1999), TP4 (Haslum & Geffner, 2001), LPG (Gerevini & Serina, 2002) and SAPA (Do &
Kambhampati, 2001). Unless noted otherwise, every planner **has been run with its default** settings. Some of the planners could not be run in some domains due to parsing problems or memory allocation errors. In such cases, we just omit that **planner from consideration** for those particular domains.

## 4.1.1 Planners Used In The Comparison Studies

STAN is a disjunctive planner, which is an optimized version **of the Graphplan algorithm**
that reasons with invariants and symmetries to reduce the size of the search space. Blackbox is also based on the Graphplan algorithm but it works by converting planning problems specified in STRIPS (Fikes & Nilsson, 1971) notation into boolean satisfiability problems and solving it using a SAT solver (the version we used defaults to SATZ).5 **LPG (Gerevini**
& Serina, 2002) was judged the best performing planner at the **3rd International Planning** Competition (Long & Fox, 2002), and it is a planner based on planning graphs and local search inspired by the Walksat approach. LPG was run with its **default heuristics and** settings. Since LPG employs an iterative improvement algorithm, the quality of the plans produced by it can be improved by running it for multiple iterations (thus increasing the running time). To make the comparisons meaningful, we decided to run LPG for two iterations (n=2), since beyond that, the running time of LPG **was generally worse than**
that of AltAltp. Finally, we have also chosen two metric temporal planners, **which are able**
to represent parallel plans because of their representation of time and durative actions. TP4 (Haslum & Geffner, 2001) is a temporal planner based on HSP*p (Haslum & Geffner, 2000), which is an optimal parallel state space planner with **an IDA* search algorithm.** The last planner in our list is SAPA (Do & Kambhampati, 2001). SAPA is a powerful domain-independent heuristic forward chaining planner for **metric temporal domains that** employs distance-based heuristics (Kambhampati & Sanchez, **2000) to control its search.**

## 4.1.2 Comparison Results In Different Domains

We have run the planners in the Gripper domain from the International Planning and Scheduling competition from 1998 (McDermott, 2000), as well as three different domains (Logistics, Scheduling, and Elevator-miconic-strips) from **2000 (Bacchus, 2001), and three** more from the 2002 competition (Long & Fox, 2002) - DriverLog, ZenoTravel, and Satellite. In cases where there were multiple versions of a domain, we used the "STRIPS Untyped" versions.6**. We discuss the results of each of the domains below.**
Gripper: **In Figure 9(a), we compare the performance of** AltAltp on the Gripper domain (McDermott, 2000) to the rest of the planners excluding **SAPA. The plot shows the**
results in terms of number of (parallel) steps. We can see that for even this simplistic domain, AltAltp **and LPG are the only planners capable of scaling up and generating parallel**