Minimization methods for non-differentiable functions
Minimization methods for non-differentiable functions
Stochastic network optimization models for investment planning
Annals of Operations Research
Nondifferentiable optimization
Optimization
The aggregation principle in scenario analysis stochastic optimization
Algorithms and model formulations in mathematical programming
Scenarios and policy aggregation in optimization under uncertainty
Mathematics of Operations Research
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Network Models in Optimization and Their Applications in Practice
Network Models in Optimization and Their Applications in Practice
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In a multiperiod dynamic network flow problem, we model uncertain arc capacities using scenario aggregation. This model is so large that it may be difficult to obtain optimal integer or even continuous solutions. We develop a Lagrangian decomposition method based on the structure recently introduced in G.D. Glockner and G.L. Nemhauser, Operations Research, vol. 48, pp. 233–242, 2000. Our algorithm produces a near-optimal primal integral solution and an optimum solution to the Lagrangian dual. The dual is initialized using marginal values from a primal heuristic. Then, primal and dual solutions are improved in alternation. The algorithm greatly reduces computation time and memory use for real-world instances derived from an air traffic control model.