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Numerical Algorithms for the Parametric Continuation of Stiff ODEs Deriving from the Modeling of Combustion with Detailed Chemical Mechanisms Read chapter Read first chapter

2020 | OriginalPaper | Chapter

Grossone Methodology for Lexicographic Mixed-Integer Linear Programming Problems

Authors : Marco Cococcioni, Alessandro Cudazzo, Massimo Pappalardo, Yaroslav D. Sergeyev

Published in: Numerical Computations: Theory and Algorithms

Publisher: Springer International Publishing

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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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previous chapter Artificial Neural Networks Training Acceleration Through Network Science Strategies
next chapter Infinite Games on Finite Graphs Using Grossone
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Metadata
Title
Grossone Methodology for Lexicographic Mixed-Integer Linear Programming Problems
Authors
Marco Cococcioni
Alessandro Cudazzo
Massimo Pappalardo
Yaroslav D. Sergeyev
Copyright Year
2020
Book
Numerical Computations: Theory and Algorithms

Print ISBN: 978-3-030-40615-8

Electronic ISBN: 978-3-030-40616-5

Copyright Year: 2020

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

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