Optimizing highway grades to minimize cost and maintain traffic speed

In practice, the task of designing the vertical alignment of a highway is done manually by an experienced engineer. As a result, the work is both time and resource consuming and relies heavily on human expertise. This work presents a mathematical model that solves for a set of optimal highway vertical grades for a given horizontal alignment. In addition to construction costs, facts considered by this model include earthwork balance and traffic speed in both directions. Code requirements and design practice are also considered. A three-layered heuristic is developed to solve the model. In the first layer, a neighborhood search heuristic is used to determine the locations where grade can change. The second layer sets penalty terms for sections where speed is undesirable, and the third layer solves a mixed integer program that has very few or no 0-1 integer variables. Computational testing on a 2-km road segment shows that the model yields good solutions.