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A fast and scalable bottom-left-fill algorithm to solve nesting problems using a semi-discrete representation

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  • Chehrazad, Sahar
  • Roose, Dirk
  • Wauters, Tony

Abstract

We present a fast algorithm to solve nesting problems based on a semi-discrete representation of both the 2D non-convex pieces and the strip. The pieces and the strip are represented by a set of equidistant vertical line segments. The discretization algorithm uses a sweep-line method and applies minimal extensions to the line segments of a piece to ensure that non-overlapping placement of the segments, representing two pieces, cannot cause overlap of the original pieces. We implemented a bottom-left-fill greedy placement procedure, using an optimised ordering of the segments overlap tests. The C++ implementation of our algorithm uses appropriate data structures that allow fast execution. It executes the bottom-left-fill algorithm for typical ESICUP data sets in a few milliseconds, even when rotation of the pieces is considered, and thus provides a suitable ‘building block’ for integration in metaheuristics. Moreover, we show that the algorithm scales well when the number of pieces increases.

Suggested Citation

  • Chehrazad, Sahar & Roose, Dirk & Wauters, Tony, 2022. "A fast and scalable bottom-left-fill algorithm to solve nesting problems using a semi-discrete representation," European Journal of Operational Research, Elsevier, vol. 300(3), pages 809-826.
    • Handle: RePEc:eee:ejores:v:300:y:2022:i:3:p:809-826
    DOI: 10.1016/j.ejor.2021.10.043
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    References listed on IDEAS

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    1. Hagspihl, Thomas & Kolisch, Rainer & Fontaine, Pirmin & Schiffels, Sebastian, 2024. "Apron layout planning–Optimal positioning of aircraft stands," Transportation Research Part B: Methodological, Elsevier, vol. 179(C).

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