Abstract
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.
Highlights
In this paper we propose to enhance a width-beam search in order to solve the three-dimensional sphere packing problem
Beam Search (BS) has been first proposed in [15] for tackling the scheduling problem and it has since been successfully applied to many other combinatorial optimization problems
We introduce the HC strategy that is used for avoiding exhaustive search that is equivalent to an augmented beam search (Hifi et al [7] and Yavuza [21])), where a subset of paths are taken for further branchings and the other nodes are discarded
Summary
The problem representation and strategies used are first described in Secsion III-A.
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