.2 Heuristic

1.1 Introduction hsp is a planner based on the ideas of heuristic search. 1 Heuristic search algorithms perform forward search from an initial state to a goal state using an heuristic function that provides an estimate of the distance to the goal. The 8-puzzle is the standard example of heuristic search and is treated in most AI textbooks 9, 10]. The main diierence between the 8-puzzle and our approach to planning is in the heuristic function. While in domains speciic tasks like the 8-puzzle the heuristic function is given (e.g., as the sum of the Manhat-tan distances); in domain independent planning, it has to be derived from the high-level representation of the actions and goals. A common way to derive an heuristic function h(s) for a problem P is by relaxing P into a simpler problem P 0 whose optimal solution can be computed eeciently. Then, the optimal cost for solving P 0 can be used as an heuristic for solving P 10]. For example, if P is the 8-puzzle, P 0 can be obtained from P by allowing the tiles to move into any neighboring position. The optimal cost function of the relaxed problem is precisely the Manhattan distance heuristic. In Strips planning, we obtain the heuristic values for a planning problem P by considering thèrelaxed' planning problem P 0 in which all delete lists are ignored. In other words, P 0 is like P except that delete lists are assumed empty. As a result, actions may add new atoms but not remove existing ones, and a sequence of actions solves P 0 when all goal atoms have been generated. As in recent planners such as satplan 5] and graphplan 1], we assume that action schemas have been replaced by all their ground instances, and we do not deal with variables. It is not diicult to show that for any initial state s, the optimal cost h 0 (s) to reach a goal in P 0 is a lower bound on the optimal cost h (s) to reach a goal in the original problem P. We could thus set the heuristic function h(s) to h 0 (s) and hence obtain an informative and admissible (non-overestimating) heuristic. The problem, however, is that computing h 0 (s) is still NP-hard. 2 We thus set for an approximation: we set the heuristic values h(s) to an estimate of the optimal values h …