these domains the closed-list of states has been proved invaluable, improving drastically the performance of GRT. For example, in the *freecell* domain and without the closed list of visited states, the GRT planner in the AIPS-00 planning competition succeeded in solving problems with up to 6 cards per suit, while with this data structure it can solve some of the more difficult ones (13 cards per suit). Note that for an efficient implementation of the closed-list of visited states a hashtable data structure has been adopted.

## 8.6 Comparison To Other Planners

In this section, we present comparative results between the GRT planner and other planners. We decided to use HSP-2 (Bonet & Geffner, 2001), FF (Hoffman & Nebel, 2001), STAN (Long & Fox, 2000; Fox & Long, 2000, 2001) and ALTALT (Nigenda, Nguyen & Kambhampati, 2000)
7. All these planners took part in the domain independent track of the AIPS-00 planning competition. We selected these planners because HSP-2 and STAN are state-of–the-art planning systems, FF has been awarded for its outstanding performance in the last competition and ALTALT is a new but very promising domain-independent state-space heuristic planner.

The aim of our experiments is to have an overall view of the performance of the evaluated systems. Performing pair wise comparisons between specific optimization techniques is not possible, since these techniques are implemented on top of different systems. Moreover, this kind of comparisons is out of the scope of this paper, which focuses in the use of specific directions for constructing the heuristic and traversing the space of the states, in the area of domain-independent heuristic state-space planning, and not in the evaluation of the numerous pre-processing optimization techniques. However, in the cases where we identify the contribution of a specific feature in the performance of a planner, we comment on this.

In order to have fair comparisons, we used exactly the same problem and domain description files for all planners. So, GRT ran without XOR-constraints or numerical representation of resources. Moreover, although the irrelevant object elimination technique is an integral feature of GRT, it had no contribution in these domains, since there were not irrelevant objects. We believe that the absence of irrelevant objects in these domains does not mean that this technique has limited applicability, but it is an indication that more real domains for testing purposes have to be used in the future, since the planning tasks in our real-life are full of irrelevant objects. Finally, the domain enrichment technique proved valuable for the *elevator* domain only. However, this technique, as well as the goal enhancement one, has not to be seen as an optimization technique, but as a way to overcome the problems that arise from the backward direction of the heuristic construction.

We tested the planners in several domains taken from the planning competitions and from the literature, in the same workstation and within the 5 minutes time limit. The results are presented in the following.

## 8.6.1 Logistics

For the *logistics* domain we used the test suite of the AIPS-00 competition. The results are shown in Figure 14. In this domain GRT, as well as FF and STAN, performed well, solving all the problems. 

HSP and ALTALT failed to solve the large problems within the time-limit. In general, best plans are found by STAN, which uses special domain-dependent heuristics for problems identified as 