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We introduce a variant of Multicut Decomposition Algorithms (MuDA), calledCuSMuDA (Cut Selection for Multicut Decomposition Algorithms), for solvingmultistage stochastic linear programs that incorporates a class of cutselection strategies to choose the most relevant cuts of the approximaterecourse functions. This class contains Level 1 and Limited Memory Level 1 cutselection strategies, initially introduced for respectively Stochastic DualDynamic Programming (SDDP) and Dual Dynamic Programming (DDP). We prove thealmost sure convergence of the method in a finite number of iterations andobtain as a by-product the almost sure convergence in a finite number ofiterations of SDDP combined with our class of cut selection strategies. Wecompare the performance of MuDA, SDDP, and their variants with cut selection(using Level 1 and Limited Memory Level 1) on several instances of a portfolioproblem and of an inventory problem. On these experiments, in general, SDDP isquicker (i.e., satisfies the stopping criterion quicker) than MuDA and cutselection allows us to decrease the computational bulk with Limited MemoryLevel 1 being more efficient (sometimes much more) than Level 1.

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