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Cutting plane method in decision analysis
Mid Sweden University, Faculty of Science, Technology and Media, Department of Information Technology and Media. (FSCN - Fibre Science and Communication Network)
2004 (English)In: Proceedings of the Ninth Meeting of the Nordic Section of the Mathematical Programming Society, October 22–23, 2004, Linköpings universitet, Norrköping, Sweden, 2004Conference paper, Published paper (Other academic)
Abstract [en]

Several computational decision analysis approaches have been developed over a number of years for solving decision problems when vague and numerically imprecise information prevails. However, the evaluation phases in the DELTA method and similar methods often give rise to special bilinear programming problems, which are time-consuming to solve in an interactive environment with general nonlinear programming solvers. This paper proposes a linear programming based global optimization algorithm that combines the cutting plane method together with the lower bound information for solving this type of problems. The central theme is to identify the global optimum as early as possible in order to save additional computational efforts.

Place, publisher, year, edition, pages
2004.
Series
Linköping Electronic Conference Proceedings, ISSN 1650-3740
Keyword [en]
cutting plane, lower bound, global optimization
National Category
Computer Science
Identifiers
URN: urn:nbn:se:miun:diva-5688Local ID: 2199OAI: oai:DiVA.org:miun-5688DiVA: diva2:30721
Available from: 2008-09-30 Created: 2008-09-30 Last updated: 2011-04-21Bibliographically approved
In thesis
1. Bilinear optimization in computational decision analysis
Open this publication in new window or tab >>Bilinear optimization in computational decision analysis
2005 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In real-life decision analysis, significant recognition has been given to theunrealistic expectation of numerically precise information. Many modernapproaches attempting to handle imprecision have focused more on representationand less on evaluation. The DELTA method, as one of the fewleading approaches, challenges this issue by its evaluation framework thatcan accommodate both precision and imprecision. However, computationally,DELTA and similar approaches may incur time-consuming calculationsdue to the introduction of imprecise information concerning probability andutility. In general, those problems are bounded non-convex bilinear optimizationprograms with disjoint linear constraints, which cannot be solvedeffectively by any existing general-purpose global optimization technique.This thesis presents two enhanced cutting plane algorithms for solvingbounded disjoint bilinear programs arising in computational decision analysis.Each algorithm consists of a local phase designed to determine a localoptimizer from an approximate solution, and a global phase designed to systematicallyexplore the feasible region, subset by subset. These two phasesare switched automatically during the global search procedure. The basicframework builds upon previously developed efficient cutting plane methods.By embedding the lower bounding technique in a branch and bound procedure,the improvement of their performances seems encouraging in the lightof computational experience. Even though the motivation to develop thesealgorithms stems from computational decision analysis, the idea can also beextended to the development of optimization approaches for handling generalbounded disjoint bilinear programs, especially for larger sized ones.

Place, publisher, year, edition, pages
Sundsvall: Mittuniversitetet, 2005
Series
Mid Sweden University doctoral thesis, ISSN 1652-893X ; 2
National Category
Information Science
Identifiers
urn:nbn:se:miun:diva-8856 (URN)
Public defence
2005-05-27, O102, Åkroken, Sundsvall, 13:15 (English)
Opponent
Supervisors
Available from: 2009-05-06 Created: 2009-05-06 Last updated: 2009-07-13Bibliographically approved

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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf