Large Neighborhoods with Implicit Customer Selection for Vehicle Routing Problems with Profits

Thibaut Vidal (), Nelson Maculan (), Luiz Satoru Ochi () and Puca Huachi Vaz Penna ()
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Thibaut Vidal: Departamento de Informática – Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro 22451-900, Brazil
Nelson Maculan: Universidade Federal do Rio de Janeiro, Rio de Janeiro 21941-972, Brazil
Luiz Satoru Ochi: Instituto de Computação – Universidade Federal Fluminense, Niterói 24210-240, Brazil
Puca Huachi Vaz Penna: Instituto de Computação – Universidade Federal Fluminense, Niterói 24210-240, Brazil

Transportation Science, 2016, vol. 50, issue 2, 720-734

Abstract: We consider several vehicle routing problems (VRP) with profits, which seek to select a subset of customers, each one being associated with a profit, and to design service itineraries. When the sum of profits is maximized under distance constraints, the problem is usually called the team orienteering problem. The capacitated profitable tour problem seeks to maximize profits minus travel costs under capacity constraints. Finally, in the VRP with a private fleet and common carrier, some customers can be delegated to an external carrier subject to a cost. Three families of combined decisions must be taken: customer’s selection, assignment to vehicles, and sequencing of deliveries for each route.We propose a new neighborhood search for these problems, which explores an exponential number of solutions in pseudo-polynomial time. The search is conducted with standard VRP neighborhoods on an exhaustive solution representation, visiting all customers. Since visiting all customers is usually infeasible or suboptimal, an efficient select algorithm, based on resource constrained shortest paths, is repeatedly used on any new route to find the optimal subsequence of visits to customers. The good performance of these neighborhood structures is demonstrated by extensive computational experiments with a local search, an iterated local search, and a hybrid genetic algorithm. Intriguingly, even a local-improvement method to the first local optimum of this neighborhood achieves an average gap of 0.09% on classic team orienteering benchmark instances, rivaling with the current state-of-the-art metaheuristics. Promising research avenues on hybridizations with more standard routing neighborhoods are also open.

Keywords: vehicle routing; team orienteering; prize collecting VRP; local search; large neighborhoods; dynamic programming (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (12)

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