An Iterative Solution Approach for a Bi-level Optimization Problem for Congestion Avoidance on Road Networks
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.
KeywordsBi-level optimization Traffic control Time-optimal control Network optimization Iterative methods
- 4.Cristiani, E., Piccoli, B., Tosin, A.: How can macroscopic models reveal self-organization in traffic flow? In: 2012 IEEE 51st IEEE Conference on Decision and Control (CDC), pp. 6989–6994, 12 (2012)Google Scholar
- 6.Garavello, M., Piccoli, B.: Traffic Flow on Networks. AIMS Series on Applied Mathematics. American Institute of Mathematical Sciences, Springfield, MO (2006)Google Scholar
- 8.Palagachev, K.D., Gerdts, M.: Numerical approaches towards bi-level optimal control problems with scheduling tasks. In: Ghezzi, L., Hömberg, D., Landry, C. (eds.) Math for the Digital Factory. Mathematics in Industry, vol. 27, pp. 205–228. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63957-4 CrossRefGoogle Scholar
- 11.Wardrop, J.G.: Some theoretical aspects of road traffic research. In: Proc. Inst. Civ. Eng. Part II 1(3), 325–362 (1952)Google Scholar