# A Piecewise Linearization Algorithm for Solving MINLP in Intersection Management

### Matthias Gerdts, Sergejs Rogovs, Giammarco Valenti

#### Abstract

In this paper, we propose a linearization algorithm for solving a Mixed Integer NonLinear Problem (MINLP) for Intersection Management (IM) of Connected Autonomous Vehicles (CAVs). The objective of such problem is to minimize the time it takes to clear a given arbitrary intersection for all vehicles in the consideration. We treat the IM problem as a bi-level optimization problem. On the lower level we solve an Optimal Control Problem (OCP) for each individual vehicle, whereas on the higher level we deal with an optimization problem of finding the optimal sequence and starting times for every car, which essentially yields a MINLP. An intuitive linearization technique is presented to solve the emerging MINLP in a reasonable time. The actual controls, if necessary, are computed a posteriori by minimizing the L2-norm of control variables. The algorithm is tested in different intersection scenarios. Numerical results show that it is suitable for real-time applications.

Download#### Paper Citation

#### in Harvard Style

Gerdts M., Rogovs S. and Valenti G. (2021). **A Piecewise Linearization Algorithm for Solving MINLP in Intersection Management**. In *Proceedings of the 7th International Conference on Vehicle Technology and Intelligent Transport Systems - Volume 1: VEHITS,* ISBN 978-989-758-513-5, pages 438-445. DOI: 10.5220/0010437104380445

#### in Bibtex Style

@conference{vehits21,

author={Matthias Gerdts and Sergejs Rogovs and Giammarco Valenti},

title={A Piecewise Linearization Algorithm for Solving MINLP in Intersection Management},

booktitle={Proceedings of the 7th International Conference on Vehicle Technology and Intelligent Transport Systems - Volume 1: VEHITS,},

year={2021},

pages={438-445},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0010437104380445},

isbn={978-989-758-513-5},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 7th International Conference on Vehicle Technology and Intelligent Transport Systems - Volume 1: VEHITS,

TI - A Piecewise Linearization Algorithm for Solving MINLP in Intersection Management

SN - 978-989-758-513-5

AU - Gerdts M.

AU - Rogovs S.

AU - Valenti G.

PY - 2021

SP - 438

EP - 445

DO - 10.5220/0010437104380445