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

  • Authors:

  • Daniel Guimarans;Rosa Herrero;Daniel Riera;Angel A. Juan;Juan José Ramos

  • Affiliations:

  • Dpt. de Telecomunicació i Enginyeria de Sistemes, Universitat Autònoma de Barcelona (UAB), Barcelona, Spain 08193;Dpt. de Telecomunicació i Enginyeria de Sistemes, Universitat Autònoma de Barcelona (UAB), Barcelona, Spain 08193;Universitat Oberta de Catalunya (UOC), Barcelona, Spain;Universitat Oberta de Catalunya (UOC), Barcelona, Spain;Dpt. de Telecomunicació i Enginyeria de Sistemes, Universitat Autònoma de Barcelona (UAB), Barcelona, Spain 08193

  • Venue:
  • Annals of Mathematics and Artificial Intelligence
  • Year:
  • 2011

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Abstract

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.