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Usage of Selected Swarm Intelligence Algorithms for Piecewise Linearization

Author

Listed:
  • Nicole Škorupová

    (CE IT4Innovations–IRAFM, University of Ostrava, 70103 Ostrava, Czech Republic
    These authors contributed equally to this work.)

  • Petr Raunigr

    (Department of Informatics and Computers, University of Ostrava, 30. dubna 22, 70103 Ostrava, Czech Republic
    These authors contributed equally to this work.)

  • Petr Bujok

    (Department of Informatics and Computers, University of Ostrava, 30. dubna 22, 70103 Ostrava, Czech Republic
    These authors contributed equally to this work.)

Abstract

The paper introduces a new approach to enhance optimization algorithms when solving the piecewise linearization problem of a given function. Eight swarm intelligence algorithms were selected to be experimentally compared. The problem is represented by the calculation of the distance between the original function and the estimation from the piecewise linear function. Here, the piecewise linearization of 2D functions is studied. Each of the employed swarm intelligence algorithms is enhanced by a newly proposed automatic detection of the number of piecewise linear parts that determine the discretization points to calculate the distance between the original and piecewise linear function. The original algorithms and their enhanced variants are compared on several examples of piecewise linearization problems. The results show that the enhanced approach performs sufficiently better when it creates a very promising approximation of functions. Moreover, the degree of precision is slightly decreased by the focus on the speed of the optimization process.

Suggested Citation

  • Nicole Škorupová & Petr Raunigr & Petr Bujok, 2022. "Usage of Selected Swarm Intelligence Algorithms for Piecewise Linearization," Mathematics, MDPI, vol. 10(5), pages 1-24, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:808-:d:763276
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    References listed on IDEAS

    as
    1. Jiří Kupka & Nicole Škorupová, 2021. "On PSO-Based Simulations of Fuzzy Dynamical Systems Induced by One-Dimensional Ones," Mathematics, MDPI, vol. 9(21), pages 1-26, October.
    2. Eduardo Camponogara & Luiz Fernando Nazari, 2015. "Models and Algorithms for Optimal Piecewise-Linear Function Approximation," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-9, July.
    3. Spyros Kontogiorgis, 2000. "Practical Piecewise-Linear Approximation for Monotropic Optimization," INFORMS Journal on Computing, INFORMS, vol. 12(4), pages 324-340, November.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Jian Dong, 2023. "Preface to the Special Issue on “Recent Advances in Swarm Intelligence Algorithms and Their Applications”—Special Issue Book," Mathematics, MDPI, vol. 11(12), pages 1-4, June.

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