Title: A global dichotomous search-based heuristic for the three-dimensional sphere packing problem

Authors: Mhand Hifi; Labib Yousef

Addresses: EPROAD – EA 4669, Université de Picardie Jules Verne, 7 rue du Moulin Neuf, 80000 Amiens, France ' EPROAD – EA 4669, Université de Picardie Jules Verne, 7 rue du Moulin Neuf, 80000 Amiens, France

Abstract: In this paper, we propose a global dichotomous search-based heuristic for solving the three-dimensional sphere packing problem. In the sphere packing problem, we are given a set of predefined unequal spheres and a large container with unlimited length. The goal of the problem is to determine the minimum length of the container that contains all spheres without overlapping. We propose to optimise the length of the large container by applying a truncated tree-search that combines a hill-climbing strategy, a hybrid operator that combines both priority and total-cost operators and, a dichotomous interval search in order to diversify the search space. Further, in order to enhance the quality of solutions of internal nodes, a local dichotomous search is applied almost of using a descent method. The proposed method is evaluated on benchmark instances taken from the literature and its provided results are compared to those reached by recent published methods in the literature. The proposed method is able to improve most solutions available in the literature.

Keywords: dichotomous; heuristic; hill-climbing; optimisation; tree-search; packing.

DOI: 10.1504/IJOR.2018.095195

International Journal of Operational Research, 2018 Vol.33 No.2, pp.139 - 160

Received: 03 Apr 2014
Accepted: 02 Aug 2015
Published online: 02 Oct 2018 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article