P. Haslum and H. Ge#ner, Heuristic Planning with Time and Resources, Proceedings of ECP-01, Springer, 2001.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....is a main challenge of planning tasks [12, 13] This resource is a duration of actions, where the preconditon of an action holds at the beginning and the e#ects add and del take place at some point after the beginning and before the end. In the following, two kinds of resources are distinguished [14]: Renewable resources are only used by an action and not used up. After the duration the resource has the same quantity as before the execution of the action. Consumable resources vanish when used by an action. Actions can also produce a 8 quantity of a resource, i.e. increase instead of ....

....Therefore, the (consumable) resources used in the experiments decrease the time available. The application of a planner to find an optimal temporal order for the modules of at least two call set ups requires the handling of renewable and consumable resources and of time. TP4 from the class HSP # [14] is a planner with metric time and certain kinds of resources, based on heuristic search. These features and specially the domain independence resulted in the choice of TP4 from the available planners . A heuristic planner can be described by considering the search space with the branching ....

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P. Haslum and H. Ge#ner. Heuristic planning with time and resources. In Proc. IJCAI Workshop on Planning with Resources, 2001.

....resources. If numerical effects do not bound integral values, infinite state spaces are likely to be generated. However, by assuming finitely many interesting events the problem class becomes tractable and is effectively dealt by schedulers that usually minimize the make span of concurrent actions [11]. 3. Numerical Preconditions. We distinguish finite and infinite branching problems. With finite branching, execution time of an action is not parameterized, while with infinite branching, an infinite number of actions can be applied. These problems have ever since been confronted to model ....

....for the exploration, as a byproduct the pre compiler flushes a file instance.h to be used as an interface for other planning engines. Except of grouping of facts, numerical preconditions and more complex numerical formulae, the format matches the one produced by the two phase planning system TP4 [11]. 4 Solving Zeno Travel For planning we choose the A algorithm that instantiates and generates the successor set according to a combined priority of generating path length and heuristic estimate. The important fact is that blind exploration algorithms are likely to become lost in infinite state ....

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P. Haslum and H. Geffner. Heuristic planning with time and resources. In European Conference on Planning (ECP), 2001.

....Maria Fox and Derek Long have therefore developed PDDL2.1 [5] which amongst other things incorporates the possibility to define numerical constraints and effects on a finite set of numerical state variables. Some approaches have been made to do planning in more expressive formalisms (e.g. [6, 9, 10, 7]) One of the most recent ones, and a relative of FF, is the Sapa system, developed by Do and Kambhampati [4] In FF, a heuristic estimate for a state s during forward search is obtained by extracting, in Graphplan [2] style, a relaxed plan that achieves the goals from s, where the relaxation is ....

Patrick Haslum and Hector Geffner, `Heuristic planning with time and resources', in Proc. ECP-01, pp. 121--132.

....exit distance under h ; the road map diameter in the AIPS 2002 instances varies around 1 to 6. Let us focus on the other heuristic planners. Those that are state of the art in runtime all use relaxed plan heuristics in one way or the other. There are 33 also planners based on other heuristics [41,42], but these optimal planners can not compete with the runtime performance of their sub optimal relaxed plan based counterparts. Except FF, the most successful heuristic planners in the last 3 years (speci cally in the AIPS 2000 and AIPS 2002 competitions) have been HSP2 [9] STAN4 [19] Mips ....

P. Haslum, H. Gener, Heuristic planning with time and resources, in: Cesta and Borrajo [54], pp. 121-132.

....Maria Fox and Derek Long have therefore developed PDDL2.1 [6] which amongst other things incorporates the possibility to define numerical constraints and effects on a finite set of numerical state variables. Some approaches have been made to do planning in more expressive formalisms (e.g. [7,10,11,8]) One of the most recent ones, and a relative of FF, is the Sapa system, developed by Do and Kambhampati [5] In FF, a heuristic estimate for a state s during forward search is obtained by extracting, in Graphplan [2] style, a relaxed plan that achieves the goals from s, where the relaxation is ....

Patrick Haslum and Hector Geffner, Heuristic planning with time and resources', In Cesta and Borrajo [4], pp. 121--132.

....by the competition committee, are provided in the next section. Our first test suite for the experiments, which show the ability to produce solutions with tradeoffs between time and cost quality, consisted of a set of randomly generated temporal logistics problems provided by Haslum and Geffner [19]. In this set of problems, we need to move packages between locations in different cities. There are multiple ways to move packages, and each option has different time and cost requirements. Airplanes are used to move packages between airports in different cities. Moving by airplanes takes only ....

....term of solving time and solution quality. Utility of post processing: Figure 10 shows the utility of the greedy post processing technique discussed in Section 5. The test suite contains the same set of problems discussed earlier (i.e. random generated temporal logistics problem provided with TP4[19], and the metric temporal logistics problem) These graphs show the comparisons of makespan values of original parallel position constrained (p.c) plans and the order constrained (o.c) plans returned after post processed. In the left side of Figure 10, we show the comparison between four ....

