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Grossone Methodology for Lexicographic Mixed-Integer Linear Programming Problems

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Numerical Computations: Theory and Algorithms (NUMTA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11974))

Abstract

In this work we have addressed lexicographic multi-objective linear programming problems where some of the variables are constrained to be integer. We have called this class of problems LMILP, which stands for Lexicographic Mixed Integer Linear Programming. Following one of the approach used to solve mixed integer linear programming problems, the branch and bound technique, we have extended it to work with infinitesimal/infinite numbers, exploiting the Grossone Methodology. The new algorithm, called GrossBB, is able to solve this new class of problems, by using internally the GrossSimplex algorithm (a recently introduced Grossone extension of the well-known simplex algorithm, to solve lexicographic LP problems without integer constraints). Finally we have illustrated the working principles of the GrossBB on a test problem.

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References

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Author information

Authors and Affiliations

  1. University of Pisa, Pisa, Italy

    Marco Cococcioni, Alessandro Cudazzo & Massimo Pappalardo

  2. University of Calabria, Rende, Italy

    Yaroslav D. Sergeyev

  3. Lobachevsky State University, Nizhni Novgorod, Russia

    Yaroslav D. Sergeyev

Authors
  1. Marco Cococcioni
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  2. Alessandro Cudazzo
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  3. Massimo Pappalardo
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  4. Yaroslav D. Sergeyev
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Corresponding author

Correspondence to Marco Cococcioni .

Editor information

Editors and Affiliations

  1. University of Calabria, Rende, Italy

    Yaroslav D. Sergeyev

  2. University of Calabria, Rende, Italy

    Dmitri E. Kvasov

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Cococcioni, M., Cudazzo, A., Pappalardo, M., Sergeyev, Y.D. (2020). Grossone Methodology for Lexicographic Mixed-Integer Linear Programming Problems. In: Sergeyev, Y., Kvasov, D. (eds) Numerical Computations: Theory and Algorithms. NUMTA 2019. Lecture Notes in Computer Science(), vol 11974. Springer, Cham. https://doi.org/10.1007/978-3-030-40616-5_28

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  • DOI: https://doi.org/10.1007/978-3-030-40616-5_28

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-40615-8

  • Online ISBN: 978-3-030-40616-5

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