The work of detecting and
eliminating irrelevant objects has been motivated by the need to simplify the
sub-problems resulting after the decomposition of a problem, when using
XOR-constraints. Performance results for this case are presented in Section 8.4.
This section presents indicative results concerning the effectiveness of the
technique in the colored logistics domain that has been mentioned in
Section 4.1. For this purpose we enhanced the first group of logistics
problems of the Aips-00
competition with the required predicates and actions and we added propositions
defining the original color of each package to the initial states. Figure 9
presents the time needed to solve the problems, with and without the irrelevant
objects elimination technique. As it results from the experimental data, there
is an improvement in the solution time of about 20%. Note that in both cases
the same plans have been found; however, this would probably not be the case in
other domains.
In order to measure
the efficiency of the numerical representation of resources, we ran Grt both in the original mystery
domain and in a modified domain, where resources have been represented by
numbers. Figure 10 presents the time needed to solve the problems with both
cases of Grt. Note that in these
experiments only the solvable mystery problems have been taken into account.
As it results from Figure 10, Grt
was significantly faster, when a numerical representation is used. The
improvement is 65% on average. As for the solution length, in both cases the
same have been found again.
Both techniques
evaluated in this section gain their speedup mainly from the pre-processing
phase, since distances for a significantly smaller number of facts have to be
estimated. As for the search phase, there is also a speedup, but is less
important. Actually, the number of applicable actions to each state is the same
with the two alternative representations of resources, since these are
equivalent. Moreover, the detection of the applicable actions in the atom-based
representation takes about the same time, due to the effective constraint-satisfaction
techniques that Grt uses when
instantiating the action schemata. Concerning the elimination of irrelevant
objects, without this technique, there are more applicable actions to a state,
which however are usually not selected, since they do not lead to an improving
state. However, the time spent in the detection of these actions may be not
negligible.
The significance of
the two techniques lies in that the overall time needed to solve the problems
remains about the same, in the case where more irrelevant objects are used, and
exactly the same, in the case where more resource levels are used. In the case
of more irrelevant objects, these are detected (in negligible cost) and
eliminated from the subsequent stages (Figure 6). However, there is some overhead
imposed by the stages that precede the irrelevant objects elimination stage,
from where these objects have not been eliminated.
In the case of more
resource levels, these do not lead to the generation of new ground facts and
actions, so all the pre-processing stages consume exactly the same time. As for
the state-space search, this is also executed in the same time, but only in the
case where neither the initial availability of resources, nor their consumption
by the actions, nor finally the constraints over them have been changed. If
this is not the case, then we are dealing with a different planning problem,
which may be harder to solve.
Figure 9: Time (in msecs) needed to solve the colored
logistics problems,
with and without the irrelevant object elimination technique.
Figure 10: Time (in msecs) needed to
solve the solvable mystery problems,
when the original atom-based or a number-based representation for resources is
used.
Ioannis
Refanidis
14-8-2001