The original publication is available at www.springerlink.comThis paper presents a parallel computation approach for the efficient solution of very
large multistage linear and nonlinear network problems with random parameters. These
problems result from particular instances of models for the robust optimization of network
problems with uncertainty in the values of the right-hand side and the objective function
coefficients. The methodology considered here models the uncertainty using scenarios to
characterize the random parameters. A scenario tree is generated and, through the use of
full-recourse techniques, an implementable solution is obtained for each group of scenarios
at each stage along the planning horizon.
As a consequence of the size of the resulting problems, and the special structure of their
constraints, these models are particularly well-suited for the application of decomposition
techniques, and the solution of the corresponding subproblems in a parallel computation
environment. An augmented Lagrangian decomposition algorithm has been implemented
on a distributed computation environment, and a static load balancing approach has been
chosen for the parallelization scheme, given the subproblem structure of the model. Large
problems – 9000 scenarios and 14 stages with a deterministic equivalent nonlinear model
having 166000 constraints and 230000 variables – are solved in 45 minutes on a cluster of
four small (11 Mflops) workstations. An extensive set of computational experiments is
reported; the numerical results and running times obtained for our test set, composed of
large-scale real-life problems, confirm the efficiency of this procedure.Publicad
