基于双目标优化的高速铁路列车运行调整

High-Speed Railway Train Operation Adjustment Based on Bi-Objective Optimization

针对高速铁路列车运行中因干扰而产生的列车运行晚点情况,以车站作业、区间运行、追踪间隔等时间为约束条件,以最小化列车总晚点时间和最小化列车到发时刻调整次数为双优化目标,构建高速铁路列车运行调整的双目标优化模型,并通过定义辅助矩阵将其转化为线性规划模型;设计改进的ε-约束法,通过商用求解器GUROBI求解模型。以京沪高铁北京南至泰安段为例,设计3种干扰场景,采用该模型和算法进行列车运行调整,并与其分别采用加权法和先到先服务法求解的结果进行对比验证。结果表明:提出的模型和改进的ε约束法能够有效生成不同列车到发时刻调整次数下的调度策略,为调度员提供不同偏好下的决策方案;与加权法和先到先服务法相比,改进的ε-约束法能够得到整个帕累托前沿,尤其是非凸前沿,并且在非支配解个数、逆代距和超体积3个优化性能评价指标上均具有明显优势,能得到更优的列车运行调整方案。

In view of the situation of the train operation delay caused by interference during the operation of highspeed railway trains,taking the station operation time,running time in sections and headway are used as the constraints,with minimizing the total delay time of trains and minimizing the adjustment times of train arrival/departure time as double optimization objectives,a biobjective optimization model for highspeed railway train operation adjustment is constructed,and it is transformed into a linear programming model by defining auxiliary matrixes.An improvedεconstraint method is designed and the model is solved by the commercial solver GUROBI.Taking the BeijingnanTai'an section of BeijingShanghai highspeed railway as an example,three interference scenarios are designed and the model and algorithm in this paper are used to adjust the train operation.The results are compared and verified with the results obtained by the model using the weighting method and the firstcomefirstserved method.Results show that the proposed model and the improvedεconstraint method can effectively generate rescheduling strategies under different adjustment times of train arrive/departure time and can provide dispatchers with decisionmaking schemes under different preferences.Compared with the weighting method and the firstcomefirstserved method,the improvedεconstraint method can obtain the entire Pareto front,especially the nonconvex front.It has obvious advantages in the three optimization performance evaluation indicators of the number of nondominated solutions,inverted generational distance and hypervolume,and can obtain a better train operation adjustment scheme.