nextupprevious
Next: Best-First and Hill-Climbing Strategies Up: The GRT Planning System Previous: Reducing the Size of the Problem

8.4  XOR Constraints

We tested the efficiency of the XOR-constraints based decomposition in two domains: A simplified mystery domain, where resources have been removed, and the grid domain of the Aips-98 competition. We did not use the logistics domain for these experiments, since logistics problems are not difficult for the original Grt and the small profit from solving the easier sub-problems is compensated by the extra pre-processing cost of each sub-problem.

We removed resources from the original mystery domain because otherwise it would be probable to obtain unsolvable subproblems. As it has been noted in Section 5, decomposing a problem may lead to loss of completeness, thus the technique is unsuitable for domains where deadlocks may arise, as the original mystery one. Note that by removing resources, all mystery problems become solvable.

The XOR-constraints that have been defined for the simplified mystery domain were the following:

( ( xor ( at ?Truck * ) ) (truck ?Truck ))

( ( xor ( at ?Package * ) (in ?Package * ) ) ( package ?Package ) )

while for the grid domain were the following ones:

( ( xor ( at-robot * ) ) )

( ( xor ( locked ?Place ) ( open ?Place ) ) ( place ?Place ) )

( ( xor ( at ?Key * ) ( holding ?Key ) ) ( key ?Key ) )

Note that in the grid domain an XOR-constraint denoting that the arm is either empty, or the robot holds a key has not been defined, since this would lead to pointless decompositions.

In both domains, we ran Grt with and without the problem decomposition technique. Additionally, in order to demonstrate the contribution of the irrelevant objects elimination technique when solving the sub-problems, we conducted experiments for this case in the simplified mystery domain. We did not consider this case in the grid domain, because no irrelevant objects can be detected there. Figure 11 presents the results.

(a) Simplified Mystery

(b) Grid Domain

Figure 11: Solution time (in msecs) and length with and without
the XOR-constraints based problem decomposition technique.

As for the simplified mystery domain, Grt without the problem decomposition technique generally produced shorter plans, as expected. On the other hand, the use of the XOR-constraints accelerated the problem decomposition process, especially in case of difficult problems. Actually, if we only consider the seven most difficult problems, the improvement achieved by the decomposition is 60% on average. Note however that, when the irrelevant objects elimination technique was not used, there was no improvement. In not difficult problems there is no acceleration, since, as in the case of the logistics problems, the small profit from the faster solution of the easier sub-problems is compensated by the cost of repeating the pre-processing phase for each one of them.

The grid domain was the most difficult one of the Aips-98 competition. The contestants managed to solve only the first problem. Grt without XOR-constraints could only solve the first problem, too. On the other hand, with the XOR-constraints based decomposition, Grt was able to solve the first four problems in the time limit of 5 minutes, while in the fifth problem it ran out of memory. It is worth noting that this domain produces multiple levels of decompositions. Figure 12 presents these levels for the strips-grid-y-2 problem.

As far as we know, the only planner that can cope with the grid problems effectively is Ff. We ran Ff in the five grid problems and it solved the first four, within the time limit of 5 minutes, with the following results (length/time): 14/230, 39/840, 40/7810 and 45/3280, which are considerably better compared to the performance of Grt.

 

 

Figure 12: Decomposition for the strips-grid-y-2 problem using XOR-constraints.

 

nextupprevious
Next: Best-First and Hill-Climbing Strategies Up: The GRT Planning System Previous: Reducing the Size of the Problem

Ioannis Refanidis

14-8-2001