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Constraint Aggregation in Non-linear Programming Models for Nesting Problems

In: Computational Management Science

Author

Listed:
  • Pedro Rocha

    (Universidade do Porto)

  • A. Miguel Gomes

    (Universidade do Porto)

  • Rui Rodrigues

    (Universidade do Porto)

  • Franklina M. B. Toledo

    (Universidade de São Paulo)

  • Marina Andretta

    (Universidade de São Paulo)

Abstract

The Nesting problem is a complex problem that arises in industries where sets of pieces or space must be efficiently placed or allocated in order to minimize wasted space or wasted raw materials, without overlaps between pieces and fully contained inside a container. This paper analyses the impact that aggregating constraints can achieve in the reduction of computational cost of a Non-Linear Programming model for Nesting problems with continuous rotations. This is achieved by aggregating non-overlapping constraints and using spatial partition and hierarchical overlap detection methods. When aggregating constraints there is also an effect of reducing the sensitivity of the solver, which may reduce the quality of the final layout. Analyzing the trade-off between constraints aggregation and the impact on the quality of the final solution is an important issue to handle nesting instances with a large number of pieces. Computational experiments show that aggregating non-overlapping constraints allows the Non-Linear Programming model for Nesting problems to scale well to tackle large size real world problems with continuous rotations.

Suggested Citation

  • Pedro Rocha & A. Miguel Gomes & Rui Rodrigues & Franklina M. B. Toledo & Marina Andretta, 2016. "Constraint Aggregation in Non-linear Programming Models for Nesting Problems," Lecture Notes in Economics and Mathematical Systems, in: Raquel J. Fonseca & Gerhard-Wilhelm Weber & João Telhada (ed.), Computational Management Science, edition 1, pages 175-180, Springer.
    • Handle: RePEc:spr:lnechp:978-3-319-20430-7_22
    DOI: 10.1007/978-3-319-20430-7_22
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    Cited by:

    1. Romanova, Tatiana & Litvinchev, Igor & Pankratov, Alexander, 2020. "Packing ellipsoids in an optimized cylinder," European Journal of Operational Research, Elsevier, vol. 285(2), pages 429-443.
    2. Lastra-Díaz, Juan J. & Ortuño, M. Teresa, 2024. "Mixed-integer programming models for irregular strip packing based on vertical slices and feasibility cuts," European Journal of Operational Research, Elsevier, vol. 313(1), pages 69-91.
    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.

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