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

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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.

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Authors and Affiliations

  1. ISC Paris, Institut Supérieur du Commerce, 22 bd du Fort de Vaux, 75017, Paris, France

    Hakim Akeb

  2. MIS, Axe Optimisation Discrète et Réoptimisation, Université de Picardie Jules, 33 rue Saint-Leu, 80039, Amiens, France

    Mhand Hifi

  3. CES, MSE, Université Paris 1, 106-112 bd de l’Hôpital, 75634, Paris Cedex 13, France

    Mhand Hifi

Authors
  1. Hakim Akeb
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  2. Mhand Hifi
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Correspondence to Mhand Hifi.

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Akeb, H., Hifi, M. A hybrid beam search looking-ahead algorithm for the circular packing problem. J Comb Optim 20, 101–130 (2010). https://doi.org/10.1007/s10878-008-9191-8

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  • DOI: https://doi.org/10.1007/s10878-008-9191-8

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