IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v56y2013i2p279-297.html
   My bibliography  Save this article

A conic scalarization method in multi-objective optimization

Author

Listed:
  • Refail Kasimbeyli

Abstract

This paper presents the conic scalarization method for scalarization of nonlinear multi-objective optimization problems. We introduce a special class of monotonically increasing sublinear scalarizing functions and show that the zero sublevel set of every function from this class is a convex closed and pointed cone which contains the negative ordering cone. We introduce the notion of a separable cone and show that two closed cones (one of them is separable) having only the vertex in common can be separated by a zero sublevel set of some function from this class. It is shown that the scalar optimization problem constructed by using these functions, enables to characterize the complete set of efficient and properly efficient solutions of multi-objective problems without convexity and boundedness conditions. By choosing a suitable scalarizing parameter set consisting of a weighting vector, an augmentation parameter, and a reference point, decision maker may guarantee a most preferred efficient or properly efficient solution. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • Refail Kasimbeyli, 2013. "A conic scalarization method in multi-objective optimization," Journal of Global Optimization, Springer, vol. 56(2), pages 279-297, June.
    • Handle: RePEc:spr:jglopt:v:56:y:2013:i:2:p:279-297
    DOI: 10.1007/s10898-011-9789-8
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10898-011-9789-8
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10898-011-9789-8?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. Buchanan, John & Gardiner, Lorraine, 2003. "A comparison of two reference point methods in multiple objective mathematical programming," European Journal of Operational Research, Elsevier, vol. 149(1), pages 17-34, August.
    2. P. L. Yu, 1973. "A Class of Solutions for Group Decision Problems," Management Science, INFORMS, vol. 19(8), pages 936-946, April.
    3. Gasimov, Rafail N. & Sipahioglu, Aydin & Sarac, Tugba, 2007. "A multi-objective programming approach to 1.5-dimensional assortment problem," European Journal of Operational Research, Elsevier, vol. 179(1), pages 64-79, May.
    4. A.P. Wierzbicki, 1998. "Reference Point Methods in Vector Optimization and Decision Support," Working Papers ir98017, International Institute for Applied Systems Analysis.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Nergiz Kasimbeyli, 2015. "Existence and characterization theorems in nonconvex vector optimization," Journal of Global Optimization, Springer, vol. 62(1), pages 155-165, May.
    2. Shokouh Shahbeyk & Majid Soleimani-damaneh & Refail Kasimbeyli, 2018. "Hartley properly and super nondominated solutions in vector optimization with a variable ordering structure," Journal of Global Optimization, Springer, vol. 71(2), pages 383-405, June.
    3. Derya Deliktaş, 2022. "Self-adaptive memetic algorithms for multi-objective single machine learning-effect scheduling problems with release times," Flexible Services and Manufacturing Journal, Springer, vol. 34(3), pages 748-784, September.
    4. Behnam Soleimani, 2014. "Characterization of Approximate Solutions of Vector Optimization Problems with a Variable Order Structure," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 605-632, August.
    5. Abbas Sayadi-bander & Latif Pourkarimi & Refail Kasimbeyli & Hadi Basirzadeh, 2017. "Coradiant sets and $$\varepsilon $$ ε -efficiency in multiobjective optimization," Journal of Global Optimization, Springer, vol. 68(3), pages 587-600, July.
    6. Brian Dandurand & Margaret M. Wiecek, 2016. "Quadratic scalarization for decomposed multiobjective optimization," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(4), pages 1071-1096, October.
    7. Refail Kasimbeyli & Masoud Karimi, 2021. "Duality in nonconvex vector optimization," Journal of Global Optimization, Springer, vol. 80(1), pages 139-160, May.
    8. Gabriele Eichfelder & Refail Kasimbeyli, 2014. "Properly optimal elements in vector optimization with variable ordering structures," Journal of Global Optimization, Springer, vol. 60(4), pages 689-712, December.