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Haslum, P. and Geffner, H. 2001. Heuristic Planning with Time and Resources In Proc. of Sixth European Conference on Planning

....(OR) and constraint solving techniques. A number of research areas are related to our work. Workflow scheduling under temporal constraints and resource management have already been mentioned. Other related areas are job shop scheduling [10, 5, 18, 11, 38] planning in Artificial Intelligence (AI) [30, 8, 19, 9, 29, 28] and agent based workflow systems [37, 34, 25, 26, 27, 20] We discuss the relationship between these works and ours in Section 9. This paper is organized as follows. Section 2 presents a concrete example to illustrate the problem. Section 3 briefly sketches the use of CTR for workflow It ....

....work is orthogonal to the works on constraint solving we use constraint solvers in Stage 3 of our scheduling process. Planning in AI: As in the scheduling problem in OR, constraint programming is used for planning in AI [8, 30] and there also are works on planning under resource constraints [19, 9]. However, only a small number of works in this area propose planning as a workflow scheduling technique [28, 29] However, those that do deal with scheduling do not address this problem under resource allocation constraints. Instead, planning techniques are used to schedule dynamically changing ....

P. Halsum and H. Ge#ner. Heuristic planning with time and resource. In IJCAI Workshop on Planning with Resources, Seattle, USA, August 2001.

....and used for guiding the search through the search space. In [11] it is argued that also search within Graphplan may be viewed as heuristic search, although its basic principles are di erent than in other heuristic search planners. Both time and consumable renewable resources have been embedded [37] to heuristic planning to combine expressivity and performance. Although mentioned approaches represent state of the art of AI planning, we feel that our approach has certain advantages over these planners. In this thesis we give a logically clear and complete language for describing certain ....

....and other operators are handled at (possibly) lower levels of abstractions using di erent operator speci c algorithms. We certainly should experiment with heuristics while solving reachability or coverability problem as planning as heuristic search paradigm has turned out to be successful [11, 37, 41]. As propositional abstraction, in the way we interpreted it here, generates a lot of blind search for binding individuals, we certainly should experiment with di erent encodings while representing original LL programs as propositional clauses. ....

P. Haslum, H. Gener. Heuristic planning with time and resources. In Proceedings of the Seventeenth International Joint Conference on Arti cial Intelligence (IJCAI-01) Workshop on Planning with Resources, 2001.

.... s in (6) must have the form s = fpg; and the regression set R(s) contain only states s 0 = pre(a) for actions a such that p 2 add(a) As a result, for m = 1, 6) becomes H 1 T (fpg; min a:p2add(a) dur(a) H 1 T (pre(a) 9) The corresponding equations for H 2 T are in [9]. 3.3 Search Algorithm Any admissible search algorithm, e.g. a , ida or DFS branch and bound [14] can be used with the search scheme described above to find optimal solutions. The planner uses ida with some standard enhancements (cycle checking and a transposition table) and an optimality ....

P. Haslum and H. Geffner. Heuristic planning with time and resources. In Proc. IJCAI Workshop on Planning with Resources, 2001. http://www.ida.liu.se/pahas/hsps/.

....only the states s 0 = pre(a) for actions a such that p 2 add(a) As a result, for m = 1, 6) becomes H 1 T (fpg) min a:p2add(a) dur(a) H 1 T (pre(a) 9) where H 1 T (E) stands for H 1 T (E; The planner uses the heuristic H 2 T . The corresponding equations are in [8]. 4.4 Search Algorithm Any admissible search algorithm, e.g. a , ida or branch and bound [12] can be used with the search scheme described above to find optimal solutions. We have used ida with some standard enhancements: a transposition table [16] cycle checking, and an optimality ....

P. Haslum and H. Geffner. Heuristic planning with time and resources. In Proc. IJCAI Workshop on Planning with Resources, 2001. To appear. http://www.ida.liu.se/pahas/hsps/.

....hG represented in the plan graph. For a set of atoms C, hG (C) is the index of the rst layer in the plan graph in which all atoms in C appear without a mutex. This heuristic is equivalent to the h 2 heuristic for parallel planning; namely hG = h 2 [19] 3. 3 Heuristics for Temporal Planning [20] shows how the heuristics h m can be extended to estimate makespan (completion time) in a temporal setting where actions can be executed concurrently and have di erent durations. The equation for m = 1 becomes h 1 T (C) 8 : 0 if C s 0 , else min o2O(p) D(o) h 1 T (prec(o) if C ....

....h 1 T (fpg) if jCj 1 (5) where the only change from the parallel estimator h 1 to the temporal estimator h 1 T is the substitution of the xed cost 1 by D(o) the temporal duration of the operator o. For m = 2, the temporal estimator h 2 T departs from parallel h 2 in other ways; see [20] for details. While the h 1 estimators are often too weak and the h 2 estimators are normally preferred, in this paper, for simplicity, we discuss branching schemes in the context of the former only. The generalization to higher order estimators is direct but the details are involved. The ....

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P. Haslum and H. Gener. Heuristic planning with time and resources. In Proc. IJCAI-01 Workshop on Planning with Resources, 2001. To appear.

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P. Haslum and H. Ge#ner, Heuristic Planning with Time and Resources, Proceedings of ECP-01, Springer, 2001.

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Patrick Haslum and Hector Geffner. Heuristic planning with time and resources. In Cesta and Borrajo [14], pages 121--132.

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