IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v82y2015i1p1-18.html
   My bibliography  Save this article

On the effects of combining objectives in multi-objective optimization

Author

Listed:
  • Stephan Dempe
  • Gabriele Eichfelder
  • Jörg Fliege

Abstract

In multi-objective optimization, one considers optimization problems with more than one objective function, and in general these objectives conflict each other. As the solution set of a multi-objective problem is often rather large and contains points of no interest to the decision-maker, strategies are sought that reduce the size of the solution set. One such strategy is to combine several objectives with each other, i.e. by summing them up, before employing tools to solve the resulting multi-objective optimization problem. This approach can be used to reduce the dimensionality of the objective space as well as to discard certain unwanted solutions, especially the ‘extreme’ ones found by minimizing just one of the objectives given in the classical sense while disregarding all others. In this paper, we discuss in detail how the strategy of combining objectives linearly influences the set of optimal, i.e. efficient solutions. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Stephan Dempe & Gabriele Eichfelder & Jörg Fliege, 2015. "On the effects of combining objectives in multi-objective optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 82(1), pages 1-18, August.
    • Handle: RePEc:spr:mathme:v:82:y:2015:i:1:p:1-18
    DOI: 10.1007/s00186-015-0501-5
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00186-015-0501-5
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00186-015-0501-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Gal, Tomas & Hanne, Thomas, 2006. "Nonessential objectives within network approaches for MCDM," European Journal of Operational Research, Elsevier, vol. 168(2), pages 584-592, January.
    2. Alexander Engau & Margaret M. Wiecek, 2009. "Introducing Nonpolyhedral Cones to Multiobjective Programming," Lecture Notes in Economics and Mathematical Systems, in: Vincent Barichard & Matthias Ehrgott & Xavier Gandibleux & Vincent T'Kindt (ed.), Multiobjective Programming and Goal Programming, pages 35-45, Springer.
    3. Anthony Przybylski & Xavier Gandibleux & Matthias Ehrgott, 2010. "A Recursive Algorithm for Finding All Nondominated Extreme Points in the Outcome Set of a Multiobjective Integer Programme," INFORMS Journal on Computing, INFORMS, vol. 22(3), pages 371-386, August.
    4. A. Engau & M. M. Wiecek, 2007. "Cone Characterizations of Approximate Solutions in Real Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 134(3), pages 499-513, September.
    5. Gal, Tomas & Leberling, Heiner, 1977. "Redundant objective functions in linear vector maximum problems and their determination," European Journal of Operational Research, Elsevier, vol. 1(3), pages 176-184, May.
    6. Gal, Tomas & Hanne, Thomas, 1999. "Consequences of dropping nonessential objectives for the application of MCDM methods," European Journal of Operational Research, Elsevier, vol. 119(2), pages 373-378, December.
    7. Hunt, Brian J. & Wiecek, Margaret M. & Hughes, Colleen S., 2010. "Relative importance of criteria in multiobjective programming: A cone-based approach," European Journal of Operational Research, Elsevier, vol. 207(2), pages 936-945, December.
    8. C. Kaya & Helmut Maurer, 2014. "A numerical method for nonconvex multi-objective optimal control problems," Computational Optimization and Applications, Springer, vol. 57(3), pages 685-702, April.
    9. Gabriele Eichfelder, 2009. "Scalarizations for adaptively solving multi-objective optimization problems," Computational Optimization and Applications, Springer, vol. 44(2), pages 249-273, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. A. B. Malinowska & D. F. M. Torres, 2008. "Computational Approach to Essential and Nonessential Objective Functions in Linear Multicriteria Optimization," Journal of Optimization Theory and Applications, Springer, vol. 139(3), pages 577-590, December.
