DC programming and DCA for large-scale two-dimensional packing problems

Authors:
Babacar Mbaye Ndiaye;Le Thi Hoai An;Pham Dinh Tao;Yi Shuai Niu
Affiliations:
Laboratory of Mathematics of Decision and Numerical Analysis, Cheikh Anta Diop University - Dakar, Dakar-Fann, Senegal;Laboratory of Theoretical and Applied Computer Science, UFR MIM, University of Paul Verlaine, Metz, Metz, France;Laboratory of Mathematics, National Institute for Applied Sciences - Rouen, Saint-Etienne-du-Rouvray, France;Laboratory of Mathematics, National Institute for Applied Sciences - Rouen, Saint-Etienne-du-Rouvray, France
Venue:
ACIIDS'12 Proceedings of the 4th Asian conference on Intelligent Information and Database Systems - Volume Part II
Year:
2012

Citing 3
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Abstract

In this paper, we propose a global optimization method based on DC (Difference of Convex functions) programming and DCA (DC Algorithm) involving cutting plane techniques for solving two-dimensional Bin packing and Strip packing problems. Given a set of rectangular items, we consider problems of allocating each item to larger rectangular standardized units. In two-dimensional bin packing problem, these units are finite rectangles, and the objective is to pack all the items into the minimum number of units. In two-dimensional strip packing problem, there is a single standardized unit of given width, and the objective is to pack all the items within the minimum height. These problems are characterized as BLP (Binary Linear Programming) problems. Thanks to exact penalty technique in DC Programming, the BLP can be reformulated as polyhedral DC program which can be efficiently solved via the proposed DC programming approach. Computational experiments on large-scale dataset involving up to 200 items show the good performance of our algorithm.