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A global optimization point of view to handle non-standard object packing problems

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  • Giorgio Fasano

Abstract

This work originates from research carried out in support to the cargo accommodation of space vehicles/modules. The goal of this activity is to maximize the loaded cargo, taking into account the given accommodation requirements. Items can often be modelled as parallelepipeds, but it is even more frequent that real-world issues make this approximation no longer acceptable. These aspects and the presence of additional overall conditions, such as balancing, give rise to very challenging non-standard packing problems, not only in the frame of space engineering, but also in different application areas. This article considers first the orthogonal packing of tetris-like items, within a convex domain and subsequently the packing of polygons with (continuous) rotations in a convex domain. The proposed approach is based on mixed integer linear/non-linear programming (MIP, MINLP), from a global optimization point of view. The tetris-like formulation is exploited to provide the MINLP solution process with an approximated starting solution. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • Giorgio Fasano, 2013. "A global optimization point of view to handle non-standard object packing problems," Journal of Global Optimization, Springer, vol. 55(2), pages 279-299, February.
    • Handle: RePEc:spr:jglopt:v:55:y:2013:i:2:p:279-299
    DOI: 10.1007/s10898-012-9865-8
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    References listed on IDEAS

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    1. Castillo, Ignacio & Kampas, Frank J. & Pintér, János D., 2008. "Solving circle packing problems by global optimization: Numerical results and industrial applications," European Journal of Operational Research, Elsevier, vol. 191(3), pages 786-802, December.
    2. Chen, C. S. & Lee, S. M. & Shen, Q. S., 1995. "An analytical model for the container loading problem," European Journal of Operational Research, Elsevier, vol. 80(1), pages 68-76, January.
    3. Silvano Martello & David Pisinger & Daniele Vigo, 2000. "The Three-Dimensional Bin Packing Problem," Operations Research, INFORMS, vol. 48(2), pages 256-267, April.
    4. Sándor P. Fekete & Jörg Schepers, 2004. "A Combinatorial Characterization of Higher-Dimensional Orthogonal Packing," Mathematics of Operations Research, INFORMS, vol. 29(2), pages 353-368, May.
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    Cited by:

    1. Saeed Asaeedi & Farzad Didehvar & Ali Mohades, 2018. "NLP Formulation for Polygon Optimization Problems," Mathematics, MDPI, vol. 7(1), pages 1-25, December.
    2. Romanova, T. & Bennell, J. & Stoyan, Y. & Pankratov, A., 2018. "Packing of concave polyhedra with continuous rotations using nonlinear optimisation," European Journal of Operational Research, Elsevier, vol. 268(1), pages 37-53.

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