    2. Alexander Engau & Margaret M. Wiecek, 2008. "Interactive Coordination of Objective Decompositions in Multiobjective Programming," Management Science, INFORMS, vol. 54(7), pages 1350-1363, July.
    3. Gal, Tomas & Hanne, Thomas, 2006. "Nonessential objectives within network approaches for MCDM," European Journal of Operational Research, Elsevier, vol. 168(2), pages 584-592, January.
    4. Alzorba, Shaghaf & Günther, Christian & Popovici, Nicolae & Tammer, Christiane, 2017. "A new algorithm for solving planar multiobjective location problems involving the Manhattan norm," European Journal of Operational Research, Elsevier, vol. 258(1), pages 35-46.
    5. Lindroth, Peter & Patriksson, Michael & Strömberg, Ann-Brith, 2010. "Approximating the Pareto optimal set using a reduced set of objective functions," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1519-1534, December.
    6. Boland, Natashia & Charkhgard, Hadi & Savelsbergh, Martin, 2019. "Preprocessing and cut generation techniques for multi-objective binary programming," European Journal of Operational Research, Elsevier, vol. 274(3), pages 858-875.
    7. Daniel Vanderpooten & Lakmali Weerasena & Margaret M. Wiecek, 2017. "Covers and approximations in multiobjective optimization," Journal of Global Optimization, Springer, vol. 67(3), pages 601-619, March.
    8. Arne Herzel & Stephan Helfrich & Stefan Ruzika & Clemens Thielen, 2023. "Approximating biobjective minimization problems using general ordering cones," Journal of Global Optimization, Springer, vol. 86(2), pages 393-415, June.
    9. Rastegar, Narges & Khorram, Esmaile, 2014. "A combined scalarizing method for multiobjective programming problems," European Journal of Operational Research, Elsevier, vol. 236(1), pages 229-237.
    10. Dranichak, Garrett M. & Wiecek, Margaret M., 2019. "On highly robust efficient solutions to uncertain multiobjective linear programs," European Journal of Operational Research, Elsevier, vol. 273(1), pages 20-30.
    11. Tsionas, Mike G., 2019. "Multi-objective optimization using statistical models," European Journal of Operational Research, Elsevier, vol. 276(1), pages 364-378.
    12. C. Yalçın Kaya, 2019. "Markov–Dubins interpolating curves," Computational Optimization and Applications, Springer, vol. 73(2), pages 647-677, June.
    13. Przybylski, Anthony & Gandibleux, Xavier, 2017. "Multi-objective branch and bound," European Journal of Operational Research, Elsevier, vol. 260(3), pages 856-872.
    14. Cui, Yunfei & Geng, Zhiqiang & Zhu, Qunxiong & Han, Yongming, 2017. "Review: Multi-objective optimization methods and application in energy saving," Energy, Elsevier, vol. 125(C), pages 681-704.
    15. Jamain, Florian, 2014. "Représentations discrètes de l'ensemble des points non dominés pour des problèmes d'optimisation multi-objectifs," Economics Thesis from University Paris Dauphine, Paris Dauphine University, number 123456789/14002 edited by Bazgan, Cristina.
    16. Regina S. Burachik & Alexander C. Kalloniatis & C. Yalçın Kaya, 2021. "Sparse Network Optimization for Synchronization," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 229-251, October.
    17. Melih Ozlen & Benjamin A. Burton & Cameron A. G. MacRae, 2014. "Multi-Objective Integer Programming: An Improved Recursive Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 160(2), pages 470-482, February.
    18. Charles, V. & Udhayakumar, A. & Rhymend Uthariaraj, V., 2010. "An approach to find redundant objective function(s) and redundant constraint(s) in multi-objective nonlinear stochastic fractional programming problems," European Journal of Operational Research, Elsevier, vol. 201(2), pages 390-398, March.
    19. Fereshteh Akbari & Mehrdad Ghaznavi & Esmaile Khorram, 2018. "A Revised Pascoletti–Serafini Scalarization Method for Multiobjective Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 178(2), pages 560-590, August.
    20. M. Turkensteen (Marcel) & van den Heuvel, W., 2019. "The trade-off between costs and carbon emissions from lot-sizing decisions," Econometric Institute Research Papers EI2019-19, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:mathme:v:82:y:2015:i:1:p:1-18. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.