许自昌. 基于最小生成树的渠道系统优化布局模型[J]. 农业工程学报, 2017, 33(1): 124-130. DOI: 10.11975/j.issn.1002-6819.2017.01.017
    引用本文: 许自昌. 基于最小生成树的渠道系统优化布局模型[J]. 农业工程学报, 2017, 33(1): 124-130. DOI: 10.11975/j.issn.1002-6819.2017.01.017
    Xu Zichang. Optimal model of channel layout based on minimum spanning trees[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2017, 33(1): 124-130. DOI: 10.11975/j.issn.1002-6819.2017.01.017
    Citation: Xu Zichang. Optimal model of channel layout based on minimum spanning trees[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2017, 33(1): 124-130. DOI: 10.11975/j.issn.1002-6819.2017.01.017

    基于最小生成树的渠道系统优化布局模型

    Optimal model of channel layout based on minimum spanning trees

    • 摘要: 针对平原地区农田灌溉渠道优化布局问题,当前普遍采用渠道布局原则进行布局,但其不能取得成本最优的布局。通过简化平原地区农田灌溉渠道优化布局问题,该文构建了基于最小生成树的渠道优化布局模型。与传统最小生成树模型不同的是该模型涵盖了2级渠道的优化布局问题,而且该模型得到的方案要大于等于1棵最小生成树。为了能利用成熟的最小生产树理论的求解方法,该文通过创建虚拟点概念去除渠道优化布局模型和传统最小生成树模型的区别,运用凸壳理论讨论求解该模型的4种情况,编写求解该模型的LINGO程序,然后将基于最小生成树的渠道优化布局模型用于案例,得到了研究区渠道布局方案。该方案的工程量是16 095 m3,而采用渠道布局原则得到的渠道布局方案的工程量是16 938.25 m3。结果表明基于最小生成树的渠道优化布局模型能得到成本更少的渠道布局方案,即最大程度地控制土地整治费用。研究为控制土地整治项目的费用提供了一条有效途径。

       

      Abstract: Abstract: Few studies have been done on the layout of ditches, and the quantitative models for the optimization of the channel layout is lacking. Since the cost of channel layout project accounts for a large proportion of the cost of land reclamation project, it is necessary to find a design in order to reduce the cost of channel project. In this paper, a new model was developed for optimal layout of canals and ditches. The theory of minimum spanning tree was used to describe the channel layout of land reclamation project, and an optimal model based on minimum spanning tree theory was established in combination with the virtual point, the alternative water intake point and the weighted definition node. The study area was located at a coal mining subsidence area in Yongqiao District, Suzhou City, Anhui Province (33°24?-33°25?N and 117°3?-117°5?E). The channel optimization layout model based on the minimum spanning tree was constructed to optimize the layout of farmland irrigation channels in the plain areas. Different from the traditional minimum spanning tree model, this model solved the optimization problem for two-level channels, and the final solution using this model was greater than or equal to a minimum spanning tree. In order to take advantage of the mature minimum- production-tree approach, the virtual point concept was created to eliminate the difference between the channel optimization layout model and the traditional minimum spanning tree model. Four cases of solving the model were discussed by convex hull theory. The LINGO program was written for solving the model. Finally, the channel optimization model based on the minimum spanning tree was applied to a research area, and then the channel layout scheme using this model was obtained with a total length of 20 523 m containing 1 lateral canal (2 811-m length) and 22 ditches (17 712-m length). According to the traditional optimum principle, there were totally 20 572 m with 2 lateral canals (6 037-m length) and 23 ditches (14 535-m length). The lateral canal was designed as a trapezoid for the land reclamation with a mouth width of 150 cm, a base width of 50 cm and a depth of 100 cm. The ditch was designed as a rectangle with a mouth width of 80 cm and a depth of 90 cm. For the lateral canal, the engineering workload of unit length was 1 m3 and for ditch engineering workload per unit length was 0.75 m3. The unit length engineering workload of the lateral canal was 1.33 times of the ditch. Based on unit length engineering workload mentioned above, the total engineering workload of the land reclamation project was 16 095 m3 by using the channel optimization layout method based on minimum spanning tree and 16 938.25 m3 by using optimum principle method, respectively. The engineering workload of the minimum spanning tree method was 5.0% less than that of the optimum principle. According to the unit price of the lateral canal engineering project 85 yuan per meter and the unit price of ditch engineering 49.58 yuan per meter, the project cost of 116 694 yuan was saved. The result shows that the channel optimization model based on the minimum spanning tree can obtain the channel layout plan with less cost, that is, the maximum control of land reclamation cost. This study can provide an effective way to cost control of land reclamation projects.

       

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