Department of Applied Mathematics & Physics, Kyoto University

Technical Report 2007-009 (February 07, 2007)

An iterated local search algorithm based on nonlinear programming for the irregular strip packing problem
by Takashi Imamichi, Mutsunori Yagiura, Hiroshi Nagamochi

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The irregular strip packing problem is a combinatorial optimization problem that asks to place a given set of 2-dimensional polygons within a rectangular container so that no polygon overlaps with other polygons or protrudes from the container, where each polygon is not necessarily convex. The container has a fixed width, while its length can change so that all polygons are placed in it. The objective is to find a layout of the set of polygons that minimizes the length of the container. We propose an algorithm that separates overlapping polygons based on nonlinear programming, and an algorithm that swaps two polygons in a layout so as to find their new positions in the layout with the least overlap. We incorporate these algorithms as components in an iterated local search algorithm for the overlap minimization problem and then develop an algorithm for the irregular strip packing problem using the iterated local search algorithm. Computational comparisons on representative instances disclose that our algorithm is competitive with other existing algorithms. Moreover, our algorithm updates several best known results.