A parallel computation approach for solvingmultistage stochastic network problems

This paper presents a parallel computation approach for the efficient solution of verylarge multistage linear and nonlinear network problems with random parameters. Theseproblems result from particular instances of models for the robust optimization of networkproblems with uncertainty in the values of the right‐hand side and the objective functioncoefficients. The methodology considered here models the uncertainty using scenarios tocharacterize the random parameters. A scenario tree is generated and, through the use offull‐recourse techniques, an implementable solution is obtained for each group of scenariosat each stage along the planning horizon.As a consequence of the size of the resulting problems, and the special structure of theirconstraints, these models are particularly well‐suited for the application of decompositiontechniques, and the solution of the corresponding subproblems in a parallel computationenvironment. An augmented Lagrangian decomposition algorithm has been implementedon a distributed computation environment, and a static load balancing approach has beenchosen for the parallelization scheme, given the subproblem structure of the model. Largeproblems ‐ 9000 scenarios and 14 stages with a deterministic equivalent nonlinear modelhaving 166000 constraints and 230000 variables ‐ are solved in 45 minutes on a cluster offour small (11 Mflops) workstations. An extensive set of computational experiments isreported; the numerical results and running times obtained for our test set, composed oflarge‐scale real‐life problems, confirm the efficiency of this procedure.