Synthesis of railway infrastructure

摘要

This paper addresses the problem of generating a cost-optimal railway infrastructure by stating and solving a linear optimization problem. Railway infrastructure is represented by a network consisting of nodes and arcs. The nodes represent stations; the arcs lines connecting the stations. An input instance of the network design problem for railway infrastructure consists of two parts. The stations, which have to be connected in a certain way, and a traffic demand, which relates each pair of nodes (A, B) to a number of trains of different types, has to be routed from A to B in a given time horizon. A newly designed network answers two questions: what is the topology of the network, i.e. which stations are connected to each other and how does the line look like in each connection (e.g. single track, double track, single track with one overtaking station etc.)? The observed kind of routing problem can be stated and solved as a multi-commodity flow problem. In order to get the design of the network using a routing routine, a complete network is constructed. Finding a routing in such a complete network is then equal to designing the network, since the routing chooses the arcs needed and so designs the desired network. To solve the problem efficiently it is stated as a mixed integer program (MIP), which is solvable by standard MlP-solvers.