IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v58y2010i3p650-659.html
   My bibliography  Save this article

Quantitative Comparison of Approximate Solution Sets for Multicriteria Optimization Problems with Weighted Tchebycheff Preference Function

Author

Listed:
  • Bilge Bozkurt

    (Department of Industrial Engineering, Middle East Technical University, 06531 Ankara, Turkey)

  • John W. Fowler

    (School of Computing, Informatics, and Decision Systems Engineering, Arizona State University, Tempe, Arizona 85287)

  • Esma S. Gel

    (School of Computing, Informatics, and Decision Systems Engineering, Arizona State University, Tempe, Arizona 85287)

  • Bosun Kim

    (School of Computing, Informatics, and Decision Systems Engineering, Arizona State University, Tempe, Arizona 85287)

  • Murat Köksalan

    (Department of Industrial Engineering, Middle East Technical University, 06531 Ankara, Turkey)

  • Jyrki Wallenius

    (Department of Business Technology, Helsinki School of Economics, FIN-00100 Helsinki, Finland)

Abstract

We consider the problem of evaluating the quality of solution sets generated by heuristics for multiple-objective combinatorial optimization problems. We extend previous research on the integrated preference functional (IPF), which assigns a scalar value to a given discrete set of nondominated points so that the weighted Tchebycheff function can be used as the underlying implicit value function. This extension is useful because modeling the decision maker's value function with the weighted Tchebycheff function reflects the impact of unsupported points when evaluating sets of nondominated points. We present an exact calculation method for the IPF measure in this case for an arbitrary number of criteria. We show that every nondominated point has its optimal weight interval for the weighted Tchebycheff function. Accordingly, all nondominated points, and not only the supported points in a set, contribute to the value of the IPF measure when using the weighted Tchebycheff function. Two- and three-criteria numerical examples illustrate the desirable properties of the weighted Tchebycheff function, providing a richer measure than the original IPF based on a convex combination of objectives.

Suggested Citation

  • Bilge Bozkurt & John W. Fowler & Esma S. Gel & Bosun Kim & Murat Köksalan & Jyrki Wallenius, 2010. "Quantitative Comparison of Approximate Solution Sets for Multicriteria Optimization Problems with Weighted Tchebycheff Preference Function," Operations Research, INFORMS, vol. 58(3), pages 650-659, June.
    • Handle: RePEc:inm:oropre:v:58:y:2010:i:3:p:650-659
    DOI: 10.1287/opre.1090.0766
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.1090.0766
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.1090.0766?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
    ---><---

    References listed on IDEAS

    as
    1. Kim, B. & Gel, E.S. & Fowler, J.W. & Carlyle, W.M. & Wallenius, J., 2006. "Evaluation of nondominated solution sets for k-objective optimization problems: An exact method and approximations," European Journal of Operational Research, Elsevier, vol. 173(2), pages 565-582, September.
    2. Ralph E. Steuer & Joe Silverman & Alan W. Whisman, 1993. "A Combined Tchebycheff/Aspiration Criterion Vector Interactive Multiobjective Programming Procedure," Management Science, INFORMS, vol. 39(10), pages 1255-1260, October.
    3. Pekka Korhonen & Jyrki Wallenius, 1988. "A pareto race," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(6), pages 615-623, December.
    4. Robert F. Dell & Mark H. Karwan, 1990. "An interactive MCDM weight space reduction method utilizing a tchebycheff utility function," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(2), pages 263-277, April.
    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. Markus Leitner & Ivana Ljubić & Markus Sinnl, 2015. "A Computational Study of Exact Approaches for the Bi-Objective Prize-Collecting Steiner Tree Problem," INFORMS Journal on Computing, INFORMS, vol. 27(1), pages 118-134, February.
    2. Korotkov, Vladimir & Wu, Desheng, 2021. "Benchmarking project portfolios using optimality thresholds," Omega, Elsevier, vol. 99(C).
    3. Stephan Helfrich & Kathrin Prinz & Stefan Ruzika, 2024. "The Weighted p-Norm Weight Set Decomposition for Multiobjective Discrete Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 202(3), pages 1187-1216, September.
    4. Karakaya, G. & Köksalan, M. & Ahipaşaoğlu, S.D., 2018. "Interactive algorithms for a broad underlying family of preference functions," European Journal of Operational Research, Elsevier, vol. 265(1), pages 248-262.
    5. Karakaya, G. & Köksalan, M., 2021. "Evaluating solutions and solution sets under multiple objectives," European Journal of Operational Research, Elsevier, vol. 294(1), pages 16-28.
    6. Stephan Helfrich & Tyler Perini & Pascal Halffmann & Natashia Boland & Stefan Ruzika, 2023. "Analysis of the weighted Tchebycheff weight set decomposition for multiobjective discrete optimization problems," Journal of Global Optimization, Springer, vol. 86(2), pages 417-440, June.

