  The vertical alignment optimization problem for road design aims to generate
a vertical alignment of a new road with a minimum cost, while satisfying safety
and design constraints. We present a new model called multi-haul quasi network
flow (MH-QNF) for vertical alignment optimization that improves the accuracy
and reliability of previous mixed integer linear programming models. We
evaluate the performance of the new model compared to two state-of-the-art
models in the field: the complete transportation graph (CTG) and the quasi
network flow (QNF) models. The numerical results show that, within a 1%
relative error, the proposed model is robust and solves more than 93% of test
problems compared to 82% for the CTG and none for the QNF. Moreover, the MH-QNF
model solves the problems approximately 8 times faster than the CTG model.
