An Energy-saving Optimization Method of High-speed Trains Based on Time Deviation Penalty During Train Operation
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摘要: 合理的安排列车在区间的运行方式能够有效的降低列车运行能耗。采用基于区间限速的列车工况确定策略确定列车区间运行工况, 以列车运行能耗为优化目标, 以列车运行距离、时间和列车限速等为约束条件, 在目标函数中加入列车运行时间偏差惩罚项, 建立基于列车运行时间偏差惩罚的高速铁路列车运行节能优化数学模型, 采用基于高斯变异和混沌扰动的改进人工蜂群算法对优化模型进行求解。以CRH3-350型动车组数据为例对模型与算法进行验证, 求解结果显示: 考虑列车运行时间偏差惩罚比不考虑列车运行时间偏差惩罚能耗可节省2.5%, 改进人工蜂群算法与基本人工蜂群算法、粒子群算法相比, 在目标值方面分别提高了4.2%和4.1%。采用基于区间限速的列车运行工况确定策略结合能耗优化模型能够满足不同限速和不同区间运行时分要求下的列车运行情况。表明所建模型和设计的算法有良好的求解效率和优化质量。Abstract: Reasonable arranging the operation mode of the train in the section can reduce the energy consumption of train operation. A determination strategy of train operating conditions based on the speed limit of the interval is adopted to determine the operating condition of the train. The energy consumption of the train is used as the optimization objective, and the distance, time, and speed limit of the train are used as the constraints. Time deviation penalty during train operation is added to the objective function to develop a mathematical model of energy-saving optimization for high-speed railway train operation, and the improved artificial bee colony algorithm based on Gaussian mutation and chaotic disturbance is used to solve the optimization model. The model and algorithm are verified with CRH3-350 multi-unit data as an example, the solution results show that the energy consumption can be saved by 2.5% when time deviation penalty during train operation is considered. Compared with the basic artificial bee colony algorithm and particle swarm algorithm, the improved artificial bee colony algorithm has improved the target value by 4.2% and 4.1%, respectively. Adopting the determinative strategy based on the interval speed limit combined with the energy-consumption optimization model can meet the required train operation conditions under different speed limits and different intervals. It shows that the established model and the designed algorithm have good problem-solving efficiency and optimized quality.
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图 4 不考虑时间偏差惩罚的算法迭代图
Figure 4. Algorithm iteration without considering time deviation penaltydeviation penalty
图 5 不考虑时间偏差惩罚的速度-距离曲线图
Figure 5. Speed-distance graph without considering time deviation penalty
图 6 考虑时间偏差惩罚的改进人工蜂群算法迭代图
Figure 6. Iterative of the improved artificial bee colony algorithm considering time deviation penalty
图 7 考虑时间偏差惩罚的速度-距离曲线图
Figure 7. Speed-distance graph considering time deviation penalty
图 8 运行时间充裕条件下改进人工蜂群算法迭代图
Figure 8. Iteration of the improved artificial bee colony algorithm under sufficient running time
图 9 运行时间充裕条件下改进人工蜂群算法速度-距离曲线图
Figure 9. Speed-distance curve of the improved artificial bee colony algorithm under sufficient running time
表 1 列车工况转换约束
Table 1. Constraints on the conversion of train-operating conditions
工况 牵引 巡航 惰行 制动 牵引 - √ √ × 巡航 √ - √ × 惰行 √ √ - √ 制动 × × √ - 注：-为相互之间不存在转换关系；√为相互之间可以转换；×为相互之间无法直接转换 
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表 2 不考虑时间偏差惩罚时粒子群算法求解结果
Table 2. Solution of particle-swarm optimization without considering time deviation penalty
计划工况 牵引 巡航 惰行 巡航 牵引 巡航 惰行 巡航 牵引 巡航 惰行 制动 实际工况 牵引 巡航 惰行 巡航 牵引 巡航 惰行 巡航 牵引 巡航 惰行 制动 步长数量 900 1 678 575 118 257 1 451 415 299 258 1700 409 494
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表 3 不考虑时间偏差惩罚时基本人工蜂群算法求解结果
Table 3. Solution of the basic artificial bee colony algorithm without considering time deviation penalty
计划工况 牵引 巡航 惰行 巡航 牵引 巡航 惰行 巡航 牵引 巡航 惰行 制动 实际工况 牵引 巡航 惰行 巡航 牵引 巡航 惰行 巡航 牵引 巡航 惰行 制动 步长数量 911 1 597 699 200 255 1 402 523 247 260 1 548 461 451
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表 4 不考虑时间偏差惩罚时改进人工蜂群算法求解结果
Table 4. Solution of the improved artificial bee colony algorithm without considering time deviation penalty
计划工况 牵引 巡航 惰行 巡航 牵引 巡航 惰行 巡航 牵引 巡航 惰行 制动 实际工况 牵引 巡航 惰行 巡航 牵引 巡航 惰行 巡航 牵引 巡航 惰行 制动 步长数量 915 1 718 567 81 139 1 751 415 55 286 1 629 571 427
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表 5 不考虑时间偏差惩罚时算法运行结果对比
Table 5. Comparison of the computational result of the algorithm without considering time deviation penalty
算法 运行时间/s 运行能耗/(kW·h) 相比改进人工蜂群算法能耗节省/% 改进人工蜂群算法 1 278.4 660.76 基本人工蜂群算法 1 279.7 689.41 4.2 粒子群算法 1 264.8 689.31 4.1
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表 6 算法运行结果对比
Table 6. Comparison of the computational result of the algorithm
运行时间/s 目标值 运行能耗/(kW·h) 考虑时间偏差惩罚时间节省/% 考虑时间偏差惩罚能耗节省/% 考虑时间偏差惩罚 1 286.7 648.77 644.50 未考虑时间偏差惩罚 1 278.4 660.76 660.76 -0.65 2.5
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表 7 考虑时间偏差惩罚的改进人工蜂群算法求解结果
Table 7. Solution of the improved artificial bee colony algorithm considering time deviation penalty
计划工况 牵引 巡航 惰行 巡航 牵引 巡航 惰行 巡航 牵引 巡航 惰行 制动 实际工况 牵引 巡航 惰行 巡航 牵引 巡航 惰行 巡航 牵引 巡航 惰行 制动 步长数量 900 1 750 527 126 118 1 706 501 213 267 1 535 492 419
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表 8 不同运行时间要求下算法运行结果对比
Table 8. Comparison of computational results of the algorithm under different running time
运行时间/s 运行能耗/(kW·h) 运行时间充裕条件下时间节省/% 运行时间充裕条件下能耗节省/% 最短运行时间条件下 1 278.4 660.76 -1.5 9.1 运行时间充裕条件下 1 297.6 600.35
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表 9 运行时间充裕条件下改进人工蜂群算法的求解结果
Table 9. Solution of the improved artificial bee colony algorithm under sufficient running time
计划工况 牵引 巡航 惰行 巡航 牵引 巡航 惰行 巡航 牵引 巡航 惰行 制动 实际工况 牵引 巡航 惰行 巡航 牵引 巡航 惰行 制动 步长数量 900 1 638 579 2 684 200 1 591 535 427
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表 10 优化结果对比
Table 10. Comparison of optimized results
% 评价指标 文献[20]优化结果 本文优化结果 运行时间 2 1.5 运行能耗 -10.7 -9.1
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