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In this paper the authors investigated an algorithm optimizing a train speed profile by the Bellman’s Dynamic Programming (DP). The DP-based method has substantial advantages of coping with complicated conditions easily, e.g. speed limitation, non-linear tractive effort and running resistance, effects of regenerative electric energy and so on. One of the major drawbacks of DP is that it requires a lot of computation time. If high accuracy of solutions is required, computation time for the optimization will increase. In this paper, the authors introduce the parallel computing technique for DP. The parallel computing technique will shorten computation time sharply and succeed in both raising accuracy of simulation and shortening of computation time. While distance between stations for the profile optimization is 1000m at the longest in the authors previous work, it will be prolonged significantly, keeping a comparable computation time. In this paper the computation times with and without parallel computing will be compared. DP has a further advantage in its use as a real time control algorithm to which the optimal profile can be easily reconfigured against some disturbances such as signalling.

Optimal train speed profiles by dynamic programming with parallel computing and the fine-tuning of mesh