A multi-road quasi network flow model for the vertical alignment optimization of a road network

Minimizing earthwork costs is crucial in the optimization of vertical alignment. In this article, the previous quasi network flow model for the vertical alignment optimization of a single road is extended to a multi-road network. A 'one-at-a-time' method is first examined to solve the optimization problem and it is noted that this method is effectively what is currently used in practice. Two academic test problems are used to demonstrate that this method is not optimal. This leads to the development of three novel methods to solve the optimization problem: no-flow, with-flow and divide-and-conquer. It is noted that the with-flow method guarantees global optimality. All methods are compared on two real-world case studies. On small road networks, the with-flow method decreases costs by 7.4%, and achieves a 20 times speedup over the one-at-a-time method. On long road networks, the divide-and-conquer method is faster than all other methods without any notable cost difference. However, the divide-and-conquer method is an heuristic and cannot guarantee that it returns a global minimum.