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A Horizontal Method of Localizing Values of a Linear Function in Permutation-Based Optimization

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Optimization of Complex Systems: Theory, Models, Algorithms and Applications (WCGO 2019)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 991))

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Abstract

This paper is dedicated to linear constrained optimization on permutation configurations’ set, namely, to permutation-based subset sum problem (PB-SSP). To this problem, a directed structural graph is associated connected with a skeleton graph of the permutohedron and allowing to perform a directed search to solve this linear program. To solve PB-SSP, a horizontal method for localizing values of a linear objective function is offered combining Graph Theory tools, geometric and structural properties of a permutation set mapped into Euclidean space, the behavior of linear functions on the set, and Branch and Bound techniques.

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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, 61070, Kharkiv, Ukraine

    Oksana Pichugina

Authors
  1. Liudmyla Koliechkina
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  2. Oksana Pichugina
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Correspondence to Oksana Pichugina .

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Editors and Affiliations

  1. Computer science and Applications Department, LGIPM, University of Lorraine, Metz Cedex 03, France

    Hoai An Le Thi

  2. Computer Science and Applications Department, LGIPM, University of Lorraine, Metz Cedex 03, France

    Hoai Minh Le

  3. Laboratory of Mathematics, National Institute for Applied Sciences (INSA)-Rouen Normadie, Saint-Étienne-du-Rouvray Cedex, France

    Tao Pham Dinh

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Koliechkina, L., Pichugina, O. (2020). A Horizontal Method of Localizing Values of a Linear Function in Permutation-Based Optimization. In: Le Thi, H., Le, H., Pham Dinh, T. (eds) Optimization of Complex Systems: Theory, Models, Algorithms and Applications. WCGO 2019. Advances in Intelligent Systems and Computing, vol 991. Springer, Cham. https://doi.org/10.1007/978-3-030-21803-4_36

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