An exact algorithm and a metaheuristic for the generalized vehicle routing problem with flexible fleet size

The generalized vehicle routing problem (GVRP) involves finding a minimum-length set of vehicle routes passing through a set of clusters, where eachcluster contains a number of vertices, such that the tour includes exactly onevertex from each cluster and satisfies capacity constraints. We consider aversion of the GVRP where the number of vehicles is a decision variable. Thispaper introduces a new mathematical formulation based on a two-commodityflow model. We solve the problem using a branch-and-cut algorithm anda metaheuristic that is a hybrid of the greedy randomized adaptive searchprocedure (GRASP) and the evolutionary local search (ELS) proposed in [18].We perform computational experiments on instances from the literature todemonstrate the performance of our algorithms.