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We consider several Vehicle Routing Problems (VRP) with profits, which seekto select a subset of customers, each one being associated with a profit, andto design service itineraries. When the sum of profits is maximized underdistance constraints, the problem is usually called team orienteering problem.The capacitated profitable tour problem seeks to maximize profits minus travelcosts under capacity constraints. Finally, in the VRP with private fleet andcommon carrier, some customers can be delegated to an external carrier subjectto a cost. Three families of combined decisions must be taken: customersselection, assignment to vehicles, and sequencing of deliveries for each route.  We propose a new neighborhood search for these problems which explores anexponential number of solutions in pseudo polynomial time. The search isconducted with standard VRP neighborhoods on an "exhaustive" solutionrepresentation, visiting all customers. Since visiting all customers is usuallyinfeasible or sub-optimal, an efficient "Select" algorithm, based on resourceconstrained shortest paths, is repeatedly used on any new route to find theoptimal subsequence of visits to customers. The good performance of theseneighborhood structures is demonstrated by extensive computational experimentswith a local search, an iterated local search and a hybrid genetic algorithm.Intriguingly, even a local-improvement method to the first local optimum ofthis neighborhood achieves an average gap of 0.09% on classic team orienteeringbenchmark instances, rivaling with the current state-of-the-art metaheuristics.Promising research avenues on hybridizations with more standard routingneighborhoods are also open.

Large neighborhoods with implicit customer selection for vehicle routing problems with profits