In order to measure the contribution
of the related facts to the overall performance of Grt, we tested the planner, with and without related facts,
on problems from various domains. The results (solution length and time) are presented
in Figure 7 (a-f).
(a) Logistics problems (the goals have been enhanced with the most promising facts selection method)
(b) Blocks-world problems with 4 action
schemas (push, pop, pick-up, put-down)
(c) Blocks-world problems with 3 action
schemas (several cases of move)
(d) FreeCell Problems
(e) Elevator problems
(f) Puzzle problems
Figure 7:
Solution length and time (in msecs) with and without the use of related facts
for problems from several domains.
We can classify the
above domains in three groups. The first group includes the domains where the
use of related facts clearly improves both the solution length and time. This
group comprises the logistics domain (6a), the blocks-world, when
a 3-action schemas representation (move actions) is used (6c), and the puzzle
domain (6f). In these domains, there were many cases where Grt without related facts did not solve
the problems, while with the related facts it did. Moreover, in most cases when
both versions solved a problem, the version with the related facts was faster
and came up with a shorter plan.
The second group
includes domains where the use of related facts does not affect the
effectiveness of the planning process. This group comprises the elevator domain,
along with the gripper, the movie and the mystery ones. In
these domains, there is usually a single way to achieve the goals, so both
versions produce identical plans. However, due to the processing overhead, imposed
by the computation of the related facts, the version with the related facts is
slightly slower than the version without them.
Finally, the third
group includes the domains where there is no apparent predominance between the
two versions. The freecell domain and the blocks-world domain,
when a 4-action schemas representation is used (push, pop, pick-up,
put-down), fall into this class. In these domains the two versions do
not have equal performance, but there are problems where one version surpasses
the other and vice-versa.
The conclusion drawn
from the above measurements is that the effectiveness of the related facts
depends on the domain. They are more suitable in domains where there are
several ways to achieve the goals, as logistics or blocks-world.
Additionally, their
efficiency depends on the way the domain is codified. A typical example is the blocks-world
domain and the 4- and 3-action schemas representations. The problem with the
4-action schemas representation is that pushing and stacking a
block anywhere has always the same fact as precondition, i.e. that the block is
held by the arm. The consequence is that neither the related facts, nor the
distances are computed correctly. However this is not a problem of the related
facts, it is a common problem in domain independent heuristic planning, as it
results from the last planning competition. On the other hand, if a 3-action
schemas representation is used, then the paths to achieve the facts of the
domain are better tracked, so larger problems can be solved and the
contribution of the related facts is significant. We believe, finally, that
also in the freecell domain there is a representation inefficiency,
however we have not yet tried to construct an alternative one.
Ioannis
Refanidis
14-8-2001