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A parallel computation approach for solving multistage stochastic network problems

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  • Fuente, J. L. de la
  • García, C.
  • Prieto, Francisco J.
  • Escudero, L. F.

Abstract

This paper presents a parallel computation approach for the efficient solution of very large multistage linear and nonIinear network problems with random parameters. These problems resul t 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 15 minutes on a cluster of 4 small (16 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.

Suggested Citation

  • Fuente, J. L. de la & García, C. & Prieto, Francisco J. & Escudero, L. F., 1996. "A parallel computation approach for solving multistage stochastic network problems," DES - Working Papers. Statistics and Econometrics. WS 10455, Universidad Carlos III de Madrid. Departamento de Estadística.
  • Handle: RePEc:cte:wsrepe:10455
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    References listed on IDEAS

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    1. M. Alvarez & C. Cuevas & L. Escudero & J. Escudero & C. García & F. Prieto, 1994. "Network planning under uncertainty with an application to hydropower generation," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 2(1), pages 25-58, June.
    2. John R. Birge & Liqun Qi, 1988. "Computing Block-Angular Karmarkar Projections with Applications to Stochastic Programming," Management Science, INFORMS, vol. 34(12), pages 1472-1479, December.
    3. Joseph Czyzyk & Robert Fourer & Sanjay Mehrotra, 1995. "A Study of the Augmented System and Column-Splitting Approaches for Solving Two-Stage Stochastic Linear Programs by Interior-Point Methods," INFORMS Journal on Computing, INFORMS, vol. 7(4), pages 474-490, November.
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    Keywords

    Large-scale optimization;

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