Application of Computer Optimization Methods in the Reconstruction of Railway Lines

The main task that railway transport faces in the near future is to increase the speed of trains and reduce travel time on existing railway lines using computer technology and mathematical modeling methods. The problem of determining the optimal speeds of trains of each category under optimum outer rail cant, compliance with the condition of uniform load on rail tracks, in which the running time of trains along a curve of length will be minimal has been formulated. The problem is considered when train speeds are limited by the locomotive traction force and are determined on the basis of traction calculations or natural measurements. As a problem-solving technique, indefinite Lagrange multipliers method and its applicability in algebra system MathCAD have been proposed.