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Single cut and multicut SDDP with cut selection for multistage stochastic linear programs: convergence proof and numerical experiments

Vincent Guigues (vincent.guigues***at***gmail.com)
Michelle Bandarra (michelle.bandarra***at***mirow.com.br)

Abstract: We introduce a variant of Multicut Decomposition Algorithms (MuDA), called CuSMuDA (Cut Selection for Multicut Decomposition Algorithms), for solving multistage stochastic linear programs that incorporates a class of cut selection strategies to choose the most relevant cuts of the approximate recourse functions. This class contains Level 1 and Limited Memory Level 1 cut selection strategies, initially introduced for respectively Stochastic Dual Dynamic Programming (SDDP) and Dual Dynamic Programming (DDP). We prove the almost sure convergence of the method in a finite number of iterations and obtain as a by-product the almost sure convergence in a finite number of iterations of SDDP combined with our class of cut selection strategies. We compare the performance of MuDA, SDDP, and their variants with cut selection (using Level 1 and Limited Memory Level 1) on several instances of a portfolio problem and of an inventory problem. On these experiments, in general, SDDP is quicker (i.e., satisfies the stopping criterion quicker) than MuDA and cut selection allows us to decrease the computational bulk with Limited Memory Level 1 being more efficient (sometimes much more) than Level 1.

Keywords: Stochastic Programming; Stochastic Dual Dynamic Programming; Multicut Decomposition Algorithm; Portfolio selection; Inventory management

Category 1: Stochastic Programming


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Entry Submitted: 02/13/2019
Entry Accepted: 02/13/2019
Entry Last Modified: 07/22/2019

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