Packing circles in the smallest circle: An adaptive hybrid algorithm

The circular packing problem (CPP) consists of packing n circles C _i of known radii r_i, iε=N={1,.., n}, into the smallest containing circle. The objective is to determine the coordinates (x_i, y_i) of the centre of C_i, iεN, as well as the radius r and centre (x, y) of. CPP, which is a variant of the two-dimensional open-dimension problem, is NP hard. This paper presents an adaptive algorithm that incorporates nested partitioning within a tabu search and applies some diversification strategies to obtain a (near) global optimum. The tabu search is to identify the n circles ordering, whereas the nested partitioning is to determine the n circles positions that yield the smallest r. The computational results show the efficiency of the proposed algorithm.