4.5 Article

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

Journal

TRANSPORTATION SCIENCE
Volume 50, Issue 2, Pages 720-734

Publisher

INFORMS
DOI: 10.1287/trsc.2015.0584

Keywords

vehicle routing; team orienteering; prize collecting VRP; local search; large neighborhoods; dynamic programming

Funding

  1. Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior - Ministerio da Educacao (CAPES-MEC)
  2. Conselho Nacional de Desenvolvimento Cientifico e Tecnologico - Ministerio da Ciencia, Tecnologia e Inovacao (CNPq-MCTI)
  3. Fundacao Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro (FAPERJ)

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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.

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