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A Benson type algorithm for nonconvex multiobjective programming problems

Author

Listed:
  • Soghra Nobakhtian

    (University of Isfahan
    Institute for Research in Fundamental Sciences (IPM))

  • Narjes Shafiei

    (University of Isfahan)

Abstract

In this paper, an approximation algorithm for solving nonconvex multiobjective programming problems (NCMOPs) is presented. We modify Benson’s method using cones instead of hyperplanes. This algorithm uses an inner approximation and an outer approximation to generate (weakly) efficient solutions and (weakly $$\varepsilon $$ ε -) nondominated points of NCMOPs. Some numerical examples are presented to clarify the proposed algorithm.

Suggested Citation

  • Soghra Nobakhtian & Narjes Shafiei, 2017. "A Benson type algorithm for nonconvex multiobjective programming problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(2), pages 271-287, July.
    • Handle: RePEc:spr:topjnl:v:25:y:2017:i:2:d:10.1007_s11750-016-0430-3
    DOI: 10.1007/s11750-016-0430-3
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    References listed on IDEAS

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    1. JosÉ Figueira & Salvatore Greco & Matthias Ehrogott, 2005. "Multiple Criteria Decision Analysis: State of the Art Surveys," International Series in Operations Research and Management Science, Springer, number 978-0-387-23081-8, April.
    2. 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.
    3. Andreas Hamel & Andreas Löhne & Birgit Rudloff, 2014. "Benson type algorithms for linear vector optimization and applications," Journal of Global Optimization, Springer, vol. 59(4), pages 811-836, August.
    4. P. Khanh & L. Tung, 2015. "First- and second-order optimality conditions for multiobjective fractional programming," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 419-440, July.
    5. Andreas Löhne & Birgit Rudloff & Firdevs Ulus, 2014. "Primal and dual approximation algorithms for convex vector optimization problems," Journal of Global Optimization, Springer, vol. 60(4), pages 713-736, December.
    6. P. Khanh & L. Tung, 2015. "Erratum to: First- and second-order optimality conditions for multiobjective fractional programming," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 618-618, July.
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    Cited by:

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    3. Çağın Ararat & Firdevs Ulus & Muhammad Umer, 2022. "A Norm Minimization-Based Convex Vector Optimization Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 194(2), pages 681-712, August.
    4. Eichfelder, Gabriele & Warnow, Leo, 2023. "Advancements in the computation of enclosures for multi-objective optimization problems," European Journal of Operational Research, Elsevier, vol. 310(1), pages 315-327.

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