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An objective space cut and bound algorithm for convex multiplicative programmes

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  • Lizhen Shao
  • Matthias Ehrgott

Abstract

Multiplicative programming problems are global optimisation problems known to be NP-hard. In this paper we propose an objective space cut and bound algorithm for approximately solving convex multiplicative programming problems. This method is based on an objective space approximation algorithm for convex multi-objective programming problems. We show that this multi-objective optimisation algorithm can be changed into a cut and bound algorithm to solve convex multiplicative programming problems. We use an illustrative example to demonstrate the working of the algorithm. Computational experiments illustrate the superior performance of our algorithm compared to other methods from the literature. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Lizhen Shao & Matthias Ehrgott, 2014. "An objective space cut and bound algorithm for convex multiplicative programmes," Journal of Global Optimization, Springer, vol. 58(4), pages 711-728, April.
    • Handle: RePEc:spr:jglopt:v:58:y:2014:i:4:p:711-728
    DOI: 10.1007/s10898-013-0102-x
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    References listed on IDEAS

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    1. Arthur M. Geoffrion, 1967. "Solving Bicriterion Mathematical Programs," Operations Research, INFORMS, vol. 15(1), pages 39-54, February.
    2. H. P. Benson & G. M. Boger, 2000. "Outcome-Space Cutting-Plane Algorithm for Linear Multiplicative Programming," Journal of Optimization Theory and Applications, Springer, vol. 104(2), pages 301-322, February.
    3. Miettinen, Kaisa & Makela, Marko M. & Kaario, Katja, 2006. "Experiments with classification-based scalarizing functions in interactive multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 175(2), pages 931-947, December.
    4. H. P. Benson & G. M. Boger, 1997. "Multiplicative Programming Problems: Analysis and Efficient Point Search Heuristic," Journal of Optimization Theory and Applications, Springer, vol. 94(2), pages 487-510, August.
    5. Matthias Ehrgott & Lizhen Shao & Anita Schöbel, 2011. "An approximation algorithm for convex multi-objective programming problems," Journal of Global Optimization, Springer, vol. 50(3), pages 397-416, July.
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    Cited by:

    1. Hongwei Jiao & Binbin Li & Wenqiang Yang, 2024. "A criterion-space branch-reduction-bound algorithm for solving generalized multiplicative problems," Journal of Global Optimization, Springer, vol. 89(3), pages 597-632, July.
    2. Vahid Mahmoodian & Iman Dayarian & Payman Ghasemi Saghand & Yu Zhang & Hadi Charkhgard, 2022. "A Criterion Space Branch-and-Cut Algorithm for Mixed Integer Bilinear Maximum Multiplicative Programs," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1453-1470, May.

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