Modeling side slopes in vertical alignment resource road construction using convex optimization

A new convex quadratically-constrained quadratic programming (QCQP) model is proposed for modeling side-slopes volumes in the minimization of earthwork operations to compute the vertical alignment of a resource road while satisfying design and safety constraints. The new QCQP model is convex but nonlinear; it is compared to a state-of-the-art mixed integer linear programming (MILP) model. The QCQP model can be viewed as the limit of this MILP model. Numerical results show that for roads with less than 100 stations, the QCQP model has similar computation time to the MILP model. However, the QCQP model significantly outperforms the MILP model for other roads, in some cases finding a global optimum in minutes while the MILP model fails to find any solution in hours. The technique is directly applicable for resource roads and has potential for other types of road.