广义指派问题(GAP)分类与求解算法

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狂风快剑 发表于 2020/08/28 21:32:48 2020/08/28
【摘要】 指派问题(又称分配问题)在现实中有着广泛的应用背景,可以抽象为,m个物品与n个背包的匹配问题,除传统的平衡指派问题(Assignment Problem,AP)所研究的一对一匹配问题,实际中的很多问题是物品数大于背包数量,且背包容量有限的GAP问题。GAP问题是组合优化中的一个分支,也是运筹学中的一类经典问题,且已被证明是NP-难问题。

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表 1 GAP问题元启发式

算法

算法要点

主要文献

遗传算法

解的结构为一个n维数组,下标代表物品,数值代表背包

[11]

变邻域搜索

随机使用不同邻域;设计容量超出罚函数,容许非可行解

[12]

禁忌搜索

将局部最优解写入禁忌表

[13][14][15]

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参考文献

[1]    王周宏. 运筹学基础[M]. 北京交通大学出版社, 2011.

[2]    Sahni S, Gonzalez T. P-complete approximation problems[J]. Journal of the ACM (JACM), 1976, 23(3): 555-565.

[3]    Dobson G, Nambimadom R S. The batch loading and scheduling problem[J]. Operations research, 2001, 49(1): 52-65.

[4]    余英姿, 张强. 一类广义指派问题的有效解法[C]// 中国运筹学会学术交流会. 2004.

[5]    Cheng C H, Goh C H, Lee A. Solving the generalized machine assignment problem in group technology[J]. 

Journal of the Operational Research Society, 1996, 47(6): 794-802.

[6]    Kuhn H W. The Hungarian method for the assignment problem[J]. Naval research logistics quarterly, 1955, 2(12): 83-97.

[7]    Ross G T, Zoltners A A. Weighted assignment models and their application[J]. Management Science, 1979, 25(7): 683-696.

[8]    Mazzola J B, Neebe A W, Dunn C V R. Production planning of a flexible manufacturing system in a material requirements 

planning environment[J]. International Journal of Flexible Manufacturing Systems, 1989, 1(2): 115-142.

[9]    Nauss R M. The elastic generalized assignment problem[J]. Journal of the Operational Research Society, 2004, 55(12): 1333-1341.

[10] Mazzola J B, Wilcox S P. Heuristics for the multiresource generalized assignment problem[J]. Naval Research Logistics (NRL), 

2001, 48(6): 468-483.

[11] Chu P C, Beasley J E. A genetic algorithm for the generalised assignment problem[J]. Computers & Operations Research, 

1997, 24(1): 17-23.

[12] Yagiura M, Yamaguchi T, Ibaraki T. A variable depth search algorithm for the generalized assignment problem[M]//Meta-heuristics. 

Springer, Boston, MA, 1999: 459-471.

[13]Dıaz J A, Fernández E. A tabu search heuristic for the generalized assignment problem[J]. European Journal of 

Operational Research, 2001, 132(1): 22-38.

[14] Yagiura M, Ibaraki T, Glover F. An ejection chain approach for the generalized assignment problem[J].

 INFORMS Journal on computing, 2004, 16(2): 133-151.

[15]Yagiura M, Ibaraki T, Glover F. A path relinking approach with ejection chains for the generalized assignment problem[J].

 European journal of operational research, 2006, 169(2): 548-569.

[16]  Haddadi S, Ouzia H. An effective Lagrangian heuristic for the generalized assignment problem[J]. 

INFOR: Information Systems and Operational Research, 2001, 39(4): 351-356.

[17] Narciso M G, Lorena L A N. Lagrangean/surrogate relaxation for generalized assignment problems[J]. 

European Journal of Operational Research, 1999, 114(1): 165-177.

[18]邢文训, 谢金星. 现代优化计算方法[M]. 清华大学出版社, 2006.

[19]Haddadi S, Ouzia H. An effective Lagrangian heuristic for the generalized assignment problem[J]. 

INFOR: Information Systems and Operational Research, 2001, 39(4): 351-356.

[20] Jeet V, Kutanoglu E. Lagrangian relaxation guided problem space search heuristics for generalized assignment problems[J].

 European Journal of Operational Research, 2007, 182(3): 1039-1056.



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