Boosting an Exact Logic-Based Benders Decomposition Approach by Variable Neighborhood Search

Logic-based Benders decomposition (BD) extends classic BD by allowing more complex subproblems with integral variables. Metaheuristics like variable neighborhood search are becoming useful here for faster solving the subproblems' inference duals in order to separate approximate Benders cuts. After performing such a purely heuristic BD approach, we continue by exactly verifying and possibly correcting each heuristic cut to finally obtain a proven optimal solution. On a bi-level vehicle routing problem, this new hybrid approach exhibits shorter overall runtimes and yields excellent intermediate solutions much earlier than the classical exact method.