more problems and this is because the regression mechanism did not encounter invalid states. Note that, although the goal state was complete in this case, GRT treated these problems as usual, attempting to enhance the goals.

## 8.6.2 Blocks-World

For *blocks-world* problems in the AIPS-00 competition a four-actions representation was used, i.e. actions push, *pop, stack* and *unstack*. This representation is unsuitable for GRT, as it has been explained in Section 7.1. So, GRT did not solve most of the *blocks-world* problems. Figure 16 presents the results of all planners in all *blocks-world* problems. 

As shown in Figure 16, FF exhibits the best performance, solving the majority of the problems and producing better plans than the other planners. The superiority of FF in this domain is due to a technique called *Added Goal Deletion*, according to which the goal facts are ordered and achieved in a progressive manner (Hoffmann & Nebel, 2001; Koehler and Hoffmann, 2000). This technique is especially suited for the *blocks-world* domain and the 4-action schemas representation. However, this technique does not always succeeds to produce good orderings and this is the reason why FF fails to solve some of the easiest problems, which have been solved by the other planners.

As for the remaining planners, HSP-2 succeeded in solving all problems with up to 18 blocks and one problem with 24 blocks, GRT and ALTALT solved problems up to 14 blocks and STAN up to 12 blocks. Moreover, GRT produced plans of low quality.

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

In order to demonstrate the influence of the domain representation in the efficiency of GRT, we ran all the planners in the same problems using the alternative 3-action schemas domain representation. The results are shown in Figure 17.

The performance of GRT is significantly improved, solving problems with up to 33 blocks and producing better plans than the other planners. Moreover, with the exception of the smallest problems, GRT is faster than the other planners, but FF. The latter solved less large problems, but 