Solving Network Design Problems via Iterative Aggregation

Bärmann A, Liers F, Martin A, Merkert M, Thurner C, Weninger D (2015)


Publication Language: English

Publication Type: Journal article, Original article

Publication year: 2015

Journal

Edited Volumes: Mathematical Programming Computation

City/Town: Heidelberg

Book Volume: 7

Pages Range: 189-217

Journal Issue: 2

DOI: 10.1007/s12532-015-0079-1

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.

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APA:

Bärmann, A., Liers, F., Martin, A., Merkert, M., Thurner, C., & Weninger, D. (2015). Solving Network Design Problems via Iterative Aggregation. Mathematical Programming Computation, 7(2), 189-217. https://doi.org/10.1007/s12532-015-0079-1

MLA:

Bärmann, Andreas, et al. "Solving Network Design Problems via Iterative Aggregation." Mathematical Programming Computation 7.2 (2015): 189-217.

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