DC Programming and DCA for Large-Scale Two-Dimensional Packing Problems

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.KeywordsTwo-dimensional packingBin packingStrip packingBLPDC ProgrammingDCACutting plane techniques