The reduction of operation energy consumption without decreasing service quality has become a great challenge in subways daily operation. A novel DP based approach is proposed for optimizing the train driving strategy. The optimal driving problem is first considered as a multi-objective problem with five optimal targets (i.e., energy saving, punctual arriving, less switching, safe driving and accurate stopping). The optimization problem is remodelled as a multistage decision problem by discretizing the continuous train movement in space. The process of dynamic programming is carried out in the velocity-space status space. Due to the discretizing rules of searching space, the optimal goals of safe driving and accurate stopping can be satisfied during the searching process. The rest of multiple goals are spilt into cost functions and constrains for each stage. Due to the multiple cost functions, a set of pareto optimal solutions can be achieved at each vertex during the process of dynamic programming. To further improve the efficiency of algorithm, two evaluation criterions are introduced to maintain the capacity of the pareto set at each vertex. A case study of Yizhuang urban rail line in Beijing is conducted to verify the effectiveness and the efficiency of DP based algorithms.
Convergence of a distributed method for minimizing sum of convex functions with fixed point constraints
