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3.      Detecting and Enhancing Incomplete States

Backward heuristic construction induces a problem: In most of the problems the goals do not constitute a complete state description, so it is not possible to apply inverted actions to them. For example, in the commonly used logistics problems, where packages have to be moved between several locations via trucks and planes, the goals do not determine the final locations of the trucks and the planes. The source of the problem is that the Grt heuristic is constructed using a stricter than usual regression, i.e. it uses actions, the add effects and the non-deleted preconditions of which (i.e. the preconditions of the corresponding inverted actions) are included within the goals (in the usual regression, actions with at least one add effect within the goals are used). In this way Grt succeeds in obtaining more precise estimates and avoiding unreachable facts.

The solution adopted by Grt to confront the problem of incomplete goal states is to enhance the goals with new facts, which are not in contradiction to the existing ones. For example, since the goals of the 'logistics.a' problem (Veloso, 1992) do not determine the final locations of the two planes, it is supposed that each one of the planes could be at any of the three airports. So, the ground facts:

(at plane1 pgh_air) (at plane1 bos_air) (at plane1 la_air)

(at plane2 pgh_air) (at plane2 bos_air) (at plane2 la_air)

can be added to the new goal state, which is called henceforth the enhanced goal state.

It should be noted that the enhanced goal state is only used in the pre-processing phase, for the construction of the heuristic. During the search phase, attention is paid only to reach the original goals. In this way, completeness is never lost, even in the case where wrong facts have been selected to enhance the Goals. However, selecting wrong facts may significantly affect the efficiency of the heuristic function.

Two issues arise when trying to enhance the goals: The first one is how to detect the candidate new goal facts and the second one is which of them to use. Sections 3.1 and 3.2 examine these issues, while in Section 3.3 a similar technique is used for identifying and enriching poor domain representations.

 

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Next: Detecting Missing Goal Facts Up: The GRT Planning System Previous: The Preprocessing Algorithm

Ioannis Refanidis

14-8-2001