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摘要: 研究了半独立路权下有轨电车时刻表的优化问题, 基于运行区间速度限制及区间首、末端节点构成, 对有轨电车运行区间进行了分类; 考虑有轨电车区间运行过程的复杂性, 构建了以减小列车总旅行时间和总能耗为目标的有轨电车区间车速引导节能优化模型; 为了使2个优化目标拥有相同的趋优满意程度, 提出了采用模糊数学规划的方法将双目标优化问题转化为单目标优化问题; 针对节能优化模型非线性特点, 设计了基于仿真的遗传算法对优化模型进行求解; 为了验证模型的有效性, 以南京市麒麟有轨电车1号线实际数据为基础, 选取某工作日早高峰7:00~8:00作为研究时段, 采用设计优化方法对既有时刻表进行了优化; 考虑企业管理者运营服务理念侧重性对优化结果的影响, 分别以最小旅行时间、最小能耗为目标的方案与本文模型对比。优化结果表明: 采用节能优化模型综合优化后的时刻表与既有运营时刻表相比, 其上行方向总旅行时间节省了124.9 s, 减少约7.7%, 下行方向总旅行时间节省了394.9 s, 减少约24.3%, 有效提升了有轨电车运行效率; 节能优化模型与最小旅行时间方案相比, 有轨电车上、下行总能耗分别降低了56.7%和53.5%, 与最小能耗方案相比, 上、下行有轨电车总旅行时间分别降低了14.9%和14.1%, 有效消解了旅行时间目标与能耗目标的冲突。Abstract: The optimization problem of tram timetable in semi-exclusive right of way mode was studied, and the operation section was classified based on the speed limit and the composition of the head and end nodes. The complexity of tram section operation process was considered, and an energy saving optimization model of tram section speed guidance was constructed to reduce the total travel time and the total energy consumption. In order to make the two optimization objectives of total travel time and total energy consumption have the same degree of satisfaction, a fuzzy mathematical programming method was proposed to transform the double objective optimization problem into a single objective optimization problem. According to the nonlinear characteristics of the energy saving optimization model, a genetic algorithm based on simulation was proposed to solve the model. In order to test the validity of the model, based on the actual data of Qilin Tram Line 1 in Nanjing, the designed optimization method was used to optimize the existing timetable by selecting the 7:00-8:00 early peak period of a working day. Considering the influence of managers' operational service concepts on the optimization results, two schemes of minimum travel time objective and minimum energy consumption objective were designed and compared with the model. Optimization result shows that, compared with the existing operating timetable, the timetable adjusted by the energy saving optimization model saves 124.9 s in the upward direction, reducing by about 7.7%, and saves 394.9 s in the downward direction, reducing by about 24.3%. So, the optimization model can effectively improve the operation efficiency of the tram. Compared with the minimum travel time scheme, the total energy consumptions obtained by the optimization model in the upward and downward directions reduce by 56.7% and 53.5%, respectively. Compared with the minimum energy consumption scheme, the total train travel times obtained by the optimization model in the upward and downward directions reduce by 14.9% and 14.1%, respectively. So, the energy saving optimization model can effectively eliminate the conflict between travel time objective and energy consumption objective.
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Key words:
- urban rail transit /
- tram /
- timetable optimization /
- genetic algorithm /
- energy saving /
- section speed guidance
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表 1 有轨电车运行区间参数
Table 1. Parameters of tram operation sections
区间编号 区间类型 长度/m 区间编号 区间类型 长度/m 1 S-I 562 17 S-I 470 2 I 32 18 I 45 3 I-S 50 19 I-S 60 4 S-S 577 20 S-S 765 5 S-I 490 21 S-I 640 6 I 35 22 I 25 7 I-S 40 23 I-S 160 8 S-I 400 24 S-I 100 9 I 30 25 I 33 10 I-S 330 26 I-I 562 11 S-I 165 27 I 46 12 I 25 28 I-S 67 13 I-I 450 29 S-I 675 14 I 50 30 I 30 15 I-S 55 31 I-S 68 16 S-S 715 32 S-S 1200 
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表 2 信号配时参数
Table 2. Parameters of signal timing
交叉口编号 信号周期/s 绿灯时长/s 相位差/s 1 109 32 0 2 109 43 87 3 109 35 13 4 109 44 50 5 109 50 85 6 109 34 68 7 109 43 68 8 109 20 89 9 109 40 32 10 109 30 79
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表 3 早高峰乘客人数
Table 3. Passenger numbers during morning peak
编号 车站 上行 下行 上车 下车 上车 下车 1 石杨路 53 0 0 28 2 智汇路 60 8 2 14 3 水街坊 50 7 3 9 4 光华路 69 7 7 13 5 生态公园 48 8 2 5 6 启迪大街 38 8 6 4 7 天兴路 85 23 8 47 8 南湾营路 152 32 21 74 9 天泉路 55 16 12 29 10 北湾营街 145 40 21 74 11 马高路 65 11 5 2 12 百水桥 241 153 113 90 13 马群 0 748 189 0
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表 4 优化方案运行指标比较
Table 4. Comparison of operating indicators of optimized schemes
指标 上行 下行 方案1 方案2 方案3 方案1 方案2 方案3 旅行时间/s 1 465.5 1 757.0 1 495.1 1 175.8 1 426.5 1 225.1 能耗/(kW·h) 30.7 11.8 13.3 28.2 10.9 13.1 交叉口停车次数 8 6 5 5 3 1 红灯等待时间/s 251.3 239.2 77.9 102.5 67.3 6.3
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