Fast feasibility check of the multi-material vertical alignment problem in road design

Abstract

When building a road, it is critical to select a vertical alignment which ensures design and safety constraints. Finding such a vertical alignment is not necessarily a feasible problem, and the models describing it generally involve a large number of variables and constraints. This paper is dedicated to rapidly proving the feasibility or the infeasibility of a Mixed Integer Linear Program (MILP) modeling the vertical alignment problem. To do so, we take advantage of the particular structure of the MILP, and we prove that only a few of the MILP’s constraints determine the feasibility of the problem. In addition, we propose a method to build a feasible solution to the MILP that does not involve integer variables. This enables time saving to proving the feasibility of the vertical alignment problem and to find a feasible vertical alignment, as emphasized by numerical results. It is on average 75 times faster to prove the feasibility and 10 times faster to build a feasible solution.