On BFC-MSMIP strategies for scenario cluster partitioning, and twin node family branching selection and bounding for multistage stochastic mixed integer programming

In the branch-and-fix coordination (BFC-MSMIP) algorithm for solving large-scale multistage stochastic mixed integer programming problems, we find it crucial to decide the stages where the nonanticipativity constraints are explicitly considered in the model. This information is materialized when the full model is broken down into a scenario cluster partition with smaller subproblems. In this paper we present a scheme for obtaining strong bounds and branching strategies for the Twin Node Families to increase the efficiency of the procedure BFC-MSMIP, based on the information provided by the nonanticipativity constraints that are explicitly considered in the problem. Some computational experience is reported to support the efficiency of the new scheme.