The Benders by batch algorithm: design and stabilization of an enhanced algorithm to solve multicut Benders reformulation of two-stage stochastic programs

Xavier Blanchot (1, 2, 3) , François Clautiaux (1, 3) , Boris Detienne (1, 3) , Aurélien Froger (1, 3) , Manuel Ruiz (2)

1 UB - Université de Bordeaux
2 RTE - Réseau de Transport d'Electricité [Paris]
3 Realopt - Reformulations based algorithms for Combinatorial Optimization

This paper introduces a new exact algorithm to solve two-stage stochastic linear programs. Based on the multicut Benders reformulation of such problems, with one subproblem for each scenario, this method relies on a partition of the subproblems into batches. By detecting as soon as possible the non-optimality of a first-stage candidate, it solves only a few subproblems at most iterations. We also propose two primal stabilization schemes for the algorithm. We report an extensive computational study on large-scale instances of stochastic optimization literature that shows the efficiency of the proposed algorithm compared to five classical alternative algorithms and significant computational time savings brought by the primal stabilization schemes.

Keywords: Benders Decomposition; Large-scale linear programming; Cut aggregation

Domains: Operations Research [math.OC]

Xavier Blanchot, François Clautiaux, Boris Detienne, Aurélien Froger, Manuel Ruiz. The Benders by batch algorithm: design and stabilization of an enhanced algorithm to solve multicut Benders reformulation of two-stage stochastic programs. 2021. ⟨hal-03286135v1⟩