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.
Figure 16: Solution length and time
(msecs) for the blocks-world problems
using the 4-action schemas domain representation.
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 solved all the smallest ones. Hsp-2 solved all the problems with up to 19 blocks, while Altalt and Stan stopped at 14 blocks.
Figure 17: Solution length and time (msecs) for the blocks-world
problems
using the 3-action schemas domain representation.
Ioannis
Refanidis
14-8-2001