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Optimal Packing Problems: From Knapsack Problem to Open Dimension Problem

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Intelligent Computing and Optimization (ICO 2019)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1072))

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Abstract

The paper considers a packing problem of arbitrary shaped objects into an optimized container (OPP) formulated as a knapsack problem. Mathematical model of OPP in the form of a knapsack problem (KP) is provided. A new approach of reducing the knapsack problem (KP) to a sequence of the open dimension problems (ODP) is proposed. The key idea of the approach is based on the homothetic transformations of the container. The approach is most efficient for optimization packing problems into containers of complex geometry.

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Author information

Authors and Affiliations

  1. A. Pidgorny Institute of Mechanical Engineering Problems of the National Academy of Sciences of Ukraine, 2/10 Pozharsky St., Kharkiv, 61046, Ukraine

    G. Yaskov & T. Romanova

  2. Graduate Program in Systems Engineering, Nuevo Leon State University (UANL), Monterrey, Av. Universidad s/n Col. Ciudad Universitaria, 66455, San Nicolas de los Garza, Mexico

    I. Litvinchev

  3. National University of Internal Affairs, 27 L. Landau Av, Kharkiv, 61080, Ukraine

    S. Shekhovtsov

Authors
  1. G. Yaskov
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  2. T. Romanova
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  3. I. Litvinchev
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  4. S. Shekhovtsov
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Corresponding author

Correspondence to G. Yaskov .

Editor information

Editors and Affiliations

  1. Department of Fundamental and Applied Sciences, Universiti Teknologi Petronas, Tronoh, Perak, Malaysia

    Pandian Vasant

  2. Computer Science, FEI, VSB-TU Ostrava, Ostrava, Czech Republic

    Ivan Zelinka

  3. Faculty of Engineering Management, Poznan University of Technology, Poznan, Poland

    Gerhard-Wilhelm Weber

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Yaskov, G., Romanova, T., Litvinchev, I., Shekhovtsov, S. (2020). Optimal Packing Problems: From Knapsack Problem to Open Dimension Problem. In: Vasant, P., Zelinka, I., Weber, GW. (eds) Intelligent Computing and Optimization. ICO 2019. Advances in Intelligent Systems and Computing, vol 1072. Springer, Cham. https://doi.org/10.1007/978-3-030-33585-4_65

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