Combining probabilistic algorithms, Constraint Programming and Lagrangian Relaxation to solve the Vehicle Routing Problem

  • Daniel GuimaransEmail author
  • Rosa Herrero
  • Daniel Riera
  • Angel A. Juan
  • Juan José Ramos


This paper presents an original hybrid approach to solve the Capacitated Vehicle Routing Problem (CVRP). The approach combines a Probabilistic Algorithm with Constraint Programming (CP) and Lagrangian Relaxation (LR). After introducing the CVRP and reviewing the existing literature on the topic, the paper proposes an approach based on a probabilistic Variable Neighbourhood Search (VNS) algorithm. Given a CVRP instance, this algorithm uses a randomized version of the classical Clarke and Wright Savings constructive heuristic to generate a starting solution. This starting solution is then improved through a local search process which combines: (a) LR to optimise each individual route, and (b) CP to quickly verify the feasibility of new proposed solutions. The efficiency of our approach is analysed after testing some well-known CVRP benchmarks. Benefits of our hybrid approach over already existing approaches are also discussed. In particular, the potential flexibility of our methodology is highlighted.


Hybrid algorithms Variable Neighborhood Search Vehicle Routing Problem Probabilistic algorithms 

Mathematics Subject Classification (2010)



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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Daniel Guimarans
    • 1
    Email author
  • Rosa Herrero
    • 1
  • Daniel Riera
    • 2
  • Angel A. Juan
    • 2
  • Juan José Ramos
    • 1
  1. 1.Dpt. de Telecomunicació i Enginyeria de SistemesUniversitat Autònoma de Barcelona (UAB)BarcelonaSpain
  2. 2.Universitat Oberta de Catalunya (UOC)BarcelonaSpain

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