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International Conference on Optimization Problems and Their Applications

OPTA 2018: Optimization Problems and Their Applications pp 309–320Cite as

A Core Heuristic and the Branch-and-Price Method for a Bin Packing Problem with a Color Constraint

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 871))

Abstract

We study a new bin packing problem with a color constraint. A finite set of items and an unlimited number of identical bins are given. Each item has a set of colors. Each bin has a color capacity. The set of colors for a bin is the union of colors for its items and its cardinality can not exceed the bin capacity. We need to pack all items into the minimal number of bins. For this NP-hard problem, we design the core heuristic based on the column generation approach for the large-scale formulation. A hybrid VNS matheuristic with large neighborhoods is used for solving the pricing problem. We use our core heuristic in the exact branch-and-price method. Computational experiments illustrate the ability of the core heuristic to produce optimal solutions for randomly generated instances with the number of items up to 250. High-quality solutions on difficult instances with regular structure are found.

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Acknowledgements

The research in Sects. 1, 2, 3 and 4 was supported by RFBR grant 18-07-00599. The research in Sects. 5 and 6 was supported by the program of fundamental scientific researches of the SB RAS I.5.1., project 0314-2016-0014.

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Authors and Affiliations

  1. Novosibirsk State University, Novosibirsk, Russia

    Artem Kondakov & Yury Kochetov

  2. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Artem Kondakov & Yury Kochetov

Authors
  1. Artem Kondakov
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  2. Yury Kochetov
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Corresponding author

Correspondence to Yury Kochetov .

Editor information

Editors and Affiliations

  1. Sobolev Institute of Mathematics SB RAS, Omsk, Russia

    Anton Eremeev

  2. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  3. Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russia

    Yury Kochetov

  4. Industrial and Systems Engineering, University of Florida, Gainesville, Florida, USA

    Panos Pardalos

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Kondakov, A., Kochetov, Y. (2018). A Core Heuristic and the Branch-and-Price Method for a Bin Packing Problem with a Color Constraint. In: Eremeev, A., Khachay, M., Kochetov, Y., Pardalos, P. (eds) Optimization Problems and Their Applications. OPTA 2018. Communications in Computer and Information Science, vol 871. Springer, Cham. https://doi.org/10.1007/978-3-319-93800-4_25

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  • DOI: https://doi.org/10.1007/978-3-319-93800-4_25

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-93799-1

  • Online ISBN: 978-3-319-93800-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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