A beam search algorithm for the circular packing problem

  • Authors:

  • Hakim Akeb;Mhand Hifi;Rym M'Hallah

  • Affiliations:

  • Institut Supérieur du Commerce, 22 boulevard du Fort de Vaux, 75017 Paris, France and MIS, Axe Discrete Optimization and Reoptimization, Université de Picardie Jules Verne, 33 rue Saint- ...;MIS, Axe Discrete Optimization and Reoptimization, Université de Picardie Jules Verne, 33 rue Saint-Leu, 80039 Amiens, France and CES, Equipe CERMSEM, MSE, Université Paris 1, 106-112 Bd ...;Department of Statistics and Operations Research, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait

  • Venue:
  • Computers and Operations Research
  • Year:
  • 2009

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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@?N={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 packed circles C"i,i@?N. CPP is solved by using an adaptive beam search 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 algorithm.