A model for calculating optimal vertical alignments of interchanges

In this paper we propose a model to calculate an optimal vertical alignment of an interchange with a given horizontal layout. The vertical profiles of all ramps in the interchange are solved simultaneously. The problem is formulated as a mixed integer program. A heuristic that can solve the problem very efficiently is also proposed. The model and heuristic were tested by applying the technique to a real life example, a full system interchange with 4 legs and 8 ramps. Comparison of the computational results with the real layout, which was designed by a major consulting firm, indicates that the model produces designs close to those of human experts.