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Beam search-based algorithms for the circular packing problem

Author

Listed:
  • Hakim Akeb

    (Institut Sup rieur du Commerce et LaRIA)

  • Mhand Hifi

    (LaRIA et Centre d'Economie de la Sorbonne)

Abstract

In this paper, we propose to solve the circular packing problem (CPP) whose objective is to pack n different circles C(i) of known radius r(i) , i = 1, ..., n into the smallest containing circle C. The objective is to determine the radius r of C as well as the coordinates (x(i) , y(i)) of the center of the circles C(i), i = 1, ..., n. This problem is solved by applying an adaptive algorithm that combines the beam search, the local position distance and the dichotomous search strategy. Decisions at each node of the developed tree are based on the well-known maximum hole degree that uses the local minimum distance. The computational results, on a set of instances taken from the literature, show the effectiveness of the proposed algorithms

Suggested Citation

  • Hakim Akeb & Mhand Hifi, 2007. "Beam search-based algorithms for the circular packing problem," Documents de travail du Centre d'Economie de la Sorbonne b07070, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:b07070
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    Keywords

    Circular packing; dichotomous search; beam search; maximum hole degree;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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