An Effective Hybrid Algorithm for the Circles and Spheres Packing Problems

Authors:
Jingfa Liu;Yonglei Yao;Yu Zheng;Huantong Geng;Guocheng Zhou
Affiliations:
Computer and Software Institute, Nanjing University of Information Science and Technology, Nanjing, China 210044;Computer and Software Institute, Nanjing University of Information Science and Technology, Nanjing, China 210044;Computer and Software Institute, Nanjing University of Information Science and Technology, Nanjing, China 210044;Computer and Software Institute, Nanjing University of Information Science and Technology, Nanjing, China 210044;Computer and Software Institute, Nanjing University of Information Science and Technology, Nanjing, China 210044
Venue:
COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
Year:
2009

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Abstract

Given a fixed set of equal or unequal circular objects, the problem we deal with consists in finding the smallest container within which the objects can be packed without overlap. Circular containers are considered. Moreover, 2D and 3D problems are treated. Lacking powerful optimization method is the key obstacle to solve this kind of problems. The energy landscape paving (ELP) method is a class of heuristic global optimization algorithm. By combining the improved ELP method with the gradient descent (GD) procedure based on adaptive step length, a hybrid algorithm ELPGD for the circles and spheres packing problems is put forward. The experimental results on a series of representative circular packing instances taken from the literature show the effectiveness of the proposed algorithm for the circles packing problem, and the results on a set of unitary spherical packing instances are also presented for the spheres packing problem for future comparison with other methods.