Stadium norm and Douglas-Rachford splitting: a new approach to road design optimization

TL;DR

This paper introduces a novel optimization approach for road design using Douglas-Rachford splitting and new proximity operators related to the stadium norm, demonstrating significant cost reductions.

Contribution

It develops a new optimization method combining the stadium norm and Douglas-Rachford splitting for complex road design problems.

Findings

The proposed algorithm outperforms existing projection methods.

Numerical results show substantial cost savings in road design.

The study introduces new proximity operators for the stadium norm.

Abstract

The basic optimization problem of road design is quite challenging due to a objective function that is the sum of nonsmooth functions and the presence of set constraints. In this paper, we model and solve this problem by employing the Douglas-Rachford splitting algorithm. This requires a careful study of new proximity operators related to minimizing area and to the stadium norm. We compare our algorithm to a state-of-the-art projection algorithm. Our numerical results illustrate the potential of this algorithm to significantly reduce cost in road design.