Optimization of operation scheme for full-length and short-turn routings considering operation proportion
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摘要: 分析了城市轨道交通的大小交路列车开行比例关系，划分了2种典型的大小交路列车开行比例; 基于跨交路乘客对直达列车的选择偏好与换乘行为，提出了2种开行比例模式下乘客的广义出行费用计算方法; 考虑共线区段列车运行间隔的匹配关系，计算了运营车底数量; 以乘客出行费用和企业运营费用最小化为目标，构建了适用于多编组的大小交路列车开行方案优化模型，并针对开行方案编制流程和模型特点，设计了开行时段优化算法和遗传算法对模型进行求解; 以上海地铁8号线为例，研究了全日列车开行时段划分及其最优开行方案; 考虑固定编组和多编组与大小交路的组合运营模式，分析了单一交路运营与组合运营模式下的最优方案及其运营指标; 研究了乘客选择偏好和时间价值对开行方案和小交路折返站的影响。研究结果表明：与单一交路运营模式相比，大小交路运营模式下的乘客候车时间成本增幅超过11%;固定列车编组条件下，开行比例1:1模式下的小交路长度比开行比例2:1模式下的小交路长4个区间; 多编组运营的早高峰系统总成本降幅超过1.87%，比固定编组运营更具优势; 乘客对直达列车的选择偏好对多编组开行方案的影响较固定编组更大，当选择偏好概率大于0.3时，多编组开行方案的小交路折返站位置向外围延伸; 当时间价值增至原来的1.8倍及以上时，固定编组的运营模式由大小交路变为单一交路。Abstract: Train operation proportion of full-length and short-turn routings in urban rail transit systems was analyzed and divided into two typical categories. Based on the preferences for choosing through train and transfer behaviors of cross-routing passengers, a generalized passenger fare calculation method of these two categories was proposed. The number of physical trains necessary for the operation was calculated while considering the matching relationship of train intervals. With the goal of minimizing passenger travel expenses and enterprise operating expenses, an optimization operation scheme model of hybrid formation on full-length and short-turn routings was established. In addition, based on the schedule process and model characteristics of operation scheme, the optimization and genetic algorithms for operating times were designed to solve the model. Taking Shanghai Metro Line 8 as an example, the division of time periods for all-day train operation and the optimal operational plan were studied. The optimal scheme and its operational indicators under single- and combined-routing operation modes were analyzed with considering the combined full-length and short-turn routings operations with uniform or hybrid formations. The influence of passenger preferences and time values on operation schemes and reversing stations in short-turn routing was studied. Research results show that the passenger waiting time under the full-length and short-turn routings operation mode increases by more than 11% compared with the single-routing operation mode. With uniform formation, the length of short-turn routing with a 1:1 operation ratio is four sections longer than that with a 2:1 operation ratio. The total system cost of hybrid formation in the morning rush time decreases by more than 1.87%, which has more advantages than uniform formation. The influence of passenger preferences for through train is greater on hybrid formation than uniform formation. When the preference probability is greater than 0.3, the positions of reversing stations of short-turn routing under hybrid formation are extended. When the time value increases to 1.8 times or more of its original value, the operation mode of hybrid formation changes from full-length and short-turn routings to a single routing. 7 tabs, 9 figs, 30 refs.
