Lagrangian Decomposition for large-scale two-stage stochastic mixed 0-1 problems |
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Authors: | L F Escudero M A Garín G Pérez A Unzueta |
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Institution: | 1. Dpto. Estad??stica e Investigaci??n Operativa, Universidad Rey Juan Carlos, M??stoles, Madrid, Spain 2. Dpto. de Econom??a Aplicada III, Universidad del Pa??s Vasco, Bilbao, Vizcaya, Spain 3. Dpto. de Matem??tica Aplicada, Estad??stica e Investigaci??n Operativa, Universidad del Pa??s Vasco, Leioa, Vizcaya, Spain
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Abstract: | In this paper we study solution methods for solving the dual problem corresponding to the Lagrangian Decomposition of two-stage stochastic mixed 0-1 models. We represent the two-stage stochastic mixed 0-1 problem by a splitting variable representation of the deterministic equivalent model, where 0-1 and continuous variables appear at any stage. Lagrangian Decomposition (LD) is proposed for satisfying both the integrality constraints for the 0-1 variables and the non-anticipativity constraints. We compare the performance of four iterative algorithms based on dual Lagrangian Decomposition schemes: the Subgradient Method, the Volume Algorithm, the Progressive Hedging Algorithm, and the Dynamic Constrained Cutting Plane scheme. We test the tightness of the LD bounds in a testbed of medium- and large-scale stochastic instances. |
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