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Energy-Saving Operation Synergy for Multiple Metro-Trains Using Map-Reduce Parallel Optimization

In subway systems, increasing attention has been paid to improve energy efficiency due to remarkable energy consumption for rail transportation operation. The optimization of single-train driving control and multi-train operation synergy are two critical and closely related aspects for energy saving, but they are rarely solved in an integrative manner. The comprehensive study on these two aspects is a complex, large-scale, multi-variable and constrained task, which involves nested, coupled and mutual-input optimization processes. This paper proposes an energy-efficient integrated model, which includes optimizing single-train operation control in an inner model and multi-train operation synergy, committing to the utilization of regenerative braking energy (RBE) in an outer model. A parallelized particle swarm optimization based on Map-Reduce (PPSO-MR) algorithm is proposed to solve the integrated model to reduce the execution time. Two concepts of temporal-spatial record and time shift are introduced to derive the movement of a train at inter-stations for the operation adjustment of multiple trains on a subway line. Experimental results show that the proposed control model solved by the holistic optimization approach can achieve lower energy consumption with fast execution time. This study provides the novel model and algorithm to obtain energy-saving schedules serving the multi-train operation coordination.