IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v260y2017i3p829-840.html
   My bibliography  Save this article

Reference points and approximation algorithms in multicriteria discrete optimization

Author

Listed:
  • Büsing, Christina
  • Goetzmann, Kai-Simon
  • Matuschke, Jannik
  • Stiller, Sebastian

Abstract

Mathematical research on multicriteria optimization problems predominantly revolves around the set of Pareto optimal solutions. In practice, on the other hand, methods that output a single solution are more widespread. Reference point methods are a successful example of this approach and are widely used in real-world multicriteria optimization. A reference point solution is the solution closest to a given reference point in the objective space.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:260:y:2017:i:3:p:829-840
    DOI: 10.1016/j.ejor.2016.05.027
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221716303472
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.ejor.2016.05.027?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. Allouche, Mohamed Anis & Aouni, Belaïd & Martel, Jean-Marc & Loukil, Taïcir & Rebaï, Abdelwaheb, 2009. "Solving multi-criteria scheduling flow shop problem through compromise programming and satisfaction functions," European Journal of Operational Research, Elsevier, vol. 192(2), pages 460-467, January.
    2. Enrique Ballestero & Ana Garcia-Bernabeu, 2015. "Compromise Programming and Utility Functions," International Series in Operations Research & Management Science, in: Enrique Ballestero & Blanca Pérez-Gladish & Ana Garcia-Bernabeu (ed.), Socially Responsible Investment, edition 127, chapter 0, pages 155-175, Springer.
    3. Leslie A. Hall & Andreas S. Schulz & David B. Shmoys & Joel Wein, 1997. "Scheduling to Minimize Average Completion Time: Off-Line and On-Line Approximation Algorithms," Mathematics of Operations Research, INFORMS, vol. 22(3), pages 513-544, August.
    4. M. Voorneveld & A. Nouweland & R. McLean, 2011. "Axiomatizations of the Euclidean compromise solution," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(3), pages 427-448, August.
    5. P. L. Yu, 1973. "A Class of Solutions for Group Decision Problems," Management Science, INFORMS, vol. 19(8), pages 936-946, April.
    6. M. Freimer & P. L. Yu, 1976. "Some New Results on Compromise Solutions for Group Decision Problems," Management Science, INFORMS, vol. 22(6), pages 688-693, February.
    7. Opricovic, Serafim & Tzeng, Gwo-Hshiung, 2004. "Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS," European Journal of Operational Research, Elsevier, vol. 156(2), pages 445-455, July.
    8. Korhonen, Pekka J. & Laakso, Jukka, 1986. "A visual interactive method for solving the multiple criteria problem," European Journal of Operational Research, Elsevier, vol. 24(2), pages 277-287, February.
    9. Arthur Warburton, 1987. "Approximation of Pareto Optima in Multiple-Objective, Shortest-Path Problems," Operations Research, INFORMS, vol. 35(1), pages 70-79, February.
    10. Aissi, Hassene & Bazgan, Cristina & Vanderpooten, Daniel, 2007. "Approximation of min-max and min-max regret versions of some combinatorial optimization problems," European Journal of Operational Research, Elsevier, vol. 179(2), pages 281-290, June.
    11. Kanellopoulos, A. & Gerdessen, J.C. & Claassen, G.D.H., 2015. "Compromise programming: Non-interactive calibration of utility-based metrics," European Journal of Operational Research, Elsevier, vol. 244(2), pages 519-524.
    12. Shashi Mittal & Andreas S. Schulz, 2013. "A General Framework for Designing Approximation Schemes for Combinatorial Optimization Problems with Many Objectives Combined into One," Operations Research, INFORMS, vol. 61(2), pages 386-397, April.
    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. Gwo-Hshiung Tzeng & Chi-Yo Huang, 2012. "Combined DEMATEL technique with hybrid MCDM methods for creating the aspired intelligent global manufacturing & logistics systems," Annals of Operations Research, Springer, vol. 197(1), pages 159-190, August.
