Scenarios and policy aggregation in optimization under uncertainty
Mathematics of Operations Research
Applications of Stochastic Programming (Mps-Siam Series on Optimization) (Mps-Saimseries on Optimization)
The Million-Variable "March" for Stochastic Combinatorial Optimization
Journal of Global Optimization
Computers and Operations Research
Scenario Cluster Decomposition of the Lagrangian dual in two-stage stochastic mixed 0-1 optimization
Computers and Operations Research
Fix-and-Relax-Coordination for a multi-period location-allocation problem under uncertainty
Computers and Operations Research
Scenario grouping in a progressive hedging-based meta-heuristic for stochastic network design
Computers and Operations Research
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In this paper we present a parallelizable Branch-and-Fix Coordination algorithm for solving medium and large-scale multistage mixed 0-1 optimization problems under uncertainty. The uncertainty is represented via a nonsymmetric scenario tree. An information structuring for scenario cluster partitioning of nonsymmetric scenario trees is also presented, given the general model formulation of a multistage stochastic mixed 0-1 problem. The basic idea consists of explicitly rewriting the nonanticipativity constraints (NAC) of the 0-1 and continuous variables in the stages with common information. As a result an assignment of the constraint matrix blocks into independent scenario cluster submodels is performed by a so-called cluster splitting-compact representation. This partitioning allows to generate a new information structure to express the NAC which link the related clusters, such that the explicit NAC linking the submodels together is performed by a splitting variable representation. The new algorithm has been implemented in a C++ experimental code. Some computational experience is reported on a test of randomly generated instances as well as a large-scale real-life problem by using CPLEX as a solver of the auxiliary submodels within the open source engine COIN-OR.