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Abstract

The vertical alignment optimization problem for road design focuses on finding the optimum vertical alignment of a single road with a minimum cost considering earthwork and satisfying all safety and design constraints. We proposed a new model named the multi-road quasi network flow model (MR-QNF) for vertical alignment optimization of the entire road network instead of just a single road. We then presented four different methods: one-at-a-time, no-flow, with-flow and divide and conquer methods to solve the vertical alignments of a road network. Here, the one-at-a-time method uses the old model named quasi network flow model (QNF) and is considered as the base model for comparison. The other three methods use the new MR-QNF model to solve this problem. We evaluated the performances of these methods on two real-world road network examples: one small road network (total road length is around 6 km) and one comparatively extensive road network (total length is around 66 km). The numerical results show that in the case of a small road network, it is possible to lower the total cost by 7.2\% by using the with-flow method and a speedup of 20 was achieved when compare to the one-at-a-time method. However, in the case of an extensive road network, the computation time of the one-at-a-time method is significantly lower than the other two methods without any notable differences in their costs.