NetSim: Simulation and Optimization of Networks
Project Topic
Simulation and optimization of flows in complex networks.
Project Description
The project considers transportation and dynamic flows in networks ranging from traffic flow networks or networks of gas pipelines to supply chain networks. The goal of the project is the development of mathematical concepts and simulation tools for the description of dynamical flows in networks in the framework of a theory of hierarchical modelling, optimization and control of hybrid mixed integer, discrete continuous and nonlinear dynamical systems. Main topics are the development of a model hierarchy and the selection of models out of this hierarchy. The discrete nature in terms of decision making and the continuous nature of the control of the physics behind the model are investigated. The problems concern the optimization of the networks itself as well as the dynamics carried by the networks and are characterized by discrete-continuous structures on the level of modelling, optimization and control. Using synergies and similarities between the different application areas and the very similar mathematical formulation of the problems generic procedures to treat flows in large networks are developed. Research concentrates on the interplay between detailed network models based on partial differential equations and models based on concepts from discrete optimization like linear programmes or mixed-integer programmes. The goal is to transfer as much of the detailed knowledge of the dynamical behaviour from the continuous models to the simplified (and fast) discrete models. A major focus of this research is to improve description of the dynamics on such networks by generic model reduction procedures deriving simplified network dynamics in a concise way from dynamical processes described in a detailed way by fundamental equations and physical laws.
Project Members
Project Chair
Participating Research Groups
Scientific Personnel
- Dr. M. Herty (Department of Mathematics)
- Simone Göttlich: Supply chain networks (Department of Mathematics)
- Claus Kirchner, Anita K. Singh (PhD students): Optimization of road traffic networks (Department of Mathematics)
- N.N. (PhD student) (Department of Mathematics)
- Master students (Department of Mathematics)
External Cooperation
- Fraunhofer Institute for Industrial Mathematics (ITWM), Sect. Transport Processes (R. Wegener, J. Mohring): Gas networks
- Fraunhofer Institute for Industrial Mathematics (ITWM), Sect. Optimization (K. Küfer, S. Nickel): Supply Chain Models
- Department of Mathematics, Discrete Mathematics Group (H. Hamacher, S. Krumke): Network models of discrete optimization
- M. Rascle (Nice), R. Illner (Victoria), L. Pareschi (Ferrara) regarding traffic networks
- C. Ringhofer (Tempe), P. Degond (Toulouse) regarding supply chain models based on partial differential equations
- M. Heinkenschloss (Houston), A. Martin (Darmstadt), S. Ulbrich (Darmstadt), G. Leugering (Erlangen) regarding general questions of optimization and gas networks
Project Events and Achievements
- Project start date: November 1st, 2005
- Project end date: December 31st, 2007
Project Publications
A. Fügenschuh, Simone Göttlich, Michael Herty. In:
Proceedings of Supply Chain Management and Logistics. Physica-Verlag, To appear, 2007
A. Fügenschuh, Simone Göttlich, Michael Herty. In:
Proceedings of the 8th International Conference on Information Systems. Universitätsverlag Karlsruhe, To appear, 2007
A. Fügenschuh, Simone Göttlich, Michael Herty, Axel Klar, A. Martin. Submitted, 2007
Simone Göttlich, Michael Herty. In:
Proceedings in Applied Mathematics and Mechanics (PAMM). To appear, 2007
Michael Herty, Axel Klar, Anita K. Singh. In:
Journal of Comp. and Appl. Math. (JCAM). 2007
Michael Herty. In:
Networks and Heterogenous Media (NHM). Volume 2, Number 1, 2007
Michael Herty, C. Kirchner, Axel Klar. In:
Mathematical Methods in the Applied Sciences (M2AS). To appear, 2007
P. Degond, Simone Göttlich, Michael Herty, Axel Klar. In:
SIAM Multiscale Modeling and Simulation. To appear, 2007
M. K. Banda, Michael Herty, Axel Klar. In:
Networks and Heterogenous Media. Volume 1, 2006
M. K. Banda, Michael Herty, Axel Klar. In:
Networks and Heterogenous Media. Volume 2, 2006
Michael Herty, S. Moutari, M. Rascle. In:
Networks and Heterogenous Media. Volume 2, 2006
Michael Herty, M. Rascle. In:
SIAM J. Math. Anal.. 2006
Simone Göttlich, Michael Herty, Axel Klar. In:
Communication in Mathematical Sciences. 2006
Michael Herty, M. Gugat, Axel Klar, G. Leugering. In:
MMAN. 2006
Simone Göttlich, Michael Herty, Axel Klar. In:
Communication in Mathematical Sciences. Volume 3, 2006
Michael Herty, Axel Klar, B. Piccoli. Submitted, 2006
Michael Herty, Mohammed Seaid, Anita K. Singh. In:
APNUM. 2006
C. Kirchner, Michael Herty, Simone Göttlich, Axel Klar. In:
Networks and Heterogenous Media (NHM). Volume 1, Number 4, P. 675--688, 2006
Michael Herty, C. Kirchner, S. Moutari. In:
Communications in Mathematical Sciences (CMS). Volume 4, Number 3, P. 591--608, 2006
A. Fügenschuh, Michael Herty, Axel Klar, A. Martin. In:
SIAM Journal of Optimization. Volume 16, Number 4, P. 1155--1176, 2006
Michael Herty, S. Moutari, M. Rascle. In:
Networks and Heterogeneous Media (NHM). Volume 1, Number 2, 2006
M. Heinkenschloss, Michael Herty. In: A. J. Kurdila and P. M. Pardalos and M. Zabarankin ed.,
Proceedings of Robust Optimization: Directed Design. Nonconvex Optimization and Its Applications, Volume 81, Springer Verlag, P. 71--90, 2006
Michael Herty. In:
Proceedings in Applied Mathematics and Mechanics. Volume 5, Number 1, P. 665, 2005
