Simultaneous optimization of horizontal and vertical alignments of highways

This paper presents the formulation of a three-dimensional highway alignment optimization model. The coordinates of the highway is parametrized by using a three-dimensional cubic spline polynomial interpolation. The solution is obtained by locating the optimal horizontal and vertical alignments simultaneously while subject to a wide range of possible constraints. These constraints may be bounds on the slope or curvature, as well as avoidance of inaccessible region. It is an extension from a previous research work where optimal vertical highway alignment was determined for a preselected horizontal alignment. Two numerical examples based upon the actual ground conditions in Singapore are presented to illustrate the applicabilty of the proposed model. Some computational details such as scaling and selection of initial variables which affect the rate of convergence are also briefly discussed.