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A hybrid beam search looking-ahead algorithm for the circular packing problem

Author

Listed:
  • Hakim Akeb

    (Institut Supérieur du Commerce)

  • Mhand Hifi

    (Université de Picardie Jules
    Université Paris 1)

Abstract

In this paper, we study the circular packing problem. Its objective is to pack a set of n circular pieces into a rectangular plate R of fixed dimensions L×W. Each piece’s type i, i=1,…,m, is characterized by its radius r i and its demand b i . The objective is to determine the packing pattern corresponding to the minimum unused area of R for the circular pieces placed. This problem is solved by using a hybrid algorithm that adopts beam search and a looking-ahead strategy. A node at a level ℓ of the beam-search tree contains a partial solution corresponding to the circles already placed inside R. Each node is then evaluated using a looking-ahead strategy, based on the minimum local-distance heuristic, by computing the corresponding complete solution. The nodes leading to the best solutions at level ℓ are then chosen for branching. A multi-start strategy is also considered in order to diversify the search space. The computational results show, on a set of benchmark instances, the effectiveness of the proposed algorithm.

Suggested Citation

  • Hakim Akeb & Mhand Hifi, 2010. "A hybrid beam search looking-ahead algorithm for the circular packing problem," Journal of Combinatorial Optimization, Springer, vol. 20(2), pages 101-130, August.
    • Handle: RePEc:spr:jcomop:v:20:y:2010:i:2:d:10.1007_s10878-008-9191-8
    DOI: 10.1007/s10878-008-9191-8
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    References listed on IDEAS

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    Cited by:

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