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An Exact Algorithm for Finding Extreme Supported Nondominated Points of Multiobjective Mixed Integer Programs

Author

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  • Özgür Özpeynirci

    (Department of Logistics Management, Izmir University of Economics, Izmir 35330, Turkey)

  • Murat Köksalan

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

Abstract

In this paper, we present an exact algorithm to find all extreme supported nondominated points of multiobjective mixed integer programs. The algorithm uses a composite linear objective function and finds all the desired points in a finite number of steps by changing the weights of the objective functions in a systematic way. We develop further variations of the algorithm to improve its computational performance and demonstrate our algorithm's performance on multiobjective assignment, knapsack, and traveling salesperson problems with three and four objectives.

Suggested Citation

  • Özgür Özpeynirci & Murat Köksalan, 2010. "An Exact Algorithm for Finding Extreme Supported Nondominated Points of Multiobjective Mixed Integer Programs," Management Science, INFORMS, vol. 56(12), pages 2302-2315, December.
    • Handle: RePEc:inm:ormnsc:v:56:y:2010:i:12:p:2302-2315
    DOI: 10.1287/mnsc.1100.1248
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    References listed on IDEAS

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    1. Anthony Przybylski & Xavier Gandibleux & Matthias Ehrgott, 2010. "A Recursive Algorithm for Finding All Nondominated Extreme Points in the Outcome Set of a Multiobjective Integer Programme," INFORMS Journal on Computing, INFORMS, vol. 22(3), pages 371-386, August.
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    6. Benson, Harold P. & Sun, Erjiang, 2002. "A weight set decomposition algorithm for finding all efficient extreme points in the outcome set of a multiple objective linear program," European Journal of Operational Research, Elsevier, vol. 139(1), pages 26-41, May.
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