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A novel non-linear approach to minimal area rectangular packing

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Abstract

This paper discusses the minimal area rectangular packing problem which is to pack a given set of rectangles into a rectangular container of minimal area such that no two rectangles overlap. Current approaches for this problem rely on metaheuristics like simulated annealing, on constraint programming or on non-linear models. Difficulties arise from the non-convexity and the combinatorial complexity. We investigate different mathematical programming approaches for this and introduce a novel approach based on non-linear optimization and the “tunneling effect” achieved by a relaxation of the non-overlapping constraints. We compare our optimization algorithm to a simulated annealing and a constraint programming approach and show that our approach is competitive. Additionally, since it is easy to extend, it is also applicable to a variety of related problems.

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Authors and Affiliations

  1. Fraunhofer Institute for Industrial Mathematics (Fraunhofer ITWM), Fraunhofer-Platz 1, 67663, Kaiserslautern, Germany

    Volker Maag, Martin Berger, Anton Winterfeld & Karl-Heinz Küfer

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  1. Volker Maag
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  2. Martin Berger
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  3. Anton Winterfeld
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  4. Karl-Heinz Küfer
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Correspondence to Volker Maag.

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Maag, V., Berger, M., Winterfeld, A. et al. A novel non-linear approach to minimal area rectangular packing. Ann Oper Res 179, 243–260 (2010). https://doi.org/10.1007/s10479-008-0462-7

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