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2.2       Backward Heuristic Construction

Instead of estimating the distance between each fact and the current state in a forward direction, as Asp does, Grt estimates the distance between each fact and the goals in a backward direction. This task is performed once, in a pre-processing phase. During the search phase, these estimates are used to estimate the distance between each intermediate state and the goals. The backward or forward estimation of the distance between two states often results in different values, since no heuristic is precise. However, the two directions result in estimates of equal quality on average.

The estimates of the distances between each fact and the goals are stored in a table, the records of which are indexed by the facts. We call this table the Greedy Regression Table (by which the acronym Grt comes from), since its estimates are obtained through greedy regression from the goals.

In order to construct the heuristic backwards, the actions of the problem have to be inverted. Let a be an action and S and S' be two states, such that a is applicable in S and S' = res(S,a). The inverted action a' of a is an action applicable in S', such that S = res(S', a'). The inverted action is defined by the original action as follows:

Pre(a')=Add(a) È Pre(a) \ Del(a)

Del(a')=Add(a)

Add(a')=Del(a)

(7)

The inverted ground actions are applied to the goals, assigning progressively to each ground fact p an estimate of its distance from the goals, in a way similar to Asp. Applying inverted actions to the goals presupposes that the goals form a complete state. In Section 2 it is assumed that this is always the case, whereas in Section 3 the case of incomplete goal states is treated.

 

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Next: Related Facts Up: The GRT Planning System Previous: The ASP Heuristic

Ioannis Refanidis

14-8-2001