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A new complexity result on multiobjective linear integer programming using short rational generating functions

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Abstract

This paper presents a new complexity result for solving multiobjective integer programming problems. We prove that encoding the entire set of nondominated solutions of the problem in a short sum of rational functions is polynomially doable, when the dimension of the decision space is fixed. This result extends a previous result presented in De Loera et al. (INFORMS J. Comput. 21(1):39–48, 2009) in that there the number of the objective functions is assumed to be fixed whereas ours allows this number to vary.

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Authors and Affiliations

  1. Departamento de Álgebra, Universidad de Granada, 18071, Granada, Spain

    Víctor Blanco

  2. Departamento de Estadística e Investigación Operativa, Universidad de Sevilla, 41012, Sevilla, Spain

    Justo Puerto

Authors
  1. Víctor Blanco
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  2. Justo Puerto
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Correspondence to Víctor Blanco.

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Blanco, V., Puerto, J. A new complexity result on multiobjective linear integer programming using short rational generating functions. Optim Lett 6, 537–543 (2012). https://doi.org/10.1007/s11590-011-0279-1

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  • DOI: https://doi.org/10.1007/s11590-011-0279-1

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