Optimization of horizontal alignment geometry in road design and reconstruction

- Arc length parametrization of a horizontal road alignment is detailed.
- A general methodology to design an optimal horizontal road alignment is proposed.
- The shortest horizontal layout avoiding zones and/or minimizing slopes is obtained.
- A methodology of horizontal alignments in road reconstruction projects is presented.

This paper presents a general formulation for optimization of horizontal road alignment, composed of tangential segments and circular curves suitably connected with transition curves (clothoids). It consists of a constrained optimization problem where the objective function is given by a line integral along the layout. The integrand is a function representing the cost of the road going through each point and, by considering different costs, a wide range of problems can be included in this formulation. To show it, we apply this methodology to three different situations. The two first cases are related with the design of a new road layout and used to solve a pair of academic examples. The third problem deals with the improvement of a road adapting the old path to current legislation, and it is solved taking as case study the reconstruction project for a regional road (NA-601) in the north of Spain.