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Two Approaches to Modeling and Solving the Packing Problem for Convex Polytopes

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Cybernetics and Systems Analysis Aims and scope

Abstract

We consider the problem of packing convex polytopes in a cuboid of minimum volume. To describe analytically the non-overlapping constraints for convex polytopes that allow continuous translations and rotations, we use phi-functions and quasi-phi-functions. We provide an exact mathematical model in the form of an NLP-problem and analyze its characteristics. Based on the general solution strategy, we propose two approaches that take into account peculiarities of phi-functions and quasi-phi-functions. Computational results to compare the efficiency of our approaches are given with respect to both the value of the objective function and runtime.

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Authors and Affiliations

  1. A. Pidgorny Institute of Mechanical Engineering Problems, National Academy of Sciences of Ukraine, Kharkiv, Ukraine

    Y. E. Stoian, A. M. Chugay, A. V. Pankratov & T. E. Romanova

Authors
  1. Y. E. Stoian
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  2. A. M. Chugay
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  3. A. V. Pankratov
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  4. T. E. Romanova
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Corresponding author

Correspondence to Y. E. Stoian.

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Translated from Kibernetika i Sistemnyi Analiz, No. 4, July–August, 2018, pp. 81–90.

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Stoian, Y.E., Chugay, A.M., Pankratov, A.V. et al. Two Approaches to Modeling and Solving the Packing Problem for Convex Polytopes. Cybern Syst Anal 54, 585–593 (2018). https://doi.org/10.1007/s10559-018-0059-3

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  • DOI: https://doi.org/10.1007/s10559-018-0059-3

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