A heuristic dynamic programming algorithm for 2D unconstrained guillotine cutting

Authors:
Xiang Song;Cheng-Bin Chu;Yi-Yong Nie
Affiliations:
Department of CIMS, Shenyang Institute of Automation, Chinese Academy of Sciences, School of Graduate, Shenyang, Liaoning, China and Département GSI, Université de Technologie de Troyes, ...;Département GSI, Université de Technologie de Troyes, Troyes Cedex, France;Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang, Liaoning, China
Venue:
Math'04 Proceedings of the 5th WSEAS International Conference on Applied Mathematics
Year:
2004

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Abstract

In this paper, a heuristic dynamic-programming recursion is proposed for solving unconstrained 2D knapsack problem efficiently. The algorithm we propose is an incompletely enumerative method, in which some intricate cutting patterns may not be enumerated. Compared with the traditional dynamic-programming, the algorithm gives a high percentage of optimal solutions (93%) with a much lower computational complexity. Some theoretical analyses for the algorithm are performed. Computational results are given for small and medium-sized problems.