An algorithm for train-set scheduling based on probabilistic local search

This paper focuses on development of an algorithm to quickly work out approximate optimal schedules for railway operations. The Train-Set Scheduling (TSS) work is divided into 2 subproblems: the Train-Set Regular Inspection problem and the Train-Set Connecting (TSC) problem. The TSC is transformed into a traveling salesperson problem on a network called a TSS network, where the nodes correspond to trains and the arcs correspond to connections of trains, and a weight expressing the desirability of connection is put on each arc. In the algorithm formulated herein, a regular inspection is made and a Hamilton tour is found. If the Hamilton tour satisfies the constraints concerning daily inspection, it could represent a feasible train-set schedule. Therefore, when finding a new Hamilton tour based on the local search method, the algorithm considers not only the connection of nodes, but also the inspection regulations. The authors present an approximation algorithm, and through experiments using actual data, demonstrate that practical train-set schedules can be obtained quickly.