretical comparisons between the computational complexities of the various
techniques and algorithms, apart from their experimental evaluation that is
usually adopted.
Concerning plan
length, Grt produced better plans
than the other planners in the freecell domain, in the gripper
domain (along with other planners), in many blocks problems when a
3-action schemas representation was used and in some logistics problems.
Stan exhibited the best behavior
in most of the domains and we believe this is due to its Graphplan basic architecture, which
always produces optimal parallel plans and, in many cases, sequential plans
also. Ff behaved well in the logistics
and the blocks problems, with the 4-action schemas representation (in
the latter case probably due to the goal ordering technique), however it
produced lengthy plans in other domains, as the freecell, the gripper
and the puzzle ones.
Hsp-2 produced
longer plans than Grt in many
domains, as for example the logistics, the freecell and the gripper
domains and the blocks one, when a 3-actions representation was used.
This observation means that in these domains the related facts employed by the Grt heuristic proved more valuable than
the forward and repeated reconstruction of the Hsp-2 heuristic. Finally, Altalt
has not been distinguished for the quality of its plans in any domain.
Our general impression from
the experiments is that there are specific domains that favor specific planners.
So, what is important is to investigate the reasons for that. We are currently
working in exploring the internal characteristics of each domain, classifying
them into more general categories that share common features, and associate
these features with specific heuristic search techniques. A first attempt for a
domain classification can also be found in (Hoffmann, 2001).
An alternative view of
the above problem concerns the way a domain is encoded. The same planner in the
same domain may alter its performance when a different representation is
adopted. We faced this problem with the blocks-world, with the 4- and
3-actions schemas domain representations, where the performance of Grt varies significantly, while the
performance of other planners is also altered. We also faced this problem with
the elevator and movie domains, which were the motivation for the
development of the domain enrichment technique. Our conviction is that
domain-independent planning is strongly domain-representation dependent.
Concerning Grt, we plan to extend it so as to
handle more expressive domains, supporting most of the features of the PDDL
language (types, quantifications, negations, disjunctions, etc). At this time
we are working with an extension of Grt,
which has the ability to take into account multiple criteria (i.e. solution
time, resources, safety, profit etc.). We are also interested in incorporating
domain analysis techniques, as they have been developed in Stan and Discoplan, in order to take advantage of specialized methods
for handling specific types of problems or sub-problems. Finally, we will
investigate the possibility and the utility of combining domain independent
planning techniques with domain dependent ones, without loosing the generality
of the planning system.
Ioannis
Refanidis
14-8-2001