Optimal Selection of Mountain Railway Location Design Based on Twice-Improved TOPSIS Method
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摘要:
为克服传统TOPSIS(逼近理想解排序法)在山区铁路线路方案比选中不能排除指标间相关性干扰、易使决策工作复杂化的缺点,同时为能充分考虑决策工作的不确定性特征,首先,以马氏距离代替传统TOPSIS中的欧氏距离,实现第一次改进;接着,以相关系数矩阵代替马氏距离中的协方差矩阵,实现第二次改进;然后,运用语言类模糊数、区间数、云模型等实现定性指标的定量化,并以二次改进的TOPSIS为基础构建山区铁路线路方案综合比选模型;最后,研究了综合比选模型在某山区铁路巴塘至昌都段局部线路走向方案比选中的应用. 研究结果表明:二次改进的TOPSIS能有效排除决策工作中指标间的相关性干扰,简化决策过程;云模型的运用能有效克服决策方法在处理定性语言不确定性方面的不足;线路方案综合比选模型的应用研究结果与该山区铁路工程预可研中的推荐结果一致,即比选结果均为经白玉、江达的线路方案,故该模型可作为今后线路方案比选工作中一种新的应对途经.
Abstract:This work aims to overcome the shortcomings of the traditional TOPSIS (technique for order of preference by similarity to an ideal solution) method, which cannot exclude the interference from correlation among indexes that can easily complicate decision-making operations during optimal selection of mountain railway location designs, and thus enable full consideration of any uncertain characteristics during decision-making. First, the Mahalanobis distance was used to replace the Euclidean distance in traditional TOPSIS, thus achieving the first improvement in TOPSIS. Then, the correlation coefficient matrix was used to replace the covariance matrix in the Mahalanobis distance, which represents the second improvement in the TOPSIS method. Then, linguistic fuzzy numbers, interval numbers, and a cloud model were used to achieve quantification of the qualitative indexes, and a comprehensive optimization model for mountain railway location design was constructed based on the twice-improved TOPSIS method. Finally, the comprehensive optimization model was applied to the partial route direction scheme of the Batang to Changdu section of a specific mountain railway. The results show that the twice-improved TOPSIS method can effectively exclude the interference from the correlation among indexes and thus simplifies the decision-making process. In addition, application of the cloud model can overcome the deficiency in the decision-making method with regard to its ability to deal with the uncertainty of qualitative language. The application results from the comprehensive optimization model coincide with the recommended results of the pre-feasibility study of the mountain railway, i.e., the optimization results from both approaches lead to the route scheme passing through Baiyu and Jiangda, thus indicating that the proposed model can be used as a new approach for route direction optimization in future mountain railway location designs.
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Key words:
- mountain railway /
- scheme optimization /
- twice-improved method /
- uncertainty characteristic /
- cloud model /
- TOPSIS
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表 1 山区铁路线路方案比选指标体系
Table 1. Index system of optimal selection of mountain railway location design
总目
标层宏观目标层 微观目标层 山区铁路线路方案比选 技术可行性 线路长度
输送能力
通过能力
最小曲线半径
展线系数
桥隧总长
桥隧占比
工程工期
最大坡度
拔起高度
土石方工程量
征地量
拆迁建筑物数量经济合理性 土建工程投资费
与列车有关的运营费
固定设备维修费
机车车辆购置费
预备费及其他费用
年换算工程运营费
净现值
投资回收期
内部收益率施工条件及环境影响 工程对自然生态环境的影响
工程对历史文化名胜的影响
噪音对沿线居民的影响
江河湖泊等对工程的影响
不良地质条件对工程的影响社会经济政治意义 促进周边地区经济发展的能力
吸引客货流的能力
改善路网布局的意义
满足地方需求的能力
对城市规划布局的影响表 2 语言类模糊数与区间数的转化
Table 2. Conversion between linguistic fuzzy number and interval number
语言类模糊数 区间数 很差或很小 [0,1.0] 差或小 [1.0,3.0] 较差或较小 [3.0,4.5] 一般 [4.5,5.5] 较好或较大 [5.5,7.0] 好或大 [7.0,9.0] 很好或很大 [9.0,10.0] 表 3 语言类模糊数、区间数与云模型数的转化
Table 3. Conversion among linguistic fuzzy number, interval number and cloud model number
语言类模糊数 区间数 云模型数 很差或很小 [0,1.0] (1/2,1/6,0.02) 差或小 [1.0,3.0] (2,1/3,0.02) 较差或较小 [3.0,4.5] (7.5/2,1.5/6,0.02) 一般 [4.5,5.5] (5,1/6,0.02) 较好或较大 [5.5,7.0] (12.5/2,1.5/6,0.02) 好或大 [7.0,9.0] (8,1/3,0.02) 很好或很大 [9.0,10.0] (9.5,1/6,0.02) 表 4 定性评语与云模型描述的转化
Table 4. Conversion between qualitative comment and cloud model description
定性评语 云模型描述 很低 (10,5/3,0.02) 低 (30,5/3,0.02) 较低 (45,5/3,0.02) 中等 (55,5/3,0.02) 较高 (65,5/3,0.02) 高 (80,5/3,0.02) 很高 (90,5/3,0.02) 表 5 线路走向方案及其属性指标取值
Table 5. Route direction scheme and its attribute index value
指标 A1 A2 A3 A4 A5 C1/km 274.562 267.808 243.229 234.100 204.711 C2/km 242.171 222.648 209.870 203.772 188.375 C3/亿元 330.298 324.048 297.469 287.943 254.251 C4/亿元 416.236 407.872 373.600 361.216 318.326 C5 小 一般 较小 一般 小 C6 一般 较大 大 大 很大 C7 很好 好 较差 一般 较差 C8 很大 较大 一般 较大 一般 C9 很好 很好 较好 较好 较好 表 6 由精确数表示的定性指标值
Table 6. Qualitative index value represented by exact number
方案 C5 C6 C7 C8 C9 A1 81.685 8 55.010 7 88.762 2 88.755 8 88.763 4 A2 55.010 7 44.495 9 78.354 8 64.495 7 88.760 5 A3 65.538 2 28.356 3 45.537 2 55.010 7 64.495 2 A4 55.010 7 28.355 4 55.010 8 64.494 7 64.494 6 A5 81.683 1 8.762 3 45.536 2 55.010 7 64.496 3 -
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