IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v206y2010i2p417-425.html
   My bibliography  Save this article

Interactive evolutionary multi-objective optimization for quasi-concave preference functions

Author

Listed:
  • Fowler, John W.
  • Gel, Esma S.
  • Köksalan, Murat M.
  • Korhonen, Pekka
  • Marquis, Jon L.
  • Wallenius, Jyrki

Abstract

We present a new hybrid approach to interactive evolutionary multi-objective optimization that uses a partial preference order to act as the fitness function in a customized genetic algorithm. We periodically send solutions to the decision maker (DM) for her evaluation and use the resulting preference information to form preference cones consisting of inferior solutions. The cones allow us to implicitly rank solutions that the DM has not considered. This technique avoids assuming an exact form for the preference function, but does assume that the preference function is quasi-concave. This paper describes the genetic algorithm and demonstrates its performance on the multi-objective knapsack problem.

Suggested Citation

  • Fowler, John W. & Gel, Esma S. & Köksalan, Murat M. & Korhonen, Pekka & Marquis, Jon L. & Wallenius, Jyrki, 2010. "Interactive evolutionary multi-objective optimization for quasi-concave preference functions," European Journal of Operational Research, Elsevier, vol. 206(2), pages 417-425, October.
    • Handle: RePEc:eee:ejores:v:206:y:2010:i:2:p:417-425
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(10)00158-X
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Murat Köksalan & Selcen (Pamuk) Phelps, 2007. "An Evolutionary Metaheuristic for Approximating Preference-Nondominated Solutions," INFORMS Journal on Computing, INFORMS, vol. 19(2), pages 291-301, May.
    2. Selcen (Pamuk) Phelps & Murat Köksalan, 2003. "An Interactive Evolutionary Metaheuristic for Multiobjective Combinatorial Optimization," Management Science, INFORMS, vol. 49(12), pages 1726-1738, December.
    3. Molina, Julin & Santana, Luis V. & Hernandez-Daz, Alfredo G. & Coello Coello, Carlos A. & Caballero, Rafael, 2009. "g-dominance: Reference point based dominance for multiobjective metaheuristics," European Journal of Operational Research, Elsevier, vol. 197(2), pages 685-692, September.
    4. Pekka Korhonen & Jyrki Wallenius & Stanley Zionts, 1984. "Solving the Discrete Multiple Criteria Problem using Convex Cones," Management Science, INFORMS, vol. 30(11), pages 1336-1345, November.
    5. A. M. Geoffrion & J. S. Dyer & A. Feinberg, 1972. "An Interactive Approach for Multi-Criterion Optimization, with an Application to the Operation of an Academic Department," Management Science, INFORMS, vol. 19(4-Part-1), pages 357-368, December.
    6. James S. Dyer & Peter C. Fishburn & Ralph E. Steuer & Jyrki Wallenius & Stanley Zionts, 1992. "Multiple Criteria Decision Making, Multiattribute Utility Theory: The Next Ten Years," Management Science, INFORMS, vol. 38(5), pages 645-654, May.
    7. R. Caballero & M. Luque & J. Molina & F. Ruiz, 2002. "Promoin: An Interactive System For Multiobjective Programming," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 1(04), pages 635-656.
    8. Stanley Zionts & Jyrki Wallenius, 1976. "An Interactive Programming Method for Solving the Multiple Criteria Problem," Management Science, INFORMS, vol. 22(6), pages 652-663, February.
    9. Jyrki Wallenius & James S. Dyer & Peter C. Fishburn & Ralph E. Steuer & Stanley Zionts & Kalyanmoy Deb, 2008. "Multiple Criteria Decision Making, Multiattribute Utility Theory: Recent Accomplishments and What Lies Ahead," Management Science, INFORMS, vol. 54(7), pages 1336-1349, July.
    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. Kadziński, Miłosz & Tervonen, Tommi & Tomczyk, Michał K. & Dekker, Rommert, 2017. "Evaluation of multi-objective optimization approaches for solving green supply chain design problems," Omega, Elsevier, vol. 68(C), pages 168-184.
    2. Sinha, Ankur & Korhonen, Pekka & Wallenius, Jyrki & Deb, Kalyanmoy, 2014. "An interactive evolutionary multi-objective optimization algorithm with a limited number of decision maker calls," European Journal of Operational Research, Elsevier, vol. 233(3), pages 674-688.
    3. Wang, Rui & Purshouse, Robin C. & Giagkiozis, Ioannis & Fleming, Peter J., 2015. "The iPICEA-g: a new hybrid evolutionary multi-criteria decision making approach using the brushing technique," European Journal of Operational Research, Elsevier, vol. 243(2), pages 442-453.
    4. Branke, Juergen & Corrente, Salvatore & Greco, Salvatore & Słowiński, Roman & Zielniewicz, Piotr, 2016. "Using Choquet integral as preference model in interactive evolutionary multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 250(3), pages 884-901.
    5. Katsikopoulos, Konstantinos V. & Egozcue, Martin & Garcia, Luis Fuentes, 2022. "A simple model for mixing intuition and analysis," European Journal of Operational Research, Elsevier, vol. 303(2), pages 779-789.
    6. Nasim Nasrabadi & Akram Dehnokhalaji & Pekka Korhonen & Jyrki Wallenius, 2019. "Using convex preference cones in multiple criteria decision making and related fields," Journal of Business Economics, Springer, vol. 89(6), pages 699-717, August.
    7. Shicheng Hu & Danping Li & Junmin Jia & Yang Liu, 2021. "A Self-Learning Based Preference Model for Portfolio Optimization," Mathematics, MDPI, vol. 9(20), pages 1-17, October.

