Regarding the identification of the
candidate facts to enhance the goals, there are two automatic approaches. The
first one consists of a forward Graphplan-like
(Blum & Furst, 1999) pre-preprocessing phase that computes all binary
mutual exclusion relations (or simply "mutex" relations) among the
facts of the problem. A number of optimizations of this approach are presented
in (Refanidis & Vlahavas, 1999c), based primarily on the monotonic behavior
of the mutual exclusion relations (Long & Fox, 1999; Smith & Weld,
1999) and secondly on the fact that it is not necessary to construct a complete
planning graph, since it will not be used for extracting a plan. After the
computation of the mutual exclusion relations, all the facts that are not
mutually exclusive with any goal fact are considered candidates for the
enhancement of the goals. Its advantage is that no extra information is needed,
apart from the usual Strips
domain representation. Moreover, mutual exclusion relations that are not easily
recognized by a human expert can be detected in this way. Finally, this
approach can be also exploited as a coarse-grained reachability analysis for
the problem's facts. The disadvantages of this approach are that it is time
consuming and that it does not detect mutual exclusion relations of higher
order than two.
The second approach is
to use domain specific knowledge in the form of axioms. For example, an axiom
can state that a truck or a plane is always located at some place. So, if the
goals do not determine where a truck is, we can deduce a set of candidate goal
facts using this axiom. The advantage of this approach is that the time needed
to deduce the candidate facts is negligible, in comparison with the time needed
for the rest of the planning process. Moreover, more complicated relations than
simple binary mutual exclusion ones can be encoded. The disadvantage is that
extra labor is required in the domain encoding. However, several methods for
automatic discovery of domain axioms have been proposed, e.g. the Discoplan system (Gerevini &
Schubert, 1998) and the work of Fox and Long on the automated inference of
invariants (Fox & Long, 2000), and it is in our future plans to adopt such
a method in Grt.
The Grt planner uses the first approach to
detect the missing goal facts. Thus, an overhead in total solution time is
imposed by the extra pre-processing work. The contribution of this work to the
total problem solving time varies from less than 10% in domains like blocks-world,
to more than 20% in domains like logistics. The ratio depends on the
difficulty of the domain, i.e. how much time is consumed by the search phase.
Logistics problems are easier than blocks-world problems, so in this
domain the overhead is more severe. In the future, we intend to adopt an
automatic method for detecting domain axioms, in order to avoid this overhead.
Ioannis
Refanidis
14-8-2001