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Statistical Research of Efficiency of Approximation Algorithms for Planning Processes Automation Problems

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Advances in Computer Science for Engineering and Education II (ICCSEEA 2019)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 938))

Abstract

We study the efficiency of polynomial approximation algorithms for solving NP-hard scheduling problems to minimize total tardiness and total weighted tardiness on one machine. The algorithms are based on PSC-algorithms for the considered problems given in [Zgurovsky & Pavlov, Combinatorial Optimization Problems in Planning and Decision Making: Theory and Applications, Springer, 2019]. They were developed by excluding procedures related to exponential enumeration. The approximation algorithms have a polynomial complexity and can solve problems of any practical dimension. We give a method for determining the maximum possible deviation of the approximate solution of the total tardiness problem from the optimum for each individual problem instance. We present experimental data on the solving time and the actual percentage of the deviation of the functional value from the optimum. The deviation was less than 5% after the execution of the approximate algorithm for the weighted tardiness problem and less than 2.4% for the total tardiness problem. This confirms the high efficiency of the approximation algorithms.

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Authors and Affiliations

  1. National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, 37, Prospekt Peremohy, Kyiv, 03056, Ukraine

    Alexander Anatolievich Pavlov, Elena Borisovna Misura, Oleg Valentinovich Melnikov, Iryna Pavlovna Mukha & Kateryna Igoryvna Lishchuk

Authors
  1. Alexander Anatolievich Pavlov
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  2. Elena Borisovna Misura
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  3. Oleg Valentinovich Melnikov
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  4. Iryna Pavlovna Mukha
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  5. Kateryna Igoryvna Lishchuk
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Corresponding author

Correspondence to Alexander Anatolievich Pavlov .

Editor information

Editors and Affiliations

  1. School of Educational Information Technology, Central China Normal University, Wuhan, Hubei, China

    Zhengbing Hu

  2. Mechanical Engineering Research Institute of the Russian Academy of Sciences, Moscow, Russia

    Sergey Petoukhov

  3. “Igor Sikorsky Kiev Polytechnic Institute”, National Technical University of Ukraine, Kiev, Ukraine

    Ivan Dychka

  4. Halmos College of Natural Sciences and Oceanography, Nova Southeastern University, Ft. Lauderdale, FL, USA

    Matthew He

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Pavlov, A.A., Misura, E.B., Melnikov, O.V., Mukha, I.P., Lishchuk, K.I. (2020). Statistical Research of Efficiency of Approximation Algorithms for Planning Processes Automation Problems. In: Hu, Z., Petoukhov, S., Dychka, I., He, M. (eds) Advances in Computer Science for Engineering and Education II. ICCSEEA 2019. Advances in Intelligent Systems and Computing, vol 938. Springer, Cham. https://doi.org/10.1007/978-3-030-16621-2_37

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