    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. Ishizaka, Alessio & Siraj, Sajid, 2018. "Are multi-criteria decision-making tools useful? An experimental comparative study of three methods," European Journal of Operational Research, Elsevier, vol. 264(2), pages 462-471.
    2. Behnam Malakooti, 2015. "Double Helix Value Functions, Ordinal/Cardinal Approach, Additive Utility Functions, Multiple Criteria, Decision Paradigm, Process, and Types (Z Theory I)," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 14(06), pages 1353-1400, November.
    3. 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.
    4. Nowak, Maciej, 2007. "Aspiration level approach in stochastic MCDM problems," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1626-1640, March.
    5. Dimitris Bertsimas & Allison O'Hair, 2013. "Learning Preferences Under Noise and Loss Aversion: An Optimization Approach," Operations Research, INFORMS, vol. 61(5), pages 1190-1199, October.
    6. Rafael Lazimy, 2013. "Interactive Polyhedral Outer Approximation (IPOA) strategy for general multiobjective optimization problems," Annals of Operations Research, Springer, vol. 210(1), pages 73-99, November.
    7. Park, K. Sam & Shin, Dong Eun, 2012. "Interactive multiobjective optimization approach to the input–output design of opening new branches," European Journal of Operational Research, Elsevier, vol. 220(2), pages 530-538.
    8. Wang, Rui & Purshouse, Robin C. & Giagkiozis, Ioannis & Fleming, Peter J., 2015. "The iPICEA-g: a new hybrid evolutionary multi-criteria decision making approach using the brushing technique," European Journal of Operational Research, Elsevier, vol. 243(2), pages 442-453.
    9. Korhonen, Pekka J. & Wallenius, Jyrki & Genc, Tolga & Xu, Peng, 2021. "On rational behavior in multi-attribute riskless choice," European Journal of Operational Research, Elsevier, vol. 288(1), pages 331-342.
    10. Mariano Luque & Rafael Caballero & Julian Molina & Francisco Ruiz, 2007. "Equivalent Information for Multiobjective Interactive Procedures," Management Science, INFORMS, vol. 53(1), pages 125-134, January.
    11. Nasim Nasrabadi & Akram Dehnokhalaji & Pekka Korhonen & Jyrki Wallenius, 2019. "Using convex preference cones in multiple criteria decision making and related fields," Journal of Business Economics, Springer, vol. 89(6), pages 699-717, August.
    12. Andrea C. Hupman & Jay Simon, 2023. "The Legacy of Peter Fishburn: Foundational Work and Lasting Impact," Decision Analysis, INFORMS, vol. 20(1), pages 1-15, March.
    13. Ballestero, Enrique, 2001. "Stochastic goal programming: A mean-variance approach," European Journal of Operational Research, Elsevier, vol. 131(3), pages 476-481, June.
    14. Branke, Juergen & Corrente, Salvatore & Greco, Salvatore & Słowiński, Roman & Zielniewicz, Piotr, 2016. "Using Choquet integral as preference model in interactive evolutionary multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 250(3), pages 884-901.
    15. Beccacece, Francesca & Borgonovo, Emanuele & Buzzard, Greg & Cillo, Alessandra & Zionts, Stanley, 2015. "Elicitation of multiattribute value functions through high dimensional model representations: Monotonicity and interactions," European Journal of Operational Research, Elsevier, vol. 246(2), pages 517-527.
    16. Xiaoping Li & Dan Zhu, 2011. "Object technology software selection: a case study," Annals of Operations Research, Springer, vol. 185(1), pages 5-24, May.
    17. Jacquet-Lagreze, Eric & Siskos, Yannis, 2001. "Preference disaggregation: 20 years of MCDA experience," European Journal of Operational Research, Elsevier, vol. 130(2), pages 233-245, April.
    18. Pekka Korhonen & Majid Soleimani-damaneh & Jyrki Wallenius, 2017. "The use of quasi-concave value functions in MCDM: some theoretical results," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(2), pages 367-375, October.
    19. Aksoy, Yasemin & Butler, Timothy W. & Minor, Elliott D., 1996. "Comparative studies in interactive multiple objective mathematical programming," European Journal of Operational Research, Elsevier, vol. 89(2), pages 408-422, March.
    20. Korhonen, Pekka J. & Silvennoinen, Kari & Wallenius, Jyrki & Öörni, Anssi, 2012. "Can a linear value function explain choices? An experimental study," European Journal of Operational Research, Elsevier, vol. 219(2), pages 360-367.

    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:206:y:2010:i:2:p:417-425. 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.