A Multiple Train Trajectory Optimization to Minimize Energy Consumption and Delay

In railway operations, if the journey of a preceding train is disturbed, the service interval between it and the following trains may fall below the minimum line headway distance. If this occurs, train interactions will happen, which will result in extra energy usage, knock-on delays, and penalties for the operators. This paper describes a train trajectory (driving speed curve) optimization study to consider the tradeoff between reductions in train energy usage against increases in delay penalty in a delay situation with a fixed block signaling system. The interactions between trains are considered by recalculating the behavior of the second and subsequent trains based on the performance of all trains in the network, apart from the leading train. A multitrain simulator was developed specifically for the study. Three searching methods, namely, enhanced brute force, ant colony optimization, and genetic algorithm, are implemented in order to find the optimal results quickly and efficiently. The result shows that, by using optimal train trajectories and driving styles, interactions between trains can be reduced, thereby improving performance and reducing the energy required. This also has the effect of improving safety and passenger comfort.