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Nadir Point Estimation Using Evolutionary Approaches : Better Accuracy and Computational Speed through Focused Search
Dept. of Mathematical Information Technology, University of Jyväskylä.
Indian Institute of Technology Kanpur. (Kanpur Genetic Algorithms Laboratory)
2010 (English)In: Multiple Criteria Decision Making for Sustainable Energy and Transportation Systems: Proceedings of the 19th International Conference on Multiple Criteria Decision Making, Auckland, New Zealand, 7th - 12th January 2008 / [ed] M. Ehrgott, B. Naujoks, T.J. Stewart, J. Wallenius, Springer Berlin/Heidelberg, 2010, 339-354 p.Conference paper (Refereed)
Abstract [en]

Estimation of the nadir objective vector representing worst objectivefunction values in the set of Pareto-optimal solutions is an important task, particularlyfor multi-objective optimization problems having more than two conflictingobjectives. Along with the ideal point, nadir point can be used to normalize theobjectives so that multi-objective optimization algorithms can be used more reliably.The knowledge of the nadir point is also a pre-requisite to many multiplecriteria decision making methodologies. Moreover, nadir point is useful for an aidin interactive methodologies and visualization softwares catered for multi-objectiveoptimization. However, the computation of an exact nadir point for more than twoobjectives is not an easy matter, simply because the nadir point demands the knowledgeof extreme Pareto-optimal solutions. In the past few years, researchers haveproposed several nadir point estimation procedures using evolutionary optimizationmethodologies. In this paper, we review the past studies and reveal an interestingchronicle of events in this direction. To make the estimation procedure computationallyfaster and more accurate, the methodologies were refined one after the otherby mainly focusing on finding smaller and still sufficient subset of Pareto-optimalsolutions to facilitate estimating the nadir point. Simulation results on a number ofnumerical test problems demonstrate better efficacy of the approach which aims tofind only the extreme Pareto-optimal points compared to other two approaches.

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2010. 339-354 p.
, Lecture Notes in Economics and Mathematical Systems, 634, part 4
Keyword [en]
Nadir point, Multiobjective optimization, Evolutionary multiobjective optimization, EMO, Bilevel optimization, Payoff table, Hybrid search
National Category
URN: urn:nbn:se:kth:diva-74409DOI: 10.1007/978-3-642-04045-0_29ISI: 000300517300029ScopusID: 2-s2.0-79960035194OAI: diva2:489556
The 19th International Conference on Multiple Criteria Decision Making, Auckland, New Zealand, 7th - 12th January 2008
QC 20120206Available from: 2012-02-06 Created: 2012-02-03 Last updated: 2012-02-06Bibliographically approved

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