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

Daniel Guimarans, Rosa Herrero, Daniel Riera, Angel A. Juan, Juan José Ramos

Research output: Contribution to journalReview ArticleResearchpeer-review

13 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)299-315
Number of pages17
JournalAnnals of Mathematics and Artificial Intelligence
Issue number3-4
Publication statusPublished - 1 Jul 2011
Externally publishedYes


  • Hybrid algorithms
  • Probabilistic algorithms
  • Variable Neighborhood Search
  • Vehicle Routing Problem

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