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图 2 大小交路列车运行图
Figure 2. Train operation diagrams of full-length and short-turn routings
图 8 选择偏好对换乘等待时间成本的影响
Figure 8. Influenes of preferences on cost of transfer waiting time
图 9 乘客时间价值对小交路折返站影响
Figure 9. Influences of passenger time values on reversing stations in short-turn routing
表 1 城市轨道交通线路站间距
Table 1. Station spacings of urban rail transit line
区间编号 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 长度/km 0.90 1.15 1.00 0.95 1.40 1.00 0.95 0.95 1.15 1.40 1.35 1.20 1.25 1.20 0.85 运行时间/min 0.75 1.75 1.50 1.50 2.50 1.50 1.75 1.50 1.50 1.70 1.70 1.50 1.50 1.50 1.50 区间编号 16 17 18 19 20 21 22 23 24 25 26 27 28 29 长度/km 1.00 0.85 1.10 2.10 0.90 0.90 1.20 1.60 1.80 2.50 2.70 1.40 1.20 1.45 运行时间/min 1.25 1.50 2.25 2.50 1.70 1.50 1.50 2.50 2.50 2.70 3.25 1.70 1.50 1.75 
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表 2 列车停站时间
Table 2. Dwell times of train
车站编号 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 时间/min 0.25 0.25 0.25 0.50 0.50 0.50 0.50 0.25 0.50 0.50 0.30 0.30 0.50 0.50 0.50 车站编号 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 时间/min 0.50 0.75 0.50 0.75 0.50 0.30 0.50 0.50 0.50 0.50 0.50 0.50 0.30 0.50 0.25
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表 3 固定编组下全日列车最优开行方案
Table 3. Optimal operation scheme of all-day train for uniform formation
运营时段 ηm (s0, s1) (n1, n2) f1/(对·h-1) 开行比例 Ct/106元 早高峰 1.20 (5, 30) (6, 6) 11 1:1 3.104 4 午平峰 0.75 (5, 24) (6, 6) 6 1:1 4.836 8 晚高峰 1.20 (5, 24) (6, 6) 5 2:1 2.098 2 晚平峰 0.75 (5, 24) (6, 6) 4 2:1 2.940 7
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表 4 多编组下全日列车最优开行方案
Table 4. Optimal operation scheme of all-day train for hybrid formation
运营时段 ηm (s0, s1) (n1, n2) f1/(对·h-1) 开行比例 Ct/106元 早高峰 1.20 (5, 30) (6, 6) 11 1:1 3.104 4 午平峰 0.75 (5, 24) (3, 3) 7 2:1 4.364 6 晚高峰 1.20 (1, 24) (3, 3) 9 2:1 1.916 2 晚平峰 0.75 (5, 24) (3, 3) 7 2:1 2.614 6
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表 5 最优开行方案与运行指标
Table 5. Optimal operation scheme and operating indicators
运营模式 (s0, s1) (n1, n2) f1/(对·h－1) 开行比例 F/veh Cw/105元 Ctr/103元 Ckm/105元 Cf/104元 Ct/106元 ΔCw/% ΔCtr/% ΔCkm/% ΔCf/% ΔCt/% 1 (6, -) 22 342 1.229 1.694 4.443 1 2.052 1.563 8 2 (11, 27) (6, 3) 15 1:1 273 1.366 1.688 3.940 1 1.638 1.523 1 11.13 -0.38 -11.31 -20.18 -2.60 3 (5, 30) (6, 6) 11 1:1 300 1.378 1.452 4.205 5 1.800 1.552 2 12.13 -14.29 -5.35 -12.28 -0.74 4 (14, 26) (6, 3) 9 2:1 276 1.460 1.496 4.024 1 1.656 1.540 8 18.75 -11.54 -9.43 -19.30 -1.47 5 (11, 30) (6, 6) 8 2:1 300 1.388 1.472 4.378 3 1.800 1.570 5 12.91 -13.11 -1.46 -12.28 0.43
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表 6 乘客选择偏好下开行方案
Table 6. Operation schemes of passenger preferences
运营模式 p (s0, s1) (n1, n2) f1/(对·h-1) 发车比例 Ct/106元 2 0.0~0.2 (11, 27) (6, 3) 15 1:1 1.523 4~1.522 8 0.3~1.0 (11, 28) (6, 3) 15 1:1 1.524 5~1.522 6 3 0.0~1.0 (5, 30) (6, 6) 11 1:1 1.552 3~1.551 0 4 0.0~0.8 (14, 26) (6, 3) 9 2:1 1.541 1~1.538 6 0.9~1.0 (11, 26) (6, 3) 9 2:1 1.539 4~1.539 1 5 0.0~1.0 (11, 30) (6, 6) 8 2:1 1.570 7~1.568 8
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表 7 乘客时间价值的开行方案
Table 7. Operation schemes of passenger time values
运营模式 时间价值倍数 (s0, s1) (n1, n2) f1/(对·h-1) 发车比例 Ct/106元 2 0.4~1.4 (11, 27) (6, 3) 15 1:1 0.856 5~1.967 5 1.6~1.8 (6, 27) 2.188 6~2.407 2 2.0~2.4 (3, 27) 2.625 0~3.060 1 3 0.4~1.6 (5, 30) (6, 6) 11 1:1 0.884 9~2.219 5 1.8~2.4 (1, 30) (6, -) 22 2.441 7~3.100 1 4 0.4 (17, 26) (6, 3) 9 2:1 0.866 8 0.6~1.0 (14, 26) 1.092 7~1.540 8 1.2 (11, 26) 1.763 7 1.4~2.4 (6, 26) 1.984 3~3.084 5 5 0.4~0.8 (11, 29) (6, 6) 8 2:1 0.898 9~1.346 7 1.0~1.8 (11, 30) 1.570 5~2.461 0 2.0~2.4 (1, 30) (6, -) 22 2.661 1~3.100 1
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