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.
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Liu, J., Yao, Y., Zheng, Y., Geng, H., Zhou, G. (2009). An Effective Hybrid Algorithm for the Circles and Spheres Packing Problems. In: Du, DZ., Hu, X., Pardalos, P.M. (eds) Combinatorial Optimization and Applications. COCOA 2009. Lecture Notes in Computer Science, vol 5573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02026-1_12
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DOI: https://doi.org/10.1007/978-3-642-02026-1_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02025-4
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