does, presents the advantage of preserving completeness; however, the cost is that a parallel machine is required.

We close the reference to other heuristic state-space planners with the STAN planning system 
(Fox & Long, 1998; Long & Fox, 1999). STAN is not a heuristic state-space planner, at least in its basic architecture, but a graph-based planner, which uses several pre-processing techniques for extracting useful domain information that is exploited for more efficient graph construction and solution extraction. However, in the AIPS-00 competition a hybrid architecture was used (Long & Fox, 2000; Fox & Long, 2001), where a heuristic state-space planning module was employed to solve specific identified sub-problems. Thus STAN succeeded in improving its performance, especially in cases of transportation domains.

Concerning problem decomposition, work has been done on goal ordering (Cheng & Irani, 1989; Drummond & Currie, 1989). Recently a similar approach has been proposed by Koehler 
(1998) and has been extended by Koehler and Hoffmann (2000). This approach automatically derives an ordering relation between the goal facts, which can be used by any planner to search for increasing sets of subgoals. The advantage of this approach is that no extra information is needed, except for the usual domain definition, while the disadvantage, with respect to the XOR-constraints approach, is that only the goal facts are taken into account in the intermediate states that are constructed. This approach has been adopted by the FF planning system.

## 8. Performance Results

In this section, we present performance results from several domains, taken from the literature and from the two planning competitions. First, we investigate how the several techniques of GRT
contribute to its overall performance and then we compare GRT to other planners.

The measurements that follow were taken on a SUN Enterprise 3000 machine running at 167MHz, with 256 MB main memory and operating system Solaris 2.5.1. In the experiments we set a 5 minutes time limit for all experiments and planners 6.

## 8.1 Measuring The Effectiveness Of The Related Facts

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

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).