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A reduction approach for solving the rectangle packing area minimization problem

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  • Bortfeldt, Andreas

Abstract

In the rectangle packing area minimization problem (RPAMP) we are given a set of rectangles with known dimensions. We have to determine an arrangement of all rectangles, without overlapping, inside an enveloping rectangle of minimum area. The paper presents a generic approach for solving the RPAMP that is based on two algorithms, one for the 2D Knapsack Problem (KP), and the other for the 2D Strip Packing Problem (SPP). In this way, solving an instance of the RPAMP is reduced to solving multiple SPP and KP instances. A fast constructive heuristic is used as SPP algorithm while the KP algorithm is instantiated by a tree search method and a genetic algorithm alternatively. All these SPP and KP methods have been published previously. Finally, the best variants of the resulting RPAMP heuristics are combined within one procedure. The guillotine cutting condition is always observed as an additional constraint. The approach was tested on 15 well-known RPAMP instances (above all MCNC and GSRC instances) and new best solutions were obtained for 10 instances. The computational effort remains acceptable. Moreover, 24 new benchmark instances are introduced and promising results are reported.

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  • Bortfeldt, Andreas, 2013. "A reduction approach for solving the rectangle packing area minimization problem," European Journal of Operational Research, Elsevier, vol. 224(3), pages 486-496.
    • Handle: RePEc:eee:ejores:v:224:y:2013:i:3:p:486-496
    DOI: 10.1016/j.ejor.2012.08.006
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    1. Wei, Lijun & Zhu, Wenbin & Lim, Andrew & Liu, Qiang & Chen, Xin, 2018. "An adaptive selection approach for the 2D rectangle packing area minimization problem," Omega, Elsevier, vol. 80(C), pages 22-30.
    2. He, Kun & Ji, Pengli & Li, Chumin, 2015. "Dynamic reduction heuristics for the rectangle packing area minimization problem," European Journal of Operational Research, Elsevier, vol. 241(3), pages 674-685.

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