

![0_image_0.png](0_image_0.png)

problems. However, it would be interesting to test the efficiency of this method to other heuristic state space planners.

## 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 XORconstraints. 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, 