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Benders decomposition is one of the most applied methods to solve two-stagestochastic problems (TSSP) with a large number of scenarios. The main ideabehind the Benders decomposition is to solve a large problem by replacing thevalues of the second-stage subproblems with individual variables, andprogressively forcing those variables to reach the optimal value of thesubproblems, dynamically inserting additional valid constraints, known asBenders cuts. Most traditional implementations add a cut for each scenario(multi-cut) or a single-cut that includes all scenarios. In this paper wepresent a novel Benders adaptive-cuts method, where the Benders cuts areaggregated according to a partition of the scenarios, which is dynamicallyrefined using the LP-dual information of the subproblems. This scenarioaggregation/disaggregation is based on the Generalized Adaptive PartitioningMethod (GAPM), which has been successfully applied to TSSPs. We formalize thishybridization of Benders decomposition and the GAPM, by providing sufficientconditions under which an optimal solution of the deterministic equivalent canbe obtained in a finite number of iterations. Our new method can be interpretedas a compromise between the Benders single-cuts and multi-cuts methods, drawingon the advantages of both sides, by rendering the initial iterations faster (asfor the single-cuts Benders) and ensuring the overall faster convergence (asfor the multi-cuts Benders). Computational experiments on three TSSPs validatethese statements, showing that the new method outperforms the otherimplementations of Benders method, as well as other standard methods forsolving TSSPs, in particular when the number of scenarios is very large.

Benders Adaptive-Cuts Method for Two-Stage Stochastic Programs