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A VNS Based Heuristic for a 2D Open Dimension Problem

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Variable Neighborhood Search (ICVNS 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13863))

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Abstract

This paper is related to open-dimension problems in the area of cutting and packing. The problem we are interested in considers a set of irregularly shaped items and a two-dimensional (2D) bin in which one side is open. The objective is to pack all items in the bin and, in the case of a bin with one opened side, we also want to minimize the length of such a side. A packing cannot have items overlapping each other and items extrapolating the bin’s dimensions. This problem appears in the metal-mechanic, textile, leather, and other related industries to the cutting of irregular pieces. We propose a variable neighborhood search-based heuristic for such a problem. A solution is coded as a vector of items that gives the sequence in which items will be packed. Neighborhood structures based on swap and insertion movements are considered in the local search phase, while the shaking phase contains a single neighborhood structure based on swap movements. Numerical experiments on benchmark instances show that the heuristic is competitive compared to other literature methods, obtaining equal or better solutions for 90.90% of the instances.

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Acknowledgements

The authors acknowledge the financial support of the National Council for Scientific and Technological Development (CNPq grants numbers 405369/2021-2 and 311185/2020-7) and the State of Goiás Research Foundation (FAPEG).

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Authors and Affiliations

  1. Institute of Mathematics and Technology, Federal University of Catalão, Catalão-Go, 75704-020, Brazil

    Layane Rodrigues de Souza Queiroz & Thiago Alves de Queiroz

Authors
  1. Layane Rodrigues de Souza Queiroz
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  2. Thiago Alves de Queiroz
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Correspondence to Thiago Alves de Queiroz .

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Editors and Affiliations

  1. Khalifa University, Abu Dhabi, United Arab Emirates

    Andrei Sleptchenko

  2. University of Macedonia, Thessaloniki, Greece

    Angelo Sifaleras

  3. HEC Montréal, Montréal, QC, Canada

    Pierre Hansen

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Queiroz, L.R.d.S., de Queiroz, T.A. (2023). A VNS Based Heuristic for a 2D Open Dimension Problem. In: Sleptchenko, A., Sifaleras, A., Hansen, P. (eds) Variable Neighborhood Search. ICVNS 2022. Lecture Notes in Computer Science, vol 13863. Springer, Cham. https://doi.org/10.1007/978-3-031-34500-5_10

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  • DOI: https://doi.org/10.1007/978-3-031-34500-5_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-34499-2

  • Online ISBN: 978-3-031-34500-5

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