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Euclidean Combinatorial Configurations: Continuous Representations and Convex Extensions

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Book cover Lecture Notes in Computational Intelligence and Decision Making (ISDMCI 2019)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1020))

Abstract

This paper presents general approaches to continuous functional representations (f-representations) of sets of Euclidean combinatorial configurations underlying the possibility of applying continuous programming to optimization on them. A concept of Euclidean combinatorial configurations (e-configurations) is offered. Applications of f-representations in optimization and reformulations of extreme combinatorial problems as global optimization problems are outlined. A typology of f-representations is presented and approaches to construct them for classes that were singled out are described and applied in forming a number of polynomial f-representations of basic sets of e-configurations related to permutation and Boolean configurations. The paper’s results can be applied in solving numerous real-world problems formulated as permutation-based, binary or Boolean.

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Author information

Authors and Affiliations

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

    Oksana Pichugina & Sergiy Yakovlev

Authors
  1. Oksana Pichugina
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  2. Sergiy Yakovlev
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Corresponding author

Correspondence to Oksana Pichugina .

Editor information

Editors and Affiliations

  1. Kherson National Technical University, Kherson, Ukraine

    Volodymyr Lytvynenko

  2. Jan Evangelista Purkyně University in Ústi and Labem, Usti and Labem, Czech Republic

    Sergii Babichev

  3. Lublin University of Technology, Lublin, Poland

    Waldemar Wójcik

  4. IT Step University, Lviv, Ukraine

    Olena Vynokurova

  5. Kherson National Technical University, Kherson, Ukraine

    Svetlana Vyshemyrskaya

  6. Kherson National Technical University, Kherson, Ukraine

    Svetlana Radetskaya

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Pichugina, O., Yakovlev, S. (2020). Euclidean Combinatorial Configurations: Continuous Representations and Convex Extensions. In: Lytvynenko, V., Babichev, S., Wójcik, W., Vynokurova, O., Vyshemyrskaya, S., Radetskaya, S. (eds) Lecture Notes in Computational Intelligence and Decision Making. ISDMCI 2019. Advances in Intelligent Systems and Computing, vol 1020. Springer, Cham. https://doi.org/10.1007/978-3-030-26474-1_5

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