Models and strategies for efficiently determining an optimal vertical alignment of roads

A mixed-integer linear programming model to optimize the vertical alignment considering blocks and side-slopes in road construction

“…Koch and Lucet (2010) improved the accuracy of the spline model by changing two constraints and reported that only a linear or a quadratic spline could be used while maintaining the linear structure of the model. Hare, Hossain, Lucet, and Rahman (2014) recently examined a variety of techniques to improve the speed of solving the vertical alignment problem. (For more information on these techniques we refer to Rahman (2012) and references therein.)…”

Multi-haul quasi network flow model for vertical alignment optimization

“…The side slope is defined as the steady decrease/increase of height when moving orthogonally from the road profile to the ground profile in a cut/fill section. Side slopes are represented as trapezoid shaped cross-sections and are approximated using stacked rectangles to preserve the linearity of the model, see Hare et al (2014). The model can handle nonsymmetric section-dependent side slopes to account for local soil type and sloped terrains as well as cuts and fills at the same section.…”

“…For example, for the short distances using a bulldozer may be more economical, while for a long distance movement a truck may be preferred. Therefore, to obtain a more realistic model, we extend the previous QNF model Hare et al (2014) by using multiple hauling paths, which is more realistic and yields a more precise earthwork solution. Figure 1 shows the typical flows for a section in the proposed MH-QNF model.…”

“…To evaluate the performance of the MH-QNF model, we compare the efficiency, robustness, and accuracy of the proposed model with the CTG and QNF models presented in Hare et al (2014). At this point, the QNF model of Hare et al (2014) is quite easy to describe -the QNF model is a special case of the MH-QNF model, where the number of haul types is one (n h = 1). The CTG model, which appears in Hare et al (2014Hare et al ( , 2015, is slightly harder to outline.…”

“…In Hare et al (2015) road side slopes are added to the previous MILP model proposed in Hare et al (2011) which yields a more accurate earthwork cost calculation. Hare et al (2014) also improved the performance of the MILP model (called complete transportation graph or CTG) and studied a novel quasi network flow (QNF) model for vertical alignment optimization considering the earthwork allocations. The QNF model presented significant improvements in computational time, but at a cost of decreased accuracy in the final solution.…”