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Cutting and packing problems for irregular objects with continuous rotations: mathematical modelling and non-linear optimization

Author

Listed:
  • Yuriy Stoyan

    (Institute for Mechanical Engineering Problems of the National Academy of Sciences of Ukraine, Kharkov, Ukraine)

  • Alexander Pankratov

    (Institute for Mechanical Engineering Problems of the National Academy of Sciences of Ukraine, Kharkov, Ukraine)

  • Tatiana Romanova

    (Institute for Mechanical Engineering Problems of the National Academy of Sciences of Ukraine, Kharkov, Ukraine)

Abstract

We further improve our methodology for solving irregular packing and cutting problems. We deal with an accurate representation of objects bounded by circular arcs and line segments and allow their continuous rotations and translations within rectangular and circular containers. We formulate a basic irregular placement problem which covers a wide spectrum of packing and cutting problems. We provide an exact non-linear programming (NLP) model of the problem, employing ready-to-use phi-functions. We develop an efficient solution algorithm to search for local optimal solutions for the problem in a reasonable time. The algorithm reduces our problem to a sequence of NLP subproblems and employs optimization procedures to generate starting feasible points and feasible subregions. Our algorithm allows us to considerably reduce the number of inequalities in NLP subproblems. To show the benefits of our methodology we give computational results for a number of new challenger and the best known benchmark instances.

Suggested Citation

  • Yuriy Stoyan & Alexander Pankratov & Tatiana Romanova, 2016. "Cutting and packing problems for irregular objects with continuous rotations: mathematical modelling and non-linear optimization," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(5), pages 786-800, May.
    • Handle: RePEc:pal:jorsoc:v:67:y:2016:i:5:p:786-800
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    Cited by:

    1. Juan Lu & Chengyi Ou & Chen Liao & Zhenkun Zhang & Kai Chen & Xiaoping Liao, 2021. "Formal modelling of a sheet metal smart manufacturing system by using Petri nets and first-order predicate logic," Journal of Intelligent Manufacturing, Springer, vol. 32(4), pages 1043-1063, April.
    2. Luiz H. Cherri & Adriana C. Cherri & Edilaine M. Soler, 2018. "Mixed integer quadratically-constrained programming model to solve the irregular strip packing problem with continuous rotations," Journal of Global Optimization, Springer, vol. 72(1), pages 89-107, September.
    3. Leao, Aline A.S. & Toledo, Franklina M.B. & Oliveira, José Fernando & Carravilla, Maria Antónia & Alvarez-Valdés, Ramón, 2020. "Irregular packing problems: A review of mathematical models," European Journal of Operational Research, Elsevier, vol. 282(3), pages 803-822.
    4. A. Pankratov & T. Romanova & I. Litvinchev, 2019. "Packing ellipses in an optimized convex polygon," Journal of Global Optimization, Springer, vol. 75(2), pages 495-522, October.

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