    2. Kuldeep Kavta & Arkopal K. Goswami, 2021. "A methodological framework for a priori selection of travel demand management package using fuzzy MCDM methods," Transportation, Springer, vol. 48(6), pages 3059-3084, December.
    3. Opricovic, Serafim & Tzeng, Gwo-Hshiung, 2007. "Extended VIKOR method in comparison with outranking methods," European Journal of Operational Research, Elsevier, vol. 178(2), pages 514-529, April.
    4. 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.
    5. Hisham Alidrisi, 2021. "An Innovative Job Evaluation Approach Using the VIKOR Algorithm," JRFM, MDPI, vol. 14(6), pages 1-19, June.
    6. 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.
    7. Hsu, C.-H. & Wang, Fu-Kwun & Tzeng, Gwo-Hshiung, 2012. "The best vendor selection for conducting the recycled material based on a hybrid MCDM model combining DANP with VIKOR," Resources, Conservation & Recycling, Elsevier, vol. 66(C), pages 95-111.
    8. Francisco Salas-Molina & Juan Antonio Rodr'iguez Aguilar & Filippo Bistaffa, 2020. "Shared value economics: an axiomatic approach," Papers 2006.00581, arXiv.org.
    9. Claus-Jochen Haake & Cheng-Zhong Qin, 2018. "On unification of solutions to the bargaining problem," Working Papers CIE 113, Paderborn University, CIE Center for International Economics.
    10. Francisco J. André & Carlos Romero, 2006. "On the equivalence between compromise programming and the use of composite compromise metrics," Working Papers 06.33, Universidad Pablo de Olavide, Department of Economics.
    11. Rojas-Zerpa, Juan C. & Yusta, Jose M., 2015. "Application of multicriteria decision methods for electric supply planning in rural and remote areas," Renewable and Sustainable Energy Reviews, Elsevier, vol. 52(C), pages 557-571.
    12. Kaya, Tolga & Kahraman, Cengiz, 2010. "Multicriteria renewable energy planning using an integrated fuzzy VIKOR & AHP methodology: The case of Istanbul," Energy, Elsevier, vol. 35(6), pages 2517-2527.
    13. Ma, Qiuzhuo & Song, Haiqing & Zhu, Wenbin, 2018. "Low-carbon airline fleet assignment: A compromise approach," Journal of Air Transport Management, Elsevier, vol. 68(C), pages 86-102.
    14. Song, Zhao-Yu & Lin, Cheng-Wei & Feng, Xuehao & Lee, Paul Tae-Woo, 2024. "An empirical study of the performance of the sixth generation ports model with smart ports with reference to major container ports in mainland China," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 184(C).
    15. F. Blasco & E. Cuchillo-Ibáñez & M. A. Morón & C. Romero, 1999. "On the Monotonicity of the Compromise Set in Multicriteria Problems," Journal of Optimization Theory and Applications, Springer, vol. 102(1), pages 69-82, July.
    16. M. Voorneveld & A. Nouweland & R. McLean, 2011. "Axiomatizations of the Euclidean compromise solution," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(3), pages 427-448, August.
    17. Chia-Li Lin & Chung-Ling Kuo, 2022. "Establishing Competency Development Evaluation Systems and Talent Cultivation Strategies for the Service Industry Using the Hybrid MCDM Approach," Sustainability, MDPI, vol. 14(19), pages 1-33, September.
    18. Kao-Yi Shen, 2017. "Compromise between Short- and Long-Term Financial Sustainability: A Hybrid Model for Supporting R&D Decisions," Sustainability, MDPI, vol. 9(3), pages 1-17, March.
    19. Qun Zhao & Pei-Hsuan Tsai & Jin-Long Wang, 2019. "Improving Financial Service Innovation Strategies for Enhancing China’s Banking Industry Competitive Advantage during the Fintech Revolution: A Hybrid MCDM Model," Sustainability, MDPI, vol. 11(5), pages 1-29, March.
    20. San Cristóbal, J.R., 2011. "Multi-criteria decision-making in the selection of a renewable energy project in spain: The Vikor method," Renewable Energy, Elsevier, vol. 36(2), pages 498-502.

    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:eee:ejores:v:260:y:2017:i:3:p:829-840. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.