@article{BaermannLiersMartinetal.2015, author = {B{\"a}rmann, Andreas and Liers, Frauke and Martin, Alexander and Merkert, Maximilian and Thurner, Christoph and Weninger, Dieter}, title = {Solving network design problems via iterative aggregation}, series = {Mathematical Programming Computation}, volume = {7}, journal = {Mathematical Programming Computation}, number = {2}, doi = {10.1007/s12532-015-0079-1}, pages = {189 -- 217}, year = {2015}, abstract = {In this work, we present an exact approach for solving network design problems that is based on an iterative graph aggregation procedure. The scheme allows existing preinstalled capacities. Starting with an initial aggregation, we solve a sequence of network design master problems over increasingly fine-grained representations of the original network. In each step, a subproblem is solved that either proves optimality of the solution or gives a directive where to refine the representation of the network in the subsequent iteration. The algorithm terminates with a globally optimal solution to the original problem. Our implementation uses a standard integer programming solver for solving the master problems as well as the subproblems. The computational results on random and realistic instances confirm the profitable use of the iterative aggregation technique. The computing time often reduces drastically when our method is compared to solving the original problem from scratch.}, language = {en} } @misc{LangLeugeringMartinetal., author = {Lang, Jens and Leugering, G{\"u}nter and Martin, Alexander and Tischendorf, Caren}, title = {Gasnetzwerke: Mathematische Modellierung, Simulation und Optimierung}, doi = {10.1515/dmvm-2015-0013}, abstract = {Im Mai 2014 wurde seitens der DFG der Transregio 154 Mathematische Modellierung, Simulation und Optimierung am Beispiel von Gasnetzwerken bewilligt. Die Forschungsarbeiten an den beteiligten Standorten, der Friedrich-Alexander-Universit{\"a}t Erlangen-N{\"u}rnberg (Sprecheruniversit{\"a}t; Sprecher: Alexander Martin), der Technischen Universit{\"a}t Darmstadt (stellvertretender Sprecher: Jens Lang), der Technischen Universit{\"a}t Berlin, der Humboldt Universit{\"a}t (stellvertretende Sprecherin: Caren Tischendorf) sowie den Partnerinstitutionen Weierstraß-Institut (Berlin), Konrad-Zuse-Zentrum (Berlin) und Universit{\"a}t Duisburg-Essen haben im Oktober 2014 begonnen.}, language = {de} }