Integrated optimization model and algorithm for timetable and maintenance window considering cross-line trains
There is a coupling relationship between train timetable and maintenance window,as well as between single-line trains and cross-line trains. In order to fully consider the influence of cross-line trains in the preparation of train timetable and the arrangement of maintenance window,the deviation between the actual arrival time of cross-line trains and their ideal arrival time was used to measure the deviation between cross-line train time and ideal time. With the aims of minimizing total train travel time,minimizing the deviation from ideal time for cross-line trains,and maximizing the duration of maintenance window,a multi-objective integer programming model was established to integrate the optimization of high-speed rail train timetable and comprehensive maintenance window considering cross-line trains. According to the characteristics of the problem,a NSGA-Ⅱ algorithm based on two-dimensional sorting encoding was constructed to solve it. A crossover strategy of "multi-column sequential crossover+non-crossed part re-generation+random overtaking" was adopted for situations where random selection of a single row was not conducive to generating overtaking rule and stop scheme. A conflict resolution method for operating lines was also designed. Combined with an example of a simulated high-speed rail line,a Pareto optimal solution was obtained. The results show that compared to the initial train timetable,the optimized timetable can reduce total travel time by 194 minutes (6.0％). The deviation from ideal time for cross-line trains is 3447 minutes,and the duration of maintenance windows increases by 1655 minutes (19.3％). The results of the example demonstrate that the model and designed algorithm are effective for optimizing train timetable and maintenance window. The proposed integrated model and method for train timetable and maintenance window considering cross-line trains can shorten train travel time,increase the duration of maintenance windows to reserve rail capacity,and keep cross-line train time within satisfactory ranges. The results can provide valuable decision support for rail operation planners in preparing train timetable and setting maintenance window.
万方数据
维普
