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Finding nadir points in multi-objective integer programs

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  • Murat Köksalan
  • Banu Lokman

Abstract

We address the problem of finding the nadir point in a multi-objective integer programming problem. Finding the nadir point is not straightforward, especially when there are more than three objectives. The difficulty further increases for integer programming problems. We develop an exact algorithm to find the nadir point in multi-objective integer programs with integer-valued parameters. We also develop a variation that finds bounds for each component of the nadir point with a desired level of accuracy. We demonstrate on several instances of multi-objective assignment, knapsack, and shortest path problems that the algorithms work well. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:62:y:2015:i:1:p:55-77
    DOI: 10.1007/s10898-014-0212-0
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    References listed on IDEAS

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    1. Jorge, Jesús M., 2009. "An algorithm for optimizing a linear function over an integer efficient set," European Journal of Operational Research, Elsevier, vol. 195(1), pages 98-103, May.
    2. 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.
    3. 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.
    4. 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.
    5. 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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    Cited by:

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    2. Przybylski, Anthony & Gandibleux, Xavier, 2017. "Multi-objective branch and bound," European Journal of Operational Research, Elsevier, vol. 260(3), pages 856-872.
    3. Özgür Özpeynirci, 2017. "On nadir points of multiobjective integer programming problems," Journal of Global Optimization, Springer, vol. 69(3), pages 699-712, November.
    4. Özarık, Sami Serkan & Lokman, Banu & Köksalan, Murat, 2020. "Distribution based representative sets for multi-objective integer programs," European Journal of Operational Research, Elsevier, vol. 284(2), pages 632-643.
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    6. Cristina Lopes & Ana Maria Rodrigues & Valeria Romanciuc & José Soeiro Ferreira & Elif Göksu Öztürk & Cristina Oliveira, 2023. "Divide and Conquer: A Location-Allocation Approach to Sectorization," Mathematics, MDPI, vol. 11(11), pages 1-19, June.

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