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On nadir points of multiobjective integer programming problems

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  • Özgür Özpeynirci

    (İzmir University of Economics)

Abstract

In this study, we consider the nadir points of multiobjective integer programming problems. We introduce new properties that restrict the possible locations of the nondominated points necessary for computing the nadir points. Based on these properties, we reduce the search space and propose an exact algorithm for finding the nadir point of multiobjective integer programming problems. We present an illustrative example on a three objective knapsack problem. We conduct computational experiments and compare the performances of two recent algorithms and the proposed algorithm.

Suggested Citation

  • Özgür Özpeynirci, 2017. "On nadir points of multiobjective integer programming problems," Journal of Global Optimization, Springer, vol. 69(3), pages 699-712, November.
    • Handle: RePEc:spr:jglopt:v:69:y:2017:i:3:d:10.1007_s10898-017-0534-9
    DOI: 10.1007/s10898-017-0534-9
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    References listed on IDEAS

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    1. Kalyanmoy Deb & Kaisa Miettinen, 2010. "Nadir Point Estimation Using Evolutionary Approaches: Better Accuracy and Computational Speed Through Focused Search," Lecture Notes in Economics and Mathematical Systems, in: Matthias Ehrgott & Boris Naujoks & Theodor J. Stewart & Jyrki Wallenius (ed.), Multiple Criteria Decision Making for Sustainable Energy and Transportation Systems, pages 339-354, Springer.
    2. Murat Köksalan & Banu Lokman, 2015. "Finding nadir points in multi-objective integer programs," Journal of Global Optimization, Springer, vol. 62(1), pages 55-77, May.
    3. 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.
    4. Gokhan Kirlik & Serpil Sayın, 2015. "Computing the nadir point for multiobjective discrete optimization problems," Journal of Global Optimization, Springer, vol. 62(1), pages 79-99, May.
    5. Pekka Korhonen & Seppo Salo & Ralph E. Steuer, 1997. "A Heuristic for Estimating Nadir Criterion Values in Multiple Objective Linear Programming," Operations Research, INFORMS, vol. 45(5), pages 751-757, October.
    6. Özlen, Melih & Azizoglu, Meral, 2009. "Multi-objective integer programming: A general approach for generating all non-dominated solutions," European Journal of Operational Research, Elsevier, vol. 199(1), pages 25-35, November.
    7. Granat, Janusz & Guerriero, Francesca, 2003. "The interactive analysis of the multicriteria shortest path problem by the reference point method," European Journal of Operational Research, Elsevier, vol. 151(1), pages 103-118, November.
    8. Ehrgott, Matthias & Tenfelde-Podehl, Dagmar, 2003. "Computation of ideal and Nadir values and implications for their use in MCDM methods," European Journal of Operational Research, Elsevier, vol. 151(1), pages 119-139, November.
    9. Kirlik, Gokhan & Sayın, Serpil, 2014. "A new algorithm for generating all nondominated solutions of multiobjective discrete optimization problems," European Journal of Operational Research, Elsevier, vol. 232(3), pages 479-488.
    10. 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.
    11. Miettinen, Kaisa & Eskelinen, Petri & Ruiz, Francisco & Luque, Mariano, 2010. "NAUTILUS method: An interactive technique in multiobjective optimization based on the nadir point," European Journal of Operational Research, Elsevier, vol. 206(2), pages 426-434, October.
    12. H. P. Benson & E. Sun, 2000. "Outcome Space Partition of the Weight Set in Multiobjective Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 105(1), pages 17-36, April.
    13. Alves, Maria João & Costa, João Paulo, 2009. "An exact method for computing the nadir values in multiple objective linear programming," European Journal of Operational Research, Elsevier, vol. 198(2), pages 637-646, October.
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