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The 2-D strip packing problem is an NP-hard combinatorial optimization problem. Given a strip with fixed width and infinite height, the aim of strip packing is to pack a set of rectangles with known widths and heights into the strip such that the used height of the strip is minimized. In this paper, we address the 2-D strip packing problem without guillotine constraint and present an effective corner increment-based algorithm. First, a corner increment-based rectangle selection strategy is adopted in a constructive heuristic way. Second, by using the AVL tree and the segment tree, the constructive heuristic is efficiently implemented. Finally, a multi-start random local search is combined to improve the solution. Experimental results on a wide range of benchmark instances show that the proposed algorithm is effective, especially for large instances.

An Effective Corner Increment-Based Algorithm for the Two-Dimensional Strip Packing Problem