| 条形装箱问题的优化模型和增广Lagrange算法 |
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| 引用本文： | 于洪霞,张宏伟,张立卫.条形装箱问题的优化模型和增广Lagrange算法[J].东北数学,2006,22(4):441-450. |
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| 作者姓名： | 于洪霞 张宏伟 张立卫 |
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| 作者单位： | Department of Mathematics and Physics Shanghai University of Electric Power，Shanghai，200090，Department of Applied Mathematics，Dalian University of Technology，Dalian，116024，Department of Applied Mathematics，Dalian University of Technology，Dalian，116024 |
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| 摘 要： | This paper formulates a two-dimensional strip packing problem as a non-linear programming(NLP)problem and establishes the first-order optimality con-ditions for the NLP problem.A numerical algorithm for solving this NLP problemis given to find exact solutions to strip-packing problems involving up to 10 items.Approximate solutions can be found for big-sized problems by decomposing the setof items into small-sized blocks of which each block adopts the proposed numericalalgorithm.Numerical results show that the approximate solutions to big-sized prob-lems obtained by this method are superior to those by NFDH,FFDH and BFDHapproaches.
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| 关 键 词： | 排样装箱问题 优化模型 扩展拉格朗日法 一阶最优条件 |
An Optimization Model for the Strip-packing Problem and Its Augmented Lagrangian Method |
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| YU Hong-xia,ZHANG Hong-wei,ZHANG Li-wei.An Optimization Model for the Strip-packing Problem and Its Augmented Lagrangian Method[J].Northeastern Mathematical Journal,2006,22(4):441-450. |
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| Authors: | YU Hong-xia ZHANG Hong-wei ZHANG Li-wei |
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| Institution: | [1]Department of Mathematics and Physics, Shanghai University of Electric Power, Shanghai, 200090 [2]Department of Applied Mathematics, Dalian University of Technology, Dalian, 116024 |
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| Abstract: | This paper formulates a two-dimensional strip packing problem as a non- linear programming(NLP)problem and establishes the first-order optimality con- ditions for the NLP problem.A numerical algorithm for solving this NLP problem is given to find exact solutions to strip-packing problems involving up to 10 items. Approximate solutions can be found for big-sized problems by decomposing the set of items into small-sized blocks of which each block adopts the proposed numerical algorithm.Numerical results show that the approximate solutions to big-sized prob- lems obtained by this method are superior to those by NFDH,FFDH and BFDH approaches. |
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| Keywords: | strip-packing problem augmented lagrangian method first-order optimality condition |
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