By by Patrik Haslum.
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A fact that is immediately apparent is the very large gap between the h1 and h2 heuristics: this is due to the presence of (at-most-one) invariants in the planning problems, which are detected by hm for m 2 but not by h1 . As described in chapter 2 (page 10) states (atom sets) inconsistent with some invariant are frequently encountered during a regression search, but can never be part of any solution path. Therefore, detecting such states (and pruning them from the search) is important for reducing the number of states searched.
1: the preconditions of (move C B A) are all present in the second proposition layer, but as noted above (on C B) and (clear A) are mutex, so the action is excluded from the second action layer. The addition of mutex relations refines the heuristic estimate obtained from the planning graph, in that the conjunction of two atoms is known to be unreachable in n−1 steps if the atoms appear without mutex for the first time in the nth proposition layer. It is still a relaxation though, since an action may require three (or more) preconditions, and it may be the case that even when any two of them are jointly 37 reachable the conjunction of all of them is still unreachable.
B)} are exactly-one invariants. b), making the invariant explicit. We make use of the state variable representation in the construction of pattern database heuristics, in chapter 4. Models for Planning with Time Planning problems including various temporal aspects have been addressed by several AI planning systems: actions with explicit duration, goals with deadlines and external events (events not under the control of the planner, but occurring at known times) were introduced by Vere (1983) and by Allen & Koomen (1983); the IxTeT planning system (Laborie & Ghallab 1995) combined durative actions with a model of resources, allowing finer control of concurrency and more; the planning model of the Zeno system (Penberthy & Weld 1994) described the world by continuous variables and actions causing continuous change to those variables; to name just a few.
Admissible heuristics for automated planning by by Patrik Haslum.