    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. M Köksalan & E Karasakal, 2006. "An interactive approach for multiobjective decision making," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(5), pages 532-540, May.
    2. Karakaya, G. & Köksalan, M., 2021. "Evaluating solutions and solution sets under multiple objectives," European Journal of Operational Research, Elsevier, vol. 294(1), pages 16-28.
    3. Alves, Maria Joao & Climaco, Joao, 2007. "A review of interactive methods for multiobjective integer and mixed-integer programming," European Journal of Operational Research, Elsevier, vol. 180(1), pages 99-115, July.
    4. Sun, Minghe, 2005. "Some issues in measuring and reporting solution quality of interactive multiple objective programming procedures," European Journal of Operational Research, Elsevier, vol. 162(2), pages 468-483, April.
    5. 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.
    6. Thomas L. Saaty, 2013. "The Modern Science of Multicriteria Decision Making and Its Practical Applications: The AHP/ANP Approach," Operations Research, INFORMS, vol. 61(5), pages 1101-1118, October.
    7. Zanakis, Stelios H. & Mandakovic, Tomislav & Gupta, Sushil K. & Sahay, Sundeep & Hong, Sungwan, 1995. "A review of program evaluation and fund allocation methods within the service and government sectors," Socio-Economic Planning Sciences, Elsevier, vol. 29(1), pages 59-79, March.
    8. Arbel, Ami & Korhonen, Pekka, 2001. "Using objective values to start multiple objective linear programming algorithms," European Journal of Operational Research, Elsevier, vol. 128(3), pages 587-596, February.
    9. Akram Dehnokhalaji & Mojtaba Ghiyasi & Pekka Korhonen, 2017. "Resource allocation based on cost efficiency," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(10), pages 1279-1289, October.
    10. Korhonen, Pekka & Tainio, Risto & Wallenius, Jyrki, 2001. "Value efficiency analysis of academic research," European Journal of Operational Research, Elsevier, vol. 130(1), pages 121-132, April.
    11. Liesiö, Juuso & Andelmin, Juho & Salo, Ahti, 2020. "Efficient allocation of resources to a portfolio of decision making units," European Journal of Operational Research, Elsevier, vol. 286(2), pages 619-636.
    12. Sun, Minghe, 2002. "A multiple objective programming approach for determining faculty salary equity adjustments," European Journal of Operational Research, Elsevier, vol. 138(2), pages 302-319, April.
    13. Nakayama, Hirotaka & Kaneshige, Kazuyoshi & Takemoto, Shinji & Watada, Yasuo, 1995. "An application of a multi-objective programming technique to construction accuracy control of cable-stayed bridges," European Journal of Operational Research, Elsevier, vol. 87(3), pages 731-738, December.
    14. Karaivanova, Jasmina & Korhonen, Pekka & Narula, Subhash & Wallenius, Jyrki & Vassilev, Vassil, 1995. "A reference direction approach to multiple objective integer linear programming," European Journal of Operational Research, Elsevier, vol. 81(1), pages 176-187, February.
    15. Mingue SUn, 2010. "A Branch-and-Bound Algorithm for Representative Integer Efficient Solutions in Multiple Objective Network Programming Problems," Working Papers 0007, College of Business, University of Texas at San Antonio.
    16. Hatami-Marbini, Adel & Tavana, Madjid, 2011. "An extension of the Electre I method for group decision-making under a fuzzy environment," Omega, Elsevier, vol. 39(4), pages 373-386, August.
    17. M P Estellita Lins & L Angulo-Meza & A C Moreira Da Silva, 2004. "A multi-objective approach to determine alternative targets in data envelopment analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(10), pages 1090-1101, October.
    18. P. Korhonen & A. Siljamaeki & M. Soismaa, 1998. "Practical Aspects of Value Efficiency Analysis," Working Papers ir98042, International Institute for Applied Systems Analysis.
    19. Luque, M. & Marcenaro-Gutiérrez, O.D. & López-Agudo, L.A., 2015. "On the potential balance among compulsory education outcomes through econometric and multiobjective programming analysis," European Journal of Operational Research, Elsevier, vol. 241(2), pages 527-540.
    20. Murat Köksalan & Robert D. Plante, 2003. "Interactive Multicriteria Optimization for Multiple-Response Product and Process Design," Manufacturing & Service Operations Management, INFORMS, vol. 5(4), pages 334-347, May.

    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:inm:oropre:v:58:y:2010:i:3:p:650-659. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.