Variations and Special Cases of LBBD

This chapter presents several variations and special cases of logic-based Benders decomposition (LBBD). The most important variation is branch and check, which solves the master problem only once. Other variations include enumerative methods, multilevel decomposition, and dynamic variable partitioning. Special cases include stochastic and robust LBBD and combinatorial Benders cuts for mixed integer programming. The chapter shows how a subproblem relaxation can be included in the master problem, often an essential part of successful implementations. It concludes with a discussion of automating LBBD in an off-the-shelf solver, and the pros and cons of doing so.