4 research outputs found
Packing circles in the smallest circle: an adaptive hybrid algorithm
The circular packing problem (CPP) consists of packing n circles Ci, iâN={1,ââŠ,ân}, into the smallest containing circle â. The objective is to determine the coordinates (xi) of the centre of Ci, iâN, as well as the radius r and centre (x,ây) of â. 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 circlesâ ordering, whereas the nested partitioning is to determine the n circlesâ positions that yield the smallest r. The computational results show the efficiency of the proposed algorithm.