Solving Network Design Problems via Decomposition, Aggregation and Approximation
Andreas Bärmann develops novel approaches for the solution of network design problems as they arise in various contexts of applied optimization. At the example of an optimal expansion of the German railway network until 2030, the author derives a tailor-made decomposition technique for multi-period network design problems. Next, he develops a general framework for the solution of network design problems via aggregation of the underlying graph structure. This approach is shown to save much computation time as compared to standard techniques. Finally, the author devises a modelling framework for the approximation of the robust counterpart under ellipsoidal uncertainty, an often-studied case in the literature. Each of these three approaches opens up a fascinating branch of research which promises a better theoretical understanding of the problem and an increasing range of solvable application settings at the same time.
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aggregation scheme algorithm approach Bärmann Benders decomposition BMNEP bottlenecks branch-and-bound budget capacity constraints cient components conservation constraints consider construction cutting planes DB Netz derive developed di erent disaggregation dual ellipsoidal uncertainty sets erent fastest solution formulation Furthermore German railway network given graph Gurobi's HAGGB HE-RP-SL heuristic IAGG IAGGB implementation infrastructure inner approximation instances iteration linear linear program LP relaxation master problem method MNEP Model FMNEP multi-commodity Multiple of fastest multiple-knapsack decomposition network design problems network expansion problem nodes number of trains objective function observation horizon obtain optimal solution optimal value optimization problem outer approximation parameter period planning horizon polyhedral approximation rail freight railway network expansion real-world robust counterpart robust optimization routing costs RTCs scale-free networks second-order cone shortest path signi cant single-period solution time log-scale Solving Network Design subnetworks subproblem TH-S-SA Theorem track transportation variables