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A combined scalarizing method for multiobjective programming problems

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  • Rastegar, Narges
  • Khorram, Esmaile

Abstract

In this paper, a new general scalarization technique for solving multiobjective optimization problems is presented. After studying the properties of this formulation, two problems as special cases of this general formula are considered. It is shown that some well-known methods such as the weighted sum method, the ∊-constraint method, the Benson method, the hybrid method and the elastic ∊-constraint method can be subsumed under these two problems. Then, considering approximate solutions, some relationships between ε-(weakly, properly) efficient points of a general (without any convexity assumption) multiobjective optimization problem and ∊-optimal solutions of the introduced scalarized problem are achieved.

Suggested Citation

  • Rastegar, Narges & Khorram, Esmaile, 2014. "A combined scalarizing method for multiobjective programming problems," European Journal of Operational Research, Elsevier, vol. 236(1), pages 229-237.
    • Handle: RePEc:eee:ejores:v:236:y:2014:i:1:p:229-237
    DOI: 10.1016/j.ejor.2013.11.020
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    1. Ehrgott, Matthias & Klamroth, Kathrin & Schwehm, Christian, 2004. "An MCDM approach to portfolio optimization," European Journal of Operational Research, Elsevier, vol. 155(3), pages 752-770, June.
    2. Gabriele Eichfelder, 2009. "Scalarizations for adaptively solving multi-objective optimization problems," Computational Optimization and Applications, Springer, vol. 44(2), pages 249-273, November.
    3. C. Gutiérrez & B. Jiménez & V. Novo, 2007. "Optimality Conditions for Metrically Consistent Approximate Solutions in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 133(1), pages 49-64, April.
    4. S. Ruzika & M. M. Wiecek, 2005. "Approximation Methods in Multiobjective Programming," Journal of Optimization Theory and Applications, Springer, vol. 126(3), pages 473-501, September.
    5. Engau, Alexander & Wiecek, Margaret M., 2007. "Generating [epsilon]-efficient solutions in multiobjective programming," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1566-1579, March.
    6. Steuer, Ralph E. & Na, Paul, 2003. "Multiple criteria decision making combined with finance: A categorized bibliographic study," European Journal of Operational Research, Elsevier, vol. 150(3), pages 496-515, November.
    7. César Gutiérrez & Bienvenido Jiménez & Vicente Novo, 2007. "Optimality Conditions for Tanaka’s Approximate Solutions in Vector Optimization," Lecture Notes in Economics and Mathematical Systems, in: Generalized Convexity and Related Topics, pages 279-295, Springer.
    8. Francisco Ruiz & Mariano Luque & Kaisa Miettinen, 2012. "Improving the computational efficiency in a global formulation (GLIDE) for interactive multiobjective optimization," Annals of Operations Research, Springer, vol. 197(1), pages 47-70, August.
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    Cited by:

    1. Brian Dandurand & Margaret M. Wiecek, 2016. "Quadratic scalarization for decomposed multiobjective optimization," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(4), pages 1071-1096, October.
    2. A. Y. Golubin, 2015. "A Note on Optimality Conditions for Multi-objective Problems with a Euclidean Cone of Preferences," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 791-803, September.
    3. Torabi, S.A. & Mansouri, S.A., 2015. "Integrated business continuity and disaster recovery planning: Towards organizational resilienceAuthor-Name: Sahebjamnia, N," European Journal of Operational Research, Elsevier, vol. 242(1), pages 261-273.
    4. Fereshteh Akbari & Mehrdad Ghaznavi & Esmaile Khorram, 2018. "A Revised Pascoletti–Serafini Scalarization Method for Multiobjective Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 178(2), pages 560-590, August.

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