Optimization Method for Railroad Curve Alinement

Realignment of existing railroad curves is cast in terms of a quadratic optimization problem and a method of minimizing the objective function is developed. Geometry relating track curvature and movement are presented, and quadratic objective functions which measure curve smoothness are derived. The objective function is minimized using a modified form of Cauchy's method, and integer constraints are applied. Results of the procedure are track movements required to move the existing alignment to a new smooth alignment. Computer results are presented for a typical curve. The method works well in finding smooth alignments and is not very sensitive on choice of objective function. The method presented shows much improvement over the current, hand trial and error method employed by railroads which is called Stringlining.