A quadratically constrained quadratic programming model for optimizing the vertical alignment considering side-slopes in road construction

A new convex Quadratically Constrained Quadratic Programming model (QCQP) is proposed for optimizing the vertical alignment of a road considering side-slopes by minimizing the cost of earthwork operations while satisfying the vertical alignment design and safety constraints. The new QCQP model is implemented for single-material, single-haul and without blocks. It is compared with a Mixed Integer Linear Programming model (MILP) model. The strength of the new QCQP model is that it is a convex problem that uses continuous variables whereas the MILP model has binary variables. So, QCQP's optimal solution is a global minimizer which is comparable to MILP's optimal solution. Numerical results show that our new QCQP model is an efficient and accurate model that is able to solve a wide range of problems. It outperforms the MILP model on many roads in our test set. QCQP is a more robust model than MILP since MILP could not solve all the problems in the test set before timeout. It is comparable to MILP (in terms of computational time) for smaller roads and up to 1.6 times faster than MILP for longer roads.Science, Irving K. Barber Faculty of (Okanagan)Computer Science, Mathematics, Physics and Statistics, Department of (Okanagan)Graduat