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dc.contributor.authorEscudero Bueno, Laureano F.
dc.contributor.authorGarín Martín, María Araceli ORCID
dc.contributor.authorPérez Sainz de Rozas, Gloria
dc.contributor.authorUnzueta Inchaurbe, Aitziber
dc.description.abstractIn this paper we introduce four scenario Cluster based Lagrangian Decomposition (CLD) procedures for obtaining strong lower bounds to the (optimal) solution value of two-stage stochastic mixed 0-1 problems. At each iteration of the Lagrangian based procedures, the traditional aim consists of obtaining the solution value of the corresponding Lagrangian dual via solving scenario submodels once the nonanticipativity constraints have been dualized. Instead of considering a splitting variable representation over the set of scenarios, we propose to decompose the model into a set of scenario clusters. We compare the computational performance of the four Lagrange multiplier updating procedures, namely the Subgradient Method, the Volume Algorithm, the Progressive Hedging Algorithm and the Dynamic Constrained Cutting Plane scheme for different numbers of scenario clusters and different dimensions of the original problem. Our computational experience shows that the CLD bound and its computational effort depend on the number of scenario clusters to consider. In any case, our results show that the CLD procedures outperform the traditional LD scheme for single scenarios both in the quality of the bounds and computational effort. All the procedures have been implemented in a C++ experimental code. A broad computational experience is reported on a test of randomly generated instances by using the MIP solvers COIN-OR and CPLEX for the auxiliary mixed 0-1 cluster submodels, this last solver within the open source engine COIN-OR. We also give computational evidence of the model tightening effect that the preprocessing techniques, cut generation and appending and parallel computing tools have in stochastic integer optimization. Finally, we have observed that the plain use of both solvers does not provide the optimal solution of the instances included in the testbed with which we have experimented but for two toy instances in affordable elapsed time. On the other hand the proposed procedures provide strong lower bounds (or the same solution value) in a considerably shorter elapsed time for the quasi-optimal solution obtained by other means for the original stochastic
dc.subjecttwo-stage stochastic integer programminges
dc.subjectnonanticipativity constraintses
dc.subjectscenario cluster modeles
dc.subjectsubgradient methodes
dc.subjectvolume algorithmes
dc.subjectprogressive hedging algorithmes
dc.subjectdynamic constrained cutting plane schemees
dc.titleScenario Cluster Lagrangian Decomposition in two stage stochastic mixed 0-1 optimizationes
dc.rights.holderAttribution-NonCommercial-NoDerivs 3.0 Unported*
dc.departamentoesEconomía aplicada III (Econometría y Estadística)es_ES
dc.departamentoeuEkonomia aplikatua III (ekonometria eta estatistika)es_ES

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Attribution-NonCommercial-NoDerivs 3.0 Unported
Except where otherwise noted, this item's license is described as Attribution-NonCommercial-NoDerivs 3.0 Unported