By Malte Helmert

Action making plans has consistently performed a principal position in synthetic Intelligence. Given an outline of the present scenario, an outline of attainable activities and an outline of the targets to be accomplished, the duty is to spot a series of activities, i.e., a plan that transforms the present state of affairs into person who satisfies the objective description.

This monograph is a revised model of Malte Helmert's doctoral thesis, fixing making plans projects in conception and perform, written less than the supervision of Professor Bernhard Nebel as thesis consultant at Albert-Ludwigs-Universität Freiburg, Germany, in 2006. The e-book comprises an exhaustive research of the computational complexity of the benchmark difficulties which were utilized in the prior decade, specifically the traditional benchmark domain names of the overseas making plans Competitions (IPC). even as, it contributes to the perform of fixing making plans projects through featuring a robust new method of heuristic making plans. the writer additionally presents an in-depth research of so-called routing and transportation problems.

All in all, this publication will give a contribution considerably to advancing the cutting-edge in automated making plans.

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Extra resources for Understanding Planning Tasks: Domain Complexity and Heuristic Decomposition

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Plan-D ∈ PS, then PlanEx-D ∈ P. Plan-D ∈ NPO, then PlanEx-D ∈ NP and then PlanLen-D ∈ NP. Plan-D ∈ NPS, then PlanEx-D ∈ NP. PlanLen-D is NP-hard, then Plan-D ∈ / PO unless P = NP. PlanEx-D is NP-hard, then Plan-D ∈ / PS unless P = NP. Proof. For the first statement, an optimal polynomial time planning algorithm can be used for polynomially deciding plan existence and bounded plan existence: Run the algorithm and test if it generates a solution (for plan existence) or a solution satisfying the given measure bound (for bounded plan existence).

I: capacity j: mobiles k: fuel units l: move cost m: pickup cost 1: 1: 1: 1: 0: one portable one mobile one per location unit cost free ∞: unbounded +: one type ∞: unbounded ∗: varies 1: unit cost ∗: varies ∗: many types ∗: varies ∗: varies Fig. 1. Summary of restrictions in Transportkij -[l, m] and Routekj -[l] 46 4 Transportation and Route Planning j=∗ i=∗ k=∗ l=∗ m=∗ j=+ i=1 i=∞ j=1 k=1 k=∞ l=1 m=0 m=1 Fig. 2. 2 General Results We begin our investigation of Transport and Route by proving some general results.

Which traverse the roadmap. There is a set of portables (keys, balls, passengers, . . ), which can either be at a location or carried by a mobile. These classes of entities are disjoint, and there are no other entities. M. Helmert: Understanding Planning Tasks, LNAI 4929, pp. 39–73, 2008. c Springer-Verlag Berlin Heidelberg 2008 40 – 4 Transportation and Route Planning The goal is to move (a subset of) the portables to their respective final destinations. Most domains which we consider transportation domains satisfy all these properties.

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