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8.1  Measuring the Effectiveness of the Related Facts

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.

 

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Next: Using Several Methods to Enhance the Goals Up: The GRT Planning System Previous: Performance Results

Ioannis Refanidis

14-8-2001