B07
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- 2015 (3) (remove)
Keywords
- Aggregation (1)
- Branch-and-cut (1)
- Combinatorial optimization (1)
- Mixed-integer programming (1)
- Network design (1)
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-Universität Erlangen-Nürnberg
(Sprecheruniversität; Sprecher: Alexander Martin), der
Technischen Universität Darmstadt (stellvertretender
Sprecher: Jens Lang), der Technischen Universität Berlin,
der Humboldt Universität (stellvertretende Sprecherin:
Caren Tischendorf) sowie den Partnerinstitutionen
Weierstraß-Institut (Berlin), Konrad-Zuse-Zentrum (Berlin)
und Universität Duisburg-Essen haben im Oktober
2014 begonnen.
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.