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Application of the Interpolation Approach for Approximating Single-Machine Scheduling Problem with an Unknown Objective Function

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Optimization and Applications (OPTIMA 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13781))

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Abstract

In this paper we consider an approximation-interpolation approach based on the combination of interpolation method and approximation method. An approximation method for single-machine scheduling theory problem with an unknown objective function that depends on the completion times of jobs is studied. The idea of approximating an unknown function by a linear function with some weight coefficients is considered. An approximation-interpolation algorithm has been developed, which allows to determine the values of weight coefficients of the objective function of single-machine problem of the scheduling theory. In this algorithm the minimization of the total weighted completion times according to the given set of values of the problem parameters and the corresponding known optimal schedules was carried out. Experiments with Lagrange polynomials interpolation and cubic splines have been conducted. The hypothesis of the necessity to take into account long-range bounds when calculating weighting coefficients has been confirmed.

The results of the sections 1–3 were obtained within the State Assignment of the Ministry of Science and Higher Education of the Russian Federation (theme No. 122041300137-2). The results of the section 5–6 were obtained within the RFBR and MOST grant (project No. 20-58-S52006). The results of the section 7 were obtained within the RSF grant (project No. 22-71-10131).

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Authors and Affiliations

  1. Institute of Control Sciences, 65 Profsoyuznaya Street, Moscow, 117997, Russia

    Alexander Lazarev, Egor Barashov, Darya Lemtyuzhnikova & Andrey Tyunyatkin

  2. Moscow Aviation Institute, 4 Volokolamskoe Highway, Moscow, 125993, Russia

    Darya Lemtyuzhnikova

Authors
  1. Alexander Lazarev
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  2. Egor Barashov
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  3. Darya Lemtyuzhnikova
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  4. Andrey Tyunyatkin
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Corresponding author

Correspondence to Egor Barashov .

Editor information

Editors and Affiliations

  1. Dorodnitsyn Computing Centre, Moscow, Russia

    Nicholas Olenev

  2. Dorodnitsyn Computing Centre, Moscow, Russia

    Yuri Evtushenko

  3. University of Montenegro, Podgorica, Montenegro

    Milojica Jaćimović

  4. Krasovskii Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  5. Dorodnitsyn Computing Centre, Moscow, Russia

    Vlasta Malkova

  6. Dorodnitsyn Computing Centre, Moscow, Russia

    Igor Pospelov

Appendix

Appendix

figure a
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Lazarev, A., Barashov, E., Lemtyuzhnikova, D., Tyunyatkin, A. (2022). Application of the Interpolation Approach for Approximating Single-Machine Scheduling Problem with an Unknown Objective Function. In: Olenev, N., Evtushenko, Y., Jaćimović, M., Khachay, M., Malkova, V., Pospelov, I. (eds) Optimization and Applications. OPTIMA 2022. Lecture Notes in Computer Science, vol 13781. Springer, Cham. https://doi.org/10.1007/978-3-031-22543-7_16

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  • DOI: https://doi.org/10.1007/978-3-031-22543-7_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-22542-0

  • Online ISBN: 978-3-031-22543-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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