Grt supports three methods of selecting among the candidate new goal facts:
§
Select
all candidate facts.
§
Use
the initial state facts.
§
Favor
the most promising facts.
The first method considers all the found facts as goal facts and assigns zero distances to them. In most cases, the enhanced goal state obtained in this way is not a valid state, since the new facts may be mutually exclusive to each other (but not to the original goals). The advantage of this approach is that the heuristic construction is very fast, since many facts are achieved at the beginning and a large number of actions become initially applicable. The disadvantage is that the obtained heuristic is less informative, since there are small differences between the obtained estimates. So, the best-first strategy tends towards breadth-first, visits more states, consumes more time, but generally produces better plans than the other two methods.
The second method
enhances the goals with the candidate facts that are also included in the
initial state, whereas the facts that are mutually exclusive with the selected
ones, are rejected. The advantage of this method, compared to the first one, is
that it results in greater differences between the facts' distances, and
therefore in faster search phase. On the other hand, a preference for the
initial state facts is a risk, because if these are not or - even worse - they
cannot be included within the goals, the search process may become disoriented,
leading to longer plans. This method is more suitable to problems, where there
are objects' properties that are unnecessary to solve the problem and are left
undetermined in the goals.
The third method tries
to combine the advantages of the other two. In contrast to them, where the
enhancement of the goals is performed in a single step, prior to the
construction of the heuristic, this method adds facts to the goals
progressively, in parallel with the heuristic construction. Actually, facts are
added to the goals only in the case where Agenda (Section 2.4) becomes empty. In this case, candidate facts are
progressively assigned zero distances, until a new inverted action satisfies
its preconditions. Each time a fact is selected, other candidate facts that are
mutually exclusive with the selected one are rejected from the set of candidate
facts.
The method favors
facts that can be combined with already achieved facts, in order to make an
inverted action applicable. The following four rules are applied in decreasing
preference:
-
The
facts that can be combined with the original goals are selected first.
-
Then,
the facts that can be combined with other already achieved facts are selected.
-
Next,
the facts that are included in the initial state are selected.
-
Finally,
the remaining candidate facts are selected randomly.
Generally, this method
results in the best solving speed and, in many cases, produces equal or even
better plans than the first two methods. However, especially in terms of plan
quality, there are many exceptions depending on the specific problem. It is not
difficult to create problems such that any of the methods presented above
performs best. The default method for the Grt
planner is the first one, which is the only method that has been used in the Aips-00 competition[1].
Note that there are
domains, like blocks-world, freecell and elevator of the Aips-00 competition, or the gripper
and the movie domains from the Aips-98
competition[2], where the goals are complete or
near-complete state descriptions; therefore the method used in these domains
does not affect neither solution time nor solution quality. In other domains,
as the mystery (Aips-98),
it is impossible to predict, without solving the planning problem, which of the
candidate facts could actually be goal facts, so in this case the only
acceptable method for goal completion is the first one.
Ioannis
Refanidis
14-8-2001