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A Multi-parameter Complexity Analysis of Cost-optimal and Net-benefit Planning
Linköping University, Department of Computer and Information Science, Software and Systems. Linköping University, Faculty of Science & Engineering. (TCSLAB)
Linköping University, Department of Computer and Information Science, Software and Systems. Linköping University, Faculty of Science & Engineering. (TCSLAB)
2016 (English)In: Twenty-Sixth International Conference on Automated Planning and Scheduling King's College, London June 12, 2016 – June 17, 2016 / [ed] Amanda Coles, Andrew Coles, Stefan Edelkamp, Daniele Magazzeni, Scott Sanner, AAAI Press, 2016, p. 2-10Conference paper, Published paper (Refereed)
Abstract [en]

Aghighi and Bäckström have previously studied cost-optimal planning (COP) and net-benefit planning (NBP) for three action cost domains: the positive integers (Z_+), the non-negative integers (Z_0) and the positive rationals (Q_+). These were indistinguishable under standard complexity analysis for both problems, but separated for COP using parameterised complexity analysis. With the plan cost, k, as parameter, COP was W[2]-complete for Z_+, but para-NP-hard for both Z_0 and Q_+, i.e. presumably much harder. NBP was para-NP-hard for all three domains, thus remaining unseparable. We continue by considering combinations with several additional parameters and also the non-negative rationals (Q_0). Examples of new parameters are the plan length, l, and the largest denominator of the action costs, d. Our findings include: (1) COP remains W[2]-hard for all domains, even if combining all parameters; (2) COP for Z_0 is in W[2] for the combined parameter {k,l}; (3) COP for Q_+ is in W[2] for {k,d} and (4) COP for Q_0 is in W[2] for {k,d,l}. For NBP we consider further additional parameters, where the most crucial one for reducing complexity is the sum of variable utilities. Our results help to understand the previous results, eg. the separation between Z_+ and Q_+ for COP, and to refine the previous connections with empirical findings.

Place, publisher, year, edition, pages
AAAI Press, 2016. p. 2-10
Keywords [en]
cost-optimal planning, parameterised complexity, numeric domains
National Category
Computer Systems
Identifiers
URN: urn:nbn:se:liu:diva-136278ISBN: 9781577357575 (print)OAI: oai:DiVA.org:liu-136278DiVA, id: diva2:1087081
Conference
Twenty-Sixth International Conference on Automated Planning and Scheduling (ICAPS-16), London, UK, June 12–17, 2016
Available from: 2017-04-05 Created: 2017-04-05 Last updated: 2019-05-08Bibliographically approved
In thesis
1. Computational Complexity of some Optimization Problems in Planning
Open this publication in new window or tab >>Computational Complexity of some Optimization Problems in Planning
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Automated planning is known to be computationally hard in the general case. Propositional planning is PSPACE-complete and first-order planning is undecidable. One method for analyzing the computational complexity of planning is to study restricted subsets of planning instances, with the aim of differentiating instances with varying complexity. We use this methodology for studying the computational complexity of planning. Finding new tractable (i.e. polynomial-time solvable) problems has been a particularly important goal for researchers in the area. The reason behind this is not only to differentiate between easy and hard planning instances, but also to use polynomial-time solvable instances in order to construct better heuristic functions and improve planners. We identify a new class of tractable cost-optimal planning instances by restricting the causal graph. We study the computational complexity of oversubscription planning (such as the net-benefit problem) under various restrictions and reveal strong connections with classical planning. Inspired by this, we present a method for compiling oversubscription planning problems into the ordinary plan existence problem. We further study the parameterized complexity of cost-optimal and net-benefit planning under the same restrictions and show that the choice of numeric domain for the action costs has a great impact on the parameterized complexity. We finally consider the parameterized complexity of certain problems related to partial-order planning. In some applications, less restricted plans than total-order plans are needed. Therefore, a partial-order plan is being used instead. When dealing with partial-order plans, one important question is how to achieve optimal partial order plans, i.e. having the highest degree of freedom according to some notion of flexibility. We study several optimization problems for partial-order plans, such as finding a minimum deordering or reordering, and finding the minimum parallel execution length.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2017. p. 35
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1854
National Category
Computer Systems
Identifiers
urn:nbn:se:liu:diva-136280 (URN)10.3384/diss.diva-136280 (DOI)978-91-7685-519-5 (ISBN)
Public defence
2017-06-16, Ada Lovelace, B-hus, Linköping University, SE-58183 Linköping, Linköping, 13:15 (English)
Opponent
Supervisors
Funder
CUGS (National Graduate School in Computer Science)
Available from: 2017-05-17 Created: 2017-04-05 Last updated: 2017-09-01Bibliographically approved

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