    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. Koronakos, Gregory & Sotiros, Dimitris & Despotis, Dimitris K. & Kritikos, Manolis N., 2022. "Fair efficiency decomposition in network DEA: A compromise programming approach," Socio-Economic Planning Sciences, Elsevier, vol. 79(C).
    2. Milad Zamanifar & Seyed Mohammad Seyedhoseyni, 2017. "Recovery planning model for roadways network after natural hazards," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 87(2), pages 699-716, June.
    3. Omer F. Baris, 2018. "Timing effect in bargaining and ex ante efficiency of the relative utilitarian solution," Theory and Decision, Springer, vol. 84(4), pages 547-556, June.
    4. Chen, Lisa Y. & Wang, Tien-Chin, 2009. "Optimizing partners' choice in IS/IT outsourcing projects: The strategic decision of fuzzy VIKOR," International Journal of Production Economics, Elsevier, vol. 120(1), pages 233-242, July.
    5. Nergiz Kasimbeyli, 2015. "Existence and characterization theorems in nonconvex vector optimization," Journal of Global Optimization, Springer, vol. 62(1), pages 155-165, May.
    6. Domenech, B. & Ferrer-Martí, L. & Pastor, R., 2015. "Hierarchical methodology to optimize the design of stand-alone electrification systems for rural communities considering technical and social criteria," Renewable and Sustainable Energy Reviews, Elsevier, vol. 51(C), pages 182-196.
    7. Hisham Alidrisi, 2021. "An Innovative Job Evaluation Approach Using the VIKOR Algorithm," JRFM, MDPI, vol. 14(6), pages 1-19, June.
    8. Roberto Cervelló Royo & Fernando García García & Francisco Guijarro-Martínez & Ismael Moya-Clemente, 2011. "Housing Ranking: a model of equilibrium between buyers and sellers expectations," ERSA conference papers ersa11p314, European Regional Science Association.
    9. Büsing, Christina & Goetzmann, Kai-Simon & Matuschke, Jannik & Stiller, Sebastian, 2017. "Reference points and approximation algorithms in multicriteria discrete optimization," European Journal of Operational Research, Elsevier, vol. 260(3), pages 829-840.
    10. Serafim Opricovic, 2009. "A Compromise Solution in Water Resources Planning," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 23(8), pages 1549-1561, June.
    11. Janssen, Sander & van Ittersum, Martin K., 2007. "Assessing farm innovations and responses to policies: A review of bio-economic farm models," Agricultural Systems, Elsevier, vol. 94(3), pages 622-636, June.
    12. Büyüközkan, Gülçin & Ruan, Da, 2008. "Evaluation of software development projects using a fuzzy multi-criteria decision approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(5), pages 464-475.
    13. Rubinstein, Ariel & Zhou, Lin, 1999. "Choice problems with a 'reference' point," Mathematical Social Sciences, Elsevier, vol. 37(3), pages 205-209, May.
    14. Kapeller, Jakob & Steinerberger, Stefan, 2017. "Stability, fairness and random walks in the bargaining problem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 488(C), pages 60-71.
    15. Pedro Jose Gudiel Pineda & Chao-Che Hsu & James J. H. Liou & Huai-Wei Lo, 2018. "A Hybrid Model for Aircraft Type Determination Following Flight Cancellation," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 17(04), pages 1147-1172, July.
    16. Rohmer, S.U.K. & Gerdessen, J.C. & Claassen, G.D.H., 2019. "Sustainable supply chain design in the food system with dietary considerations: A multi-objective analysis," European Journal of Operational Research, Elsevier, vol. 273(3), pages 1149-1164.
    17. Yayi Yuan & Zeshui Xu & Yixin Zhang, 2022. "The DEMATEL–COPRAS hybrid method under probabilistic linguistic environment and its application in Third Party Logistics provider selection," Fuzzy Optimization and Decision Making, Springer, vol. 21(1), pages 137-156, March.
    18. Mestre-Sanchís, Fernando & Feijóo-Bello, María Luisa, 2009. "Climate change and its marginalizing effect on agriculture," Ecological Economics, Elsevier, vol. 68(3), pages 896-904, January.
    19. María Romero & María Luisa Cuadrado & Luis Romero & Carlos Romero, 2020. "Optimum acceptability of telecommunications networks: a multi-criteria approach," Operational Research, Springer, vol. 20(3), pages 1899-1911, September.
    20. Klanac, Alan & Varsta, Petri, 2011. "Design of marine structures with improved safety for environment," Reliability Engineering and System Safety, Elsevier, vol. 96(1), pages 75-90.

    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:jglopt:v:56:y:2013:i:2:p:279-297. 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.