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A Graph-Theoretic Approach to Multiobjective Permutation-Based Optimization

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Optimization and Applications (OPTIMA 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1145))

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Abstract

A Generalized Coordinate Method (GCM) for linear permutation-based optimization is presented as a generalization of the Modified Coordinate Localization Method and Modified Coordinate Method is presented, and its applications to multiobjective linear optimization on permutations are outlined. The method is based on properties of linear function on a transposition graph, a decomposition of the graph, and extracting from it a multidimensional grid graph, where a directed search of an optimal solution is performed. Depending on the search parameters, GCM yields an exact or approximate solution to the original problem. An illustrative example is given for the method.

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Notes

  1. 1.

    For a graph \(\mathbf G = (\mathbf V , \mathbf E )\) and a function \(f: \mathbf V \rightarrow \mathbb {R}^1\), \(\overrightarrow{\mathbf{G }} = (\mathbf V , \overrightarrow{\mathbf{E }})\) is a digraph, where \(\overrightarrow{\mathbf{E }}\) is formed as follows – \(\forall u,v\in \mathbf V \): (a) if \(f(u)< f(v) \), then \((u,v)\in \overrightarrow{\mathbf{E }}\); (a) if \(f(u)> f(v) \), then \((v,u)\in \overrightarrow{\mathbf{E }}\); (c) if \(f(u)= f(v) \), then \((u,v),(v,u)\in \overrightarrow{\mathbf{E }}\).

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Author information

Authors and Affiliations

  1. University of Lodz, Uniwersytecka Str. 3, 90-137, Lodz, Poland

    Liudmyla Koliechkina

  2. National Aerospace University “Kharkiv Aviation Institute”, 17 Chkalova Street, Kharkiv, 61070, Ukraine

    Oksana Pichugina & Sergiy Yakovlev

Authors
  1. Liudmyla Koliechkina
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  2. Oksana Pichugina
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  3. Sergiy Yakovlev
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Corresponding author

Correspondence to Oksana Pichugina .

Editor information

Editors and Affiliations

  1. University of Montenegro, Podgorica, Montenegro

    Milojica Jaćimović

  2. Krasovskii Institute of Mathematics and Mechanics, Yekaterinburg, Russia

    Michael Khachay

  3. FRC CSC RAS, Moscow, Russia

    Vlasta Malkova

  4. FRC CSC RAS, Moscow, Russia

    Mikhail Posypkin

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Koliechkina, L., Pichugina, O., Yakovlev, S. (2020). A Graph-Theoretic Approach to Multiobjective Permutation-Based Optimization. In: Jaćimović, M., Khachay, M., Malkova, V., Posypkin, M. (eds) Optimization and Applications. OPTIMA 2019. Communications in Computer and Information Science, vol 1145. Springer, Cham. https://doi.org/10.1007/978-3-030-38603-0_28

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  • DOI: https://doi.org/10.1007/978-3-030-38603-0_28

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