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An interactive algorithm to find the most preferred solution of multi-objective integer programs

Author

Listed:
  • Banu Lokman

    (TED University)

  • Murat Köksalan

    (Middle East Technical University)

  • Pekka J. Korhonen

    (Aalto University)

  • Jyrki Wallenius

    (Aalto University)

Abstract

In this paper, we develop an interactive algorithm that finds the most preferred solution of a decision maker (DM) for multi-objective integer programming problems. We assume that the DM’s preferences are consistent with a quasiconcave value function unknown to us. Based on the properties of quasiconcave value functions and pairwise preference information obtained from the DM, we generate constraints to restrict the implied inferior regions. The algorithm continues iteratively and guarantees to find the most preferred solution for integer programs. We test the performance of the algorithm on multi-objective assignment, knapsack, and shortest path problems and show that it works well.

Suggested Citation

  • Banu Lokman & Murat Köksalan & Pekka J. Korhonen & Jyrki Wallenius, 2016. "An interactive algorithm to find the most preferred solution of multi-objective integer programs," Annals of Operations Research, Springer, vol. 245(1), pages 67-95, October.
  • Handle: RePEc:spr:annopr:v:245:y:2016:i:1:d:10.1007_s10479-014-1545-2
    DOI: 10.1007/s10479-014-1545-2
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    References listed on IDEAS

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    1. Srinivas Y. Prasad & Mark H. Karwan & Stanley Zionts, 1997. "Use of Convex Cones in Interactive Multiple Objective Decision Making," Management Science, INFORMS, vol. 43(5), pages 723-734, May.
    2. Ramesh, R. & Zionts, Stanley & Karwan, Mark H., 1986. "A class of practical interactive branch and bound algorithms for multicriteria integer programming," European Journal of Operational Research, Elsevier, vol. 26(1), pages 161-172, July.
    3. 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.
    4. R. Ramesh & Mark H. Karwan & Stanley Zionts, 1989. "Preference Structure Representation Using Convex Cones in Multicriteria Integer Programming," Management Science, INFORMS, vol. 35(9), pages 1092-1105, September.
    5. 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.
    6. Stanley Zionts & Jyrki Wallenius, 1983. "An Interactive Multiple Objective Linear Programming Method for a Class of Underlying Nonlinear Utility Functions," Management Science, INFORMS, vol. 29(5), pages 519-529, May.
    7. Alves, Maria Joao & Climaco, Joao, 1999. "Using cutting planes in an interactive reference point approach for multiobjective integer linear programming problems," European Journal of Operational Research, Elsevier, vol. 117(3), pages 565-577, September.
    8. Odile Marcotte & Richard M. Soland, 1986. "An Interactive Branch-and-Bound Algorithm for Multiple Criteria Optimization," Management Science, INFORMS, vol. 32(1), pages 61-75, January.
    9. Alves, Maria Joao & Climaco, Joao, 2000. "An interactive reference point approach for multiobjective mixed-integer programming using branch-and-bound," European Journal of Operational Research, Elsevier, vol. 124(3), pages 478-494, August.
    10. 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.
    11. 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.
    12. 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.
    13. Banu Lokman & Murat Köksalan, 2013. "Finding all nondominated points of multi-objective integer programs," Journal of Global Optimization, Springer, vol. 57(2), pages 347-365, October.
    14. Murat Koksalan, M. & Taner, Orhan V., 1992. "An approach for finding the most preferred alternative in the presence of multiple criteria," European Journal of Operational Research, Elsevier, vol. 60(1), pages 52-60, July.
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    Cited by:

    1. 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.
    2. Özlem Karsu & Hale Erkan, 2020. "Balance in resource allocation problems: a changing reference approach," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 42(1), pages 297-326, March.
    3. Karakaya, G. & Köksalan, M., 2023. "Finding preferred solutions under weighted Tchebycheff preference functions for multi-objective integer programs," European Journal of Operational Research, Elsevier, vol. 308(1), pages 215-228.
    4. Anderson Kenji Hirose & Cassius Tadeu Scarpin & José Eduardo Pécora Junior, 2020. "Goal programming approach for political districting in Santa Catarina State: Brazil," Annals of Operations Research, Springer, vol. 287(1), pages 209-232, April.
    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. Bashir Bashir & Özlem Karsu, 2022. "Solution approaches for equitable multiobjective integer programming problems," Annals of Operations Research, Springer, vol. 311(2), pages 967-995, April.
    7. Selin Özpeynirci & Özgür Özpeynirci & Vincent Mousseau, 2021. "An interactive algorithm for resource allocation with balance concerns," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(4), pages 983-1005, December.
    8. 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.
    9. Wassila Drici & Fatma Zohra Ouail & Mustapha Moulaï, 2018. "Optimizing a linear fractional function over the integer efficient set," Annals of Operations Research, Springer, vol. 267(1), pages 135-151, August.

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