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Approximating the nondominated frontiers of multi‐objective combinatorial optimization problems

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  • Murat Köksalan
  • Banu Lokman

Abstract

Finding all nondominated vectors for multi‐objective combinatorial optimization (MOCO) problems is computationally very hard in general. We approximate the nondominated frontiers of MOCO problems by fitting smooth hypersurfaces. For a given problem, we fit the hypersurface using a single nondominated reference vector. We experiment with different types of MOCO problems and demonstrate that in all cases the fitted hypersurfaces approximate all nondominated vectors well. We discuss that such an approximation is useful to find the neighborhood of preferred regions of the nondominated vectors with very little computational effort. Further computational effort can then be spent in the identified region to find the actual nondominated vectors the decision maker will prefer. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009

Suggested Citation

  • Murat Köksalan & Banu Lokman, 2009. "Approximating the nondominated frontiers of multi‐objective combinatorial optimization problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(2), pages 191-198, March.
    • Handle: RePEc:wly:navres:v:56:y:2009:i:2:p:191-198
    DOI: 10.1002/nav.20336
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    References listed on IDEAS

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    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. 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. Sylva, John & Crema, Alejandro, 2004. "A method for finding the set of non-dominated vectors for multiple objective integer linear programs," European Journal of Operational Research, Elsevier, vol. 158(1), pages 46-55, October.
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    1. 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.
    2. Tezcaner Öztürk, Diclehan & Köksalan, Murat, 2023. "Biobjective route planning of an unmanned air vehicle in continuous space," Transportation Research Part B: Methodological, Elsevier, vol. 168(C), pages 151-169.
    3. Nail Karabay & Murat Köksalan & Diclehan Tezcaner Öztürk, 2023. "Biobjective UAV routing for a mission to visit multiple mobile targets," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 45(3), pages 925-954, September.
    4. Ceyhan, Gökhan & Köksalan, Murat & Lokman, Banu, 2019. "Finding a representative nondominated set for multi-objective mixed integer programs," European Journal of Operational Research, Elsevier, vol. 272(1), pages 61-77.
    5. Mavrotas, George & Florios, Kostas, 2013. "An improved version of the augmented epsilon-constraint method (AUGMECON2) for finding the exact Pareto set in Multi-Objective Integer Programming problems," MPRA Paper 105034, University Library of Munich, Germany.
    6. Doğan, Ilgın & Lokman, Banu & Köksalan, Murat, 2022. "Representing the nondominated set in multi-objective mixed-integer programs," European Journal of Operational Research, Elsevier, vol. 296(3), pages 804-818.

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