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8.3  Reducing the Size of the Problem

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.

 

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Next: XOR-constraints Up: The GRT Planning System Previous: Using Several Methods to Enhance the Goals

Ioannis Refanidis

14-8-2001