# An Iterative Solution Approach for a Bi-level Optimization Problem for Congestion Avoidance on Road Networks

• Andreas Britzelmeier
• Alberto De Marchi
• Matthias Gerdts
Chapter
Part of the Springer INdAM Series book series (SINDAMS, volume 29)

## Abstract

The paper introduces an iterative solution algorithm for a bi-level optimization problem arising in traffic control. The bi-level problem consists of a shortest path problem on the upper level, which aims at minimizing the total path cost of a set of cars in a road network. The cost coefficients in the shortest path problem represent the expected driving time on each edge, accounting for congestions, and depend on the solutions of a set of lower level optimal control problems, each one describing the behavior of a single minimum-time driven car. On the other hand, each lower level problem is built upon the path planned by the upper level. This leads to a strong coupling between upper level problem and lower level problem. This coupling is decomposed by an iterative procedure fixing either the costs or the paths in the upper level and the lower level, respectively. Numerical experiments illustrate the procedure and indicate that the iterative algorithm leads to suitable distribution of cars in the network.

## Keywords

Bi-level optimization Traffic control Time-optimal control Network optimization Iterative methods

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## Authors and Affiliations

• Andreas Britzelmeier
• 1
• Alberto De Marchi
• 1
• Matthias Gerdts
• 1
Email author
1. 1.Department of Aerospace EngineeringBundeswehr University MunichNeubibergGermany