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A genetic algorithm for solving linear fractional bilevel problems

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  • Herminia Calvete
  • Carmen Galé
  • Pedro Mateo

Abstract

Bilevel programming has been proposed for dealing with decision processes involving two decision makers with a hierarchical structure. They are characterized by the existence of two optimization problems in which the constraint region of the upper level problem is implicitly determined by the lower level optimization problem. In this paper a genetic algorithm is proposed for the class of bilevel problems in which both level objective functions are linear fractional and the common constraint region is a bounded polyhedron. The algorithm associates chromosomes with extreme points of the polyhedron and searches for a feasible solution close to the optimal solution by proposing efficient crossover and mutation procedures. The computational study shows a good performance of the algorithm, both in terms of solution quality and computational time. Copyright Springer Science+Business Media, LLC 2009

Suggested Citation

  • Herminia Calvete & Carmen Galé & Pedro Mateo, 2009. "A genetic algorithm for solving linear fractional bilevel problems," Annals of Operations Research, Springer, vol. 166(1), pages 39-56, February.
    • Handle: RePEc:spr:annopr:v:166:y:2009:i:1:p:39-56:10.1007/s10479-008-0416-0
    DOI: 10.1007/s10479-008-0416-0
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    References listed on IDEAS

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    1. Calvete, Herminia I. & Gale, Carmen & Mateo, Pedro M., 2008. "A new approach for solving linear bilevel problems using genetic algorithms," European Journal of Operational Research, Elsevier, vol. 188(1), pages 14-28, July.
    2. Colin R. Reeves, 1997. "Feature Article---Genetic Algorithms for the Operations Researcher," INFORMS Journal on Computing, INFORMS, vol. 9(3), pages 231-250, August.
    3. H. I. Calvete & C. Galé, 1998. "On the Quasiconcave Bilevel Programming Problem," Journal of Optimization Theory and Applications, Springer, vol. 98(3), pages 613-622, September.
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    Cited by:

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    2. Ashenafi Woldemariam & Semu Kassa, 2015. "Systematic evolutionary algorithm for general multilevel Stackelberg problems with bounded decision variables (SEAMSP)," Annals of Operations Research, Springer, vol. 229(1), pages 771-790, June.

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