Packing circles in the smallest circle: an adaptive hybrid algorithm

The circular packing problem (CPP) consists of packing n circles Ci, i∈N={1, …, n}, into the smallest containing circle ℂ. The objective is to determine the coordinates (xi) of the centre of Ci, i∈N, as well as the radius r and centre (x, y) of ℂ. 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.