Optimization with regularization to create sensible vertical alignments in road design

We analyze the use of ℓ1-norm and Total Variation regularization within a model of road design to obtain sensible vertical alignments. With a dataset of twenty-three roads, we present a heuristic for choosing regularization parameters, and obtain cost bounds to establish a suitable choice for its use on real data. Further, we show that regularization reduces waviness on several case studies of real roads, provided by our industrial partner. While results are reported for the Quasi-Network Flow model, the techniques are easily transferred to other road design models.