A beam search algorithm for the circular packing problem

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.