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.
Ioannis
Refanidis
14-8-2001