Width beam and hill-climbing strategies for the three-dimensional sphere packing problem

In this paper we propose to enhance a width-beam search in order to solve the three-dimensional sphere packing problem. The goal of the problem is to determine the minimum length of the container having fixed width and height, that packs n predefined unequal spheres. The width-beam search uses a greedy selection phase which determines a subset of eligible positions for packing the predefined items in the target object and selects a subset of nodes for exploring some promising paths. We propose to handle lower bounds in the tree and apply a hill-climbing strategy in order to diversify the search process. The performance of the proposed method is evaluated on benchmark instances taken from the literature. The obtained results are compared to those reached by some recent methods available in the literature. Encouraging results have been obtained.