基于两阶段算法的运行图与天窗协同优化

列车运行图铺画与天窗设置存在相互影响，相互制约的耦合关系，为了达到优化列车运行图结构，合理配置铁路运力资源的目的，在分析天窗与列车运行动态影响关系的基础上，以天窗设置对列车运行线铺画影响最小为目标，建立了列车运行图与天窗协同优化的混合整数规划模型. 考虑问题复杂性,设计了包含初步优化和综合优化的两阶段求解算法. 初步优化阶段采用基于专家经验的启发式算法得到列车运行图的大体框架，综合优化阶段利用禁忌搜索算法获取全局最优解. 最后以宝成线（阳平关—成都）为例进行有效性验算. 结果表明，相较于人机交互编制所得运行图，优化得出的运行图中所有客货列车在途经车站的总停留时间降低了6.19%，共减少1 355 min，其中旅客列车和货物列车在站停留时间分别降低了3.08%和7.40%，减少总时间分别为189 min和1 166 min. 

Collaborative Optimization for Timetable and Maintenance Window Based on Two-Stage Algorithm

There is mutual coupling between train timetable generation and maintenance window setting. To achieve the purpose of optimizing the train timetable structure and reasonably configuring the railway transportation capacity. According to the dynamic analysis of train timetable generation and maintenance window setting, the minimum impact of maintenance windows setting on train timetable planning is used as the objective function, and a mixed integer programming (MIP) model is built to realize the collaborative optimization of train timetable and maintenance window. To solve this complex problem, a two-stage solving algorithm including preliminary optimization and comprehensive optimization is designed. In the preliminary optimization stage, a heuristic algorithm based on experts’ experience is used to obtain the general framework of the train timetable. In the comprehensive optimization stage, the tabu search algorithm is used to obtain the global optimal solution. Finally, a case study based on Baoji?Chengdu railway line (Yangpingguan?Chengdu section) was conducted to verify the model. The results show that compared with the timetable compiled by human-computer interaction, the proposed method can effectively reduce the total residence time of all passenger and freight trains at stations by 6.19%, a total reduction of 1 355 min, of which the passenger trains and freight trains station residence time are decreased by 3.08% and 7.40%, with the total reduction time of 189 min and 1 166 min, respectively.