基于表上作业原理的运输问题计算机寻优算法
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中图分类号:

C93-03;TP391

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河南省重点研发与推广专项(192102210223);河南省高等学校重点科研资助项目(19A410001)。


Computer-aided optimization algorithm for solving transportation problems based on table-manipulation principle
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    摘要:

    针对运输问题寻优的高度复杂性,提出了一种基于表上作业原理的计算机寻优算法。在算法中,采用"最小元素法"获取初始基可行解,采用"位势法"获取检验数数组,采用"递归过程"获取闭合回路数组,根据闭合回路数组和基可行解获取调整量,根据闭合回路数组、调整量对基可行解进行调整,通过While循环不断寻优直到最小检验数非负。While循环退出时,若存在0检验数,则任选一个0检验数,以其为起点寻找一个闭合回路数组,通过调整得到随机最优解。应用案例表明,该算法实现了表上作业求解过程的计算机程序化,提高了计算效率、确保了计算准确性。

    Abstract:

    Aimed at getting the optimal solution of transportation problems, a computer-aided optimization algorithm based on table-manipulation principle is proposed. In the algorithm, the minimum element method is used to get an initial basic feasible solution;the potential method is adopted to get the array of check numbers and the recursive process is applied to get the closed loop array. Then the adjusting quantity is got according to the closed loop array and basic feasible solution, a new feasible solution is got after the feasible solution is adjusted according to the closed loop array and adjusting quantity, and the While loop is used to get the optimal solution until the minimum check number is not less than 0. After the While loop exits, if there are one or more 0 check numbers in the array of check numbers, one 0 check number is selected randomly to get a random optimum solution through above process. Case study shows that by the proposed computer-aided optimization algorithm, the computerization of the table-manipulation process is realized, thus improving the calculation efficiency and ensuring calculation accuracy.

    参考文献
    [1] Hitchcock F L. The distribution of a product from several sources to numerous localities[J]. Journal of Mathematics and Physics, 1941, 20(1/2/3/4): 224-230.
    [2] 王有鸿, 费威. 运输问题国内外研究评述[J]. 商业时代, 2010(24): 31-32. WANG Youhong, FEI Wei. International and domestic review on transportation problems[J]. Commercial Times, 2010(24): 31-32. (in Chinese)
    [3] 彭程, 薛伟宁, 黄轶. 露天矿运输问题的模拟退火优化[J]. 中国矿业, 2018, 27(4): 138-141.PENG Cheng, XUE Weining, HUANG Yi. Simulated annealing algorithm for the open-pit mine transportation problem[J]. China Mining Magazine, 2018, 27(4): 138-141. (in Chinese)
    [4] 甘应爱, 田丰. 运筹学[M]. 修订版. 北京: 清华大学出版社, 2005.GAN Yingai, TIAN Feng. Operations research[M]. Revised ed. Beijing: Tsinghua University Press, 2005. (in Chinese)
    [5] Zhang L F, Zhao X D. Research on non-standard assignment problem based on the vogel method[J]. Applied Mechanics and Materials, 2012, 256/257/258/259: 3028-3032.
    [6] Klinz B, Woeginger G J. The Northwest corner rule revisited[J]. Discrete Applied Mathematics, 2011, 159(12): 1284-1289.
    [7] Sanchez L C, Herrera J. Solution to the multiple products transportation problem: linear programming optimization with Excel Solver[J]. IEEE Latin America Transactions, 2016, 14(2): 1018-1023.
    [8] 司守奎. 数学建模算法与应用[M]. 北京: 国防工业出版社, 2017.SI Shoukui. Mathematical modeling algorithms and applications[M]. Beijing: National Defense Industry Press, 2017. (in Chinese)
    [9] 司南, 任佳莉. 运输问题的一种计算机算法[J]. 计算机应用与软件, 2004, 21(7): 120-121.SI Nan, REN Jiali. A computer algorithm for transportation problem[J]. Computer Applications and Software, 2004, 21(7): 120-121. (in Chinese)
    [10] 程国忠. 运输问题的神经网络解法[J]. 计算机应用研究, 2001, 18(11): 16-18.CHENG Guozhong. A neural network method for solving transportation problem(TRP)[J]. Application Research of Computers, 2001, 18(11): 16-18.(in Chinese)
    [11] 毛云英, 亢京力, 杨正方. 运输问题的人工神经网络方法[J]. 天津商学院学报, 2001(6): 15-16,23.MAO Yunying, KANG Jingli, YANG Zhengfang. Artificial neural network method of transportation problem[J]. Journal of Tianjin University of Commerce, 2001(6): 15-16,23.(in Chinese)
    [12] 刘云飞, 赵磊, 朱道立. 出口汽车零部件集货运输问题的双层遗传算法[J]. 计算机集成制造系统, 2016, 22(9): 2227-2234.LIU Yunfei, ZHAO Lei, ZHU Daoli,. Two-level genetic algorithm for consolidated transportation problem of exporting auto-parts[J]. Computer Integrated Manufacturing Systems, 2016, 22(9): 2227-2234.(in Chinese)
    [13] Ghassemi Tari F, Hashemi Z. A priority based genetic algorithm for nonlinear transportation costs problems[J]. Computers & Industrial Engineering, 2016, 96: 86-95.
    [14] Abdulkader M M S, Gajpal Y, ElMekkawy T Y. Hybridized ant colony algorithm for the multi compartment vehicle routing problem[J]. Applied Soft Computing, 2015, 37: 196-203.
    [15] Bulut H. Multiloop transportation simplex algorithm[J]. Optimization Methods and Software, 2017, 32(6): 1206-1217.
    [16] 沈爱凤. 基于区间数/贝叶斯的不确定性改进表上作业法与运用[J]. 统计与决策, 2015(10): 76-78.SHEN Aifeng. An improved tableau working method and application based on interval number/Bayesian uncertainty[J]. Statistics and Decision, 2015(10): 76-78. (in Chinese)
    [17] 盛秀艳, 窦志伟. 农业运输问题的表上作业法与图上作业法的比较[J]. 安徽农业科学, 2010, 38(14): 7202-7203.SHENG Xiuyan, DOU Zhiwei. Comparison of tableau working method and graphic operation method for agricultural transportation problems[J]. Journal of Anhui Agricultural Sciences, 2010, 38(14): 7202-7203. (in Chinese)
    [18] 李怀祖. 生产计划与控制[M]. 北京: 中国科学技术出版社, 2005.LI Huaizu. Production planning and control[M]. Beijing: Science and Technology of China Press, 2005. (in Chinese)
    [19] Munapo E, Lesaoana 'M, Nyamugure P, et al. A transportation branch and bound algorithm for solving the generalized assignment problem[J]. International Journal of System Assurance Engineering and Management, 2015, 6(3): 217-223.
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沈玲,曾强,常梦辉.基于表上作业原理的运输问题计算机寻优算法[J].重庆大学学报,2019,42(10):92-105.

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  • 收稿日期:2019-05-01
  • 在线发布日期: 2019-11-02
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