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

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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.

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Authors and Affiliations

  1. Dpt. de Telecomunicació i Enginyeria de Sistemes, Universitat Autònoma de Barcelona (UAB), Cerdanyola del Vallès, 08193, Barcelona, Spain

    Daniel Guimarans, Rosa Herrero & Juan José Ramos

  2. Universitat Oberta de Catalunya (UOC), Barcelona, Spain

    Daniel Riera & Angel A. Juan

Authors
  1. Daniel Guimarans
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  2. Rosa Herrero
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  3. Daniel Riera
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  4. Angel A. Juan
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  5. Juan José Ramos
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Correspondence to Daniel Guimarans.

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Guimarans, D., Herrero, R., Riera, D. et al. Combining probabilistic algorithms, Constraint Programming and Lagrangian Relaxation to solve the Vehicle Routing Problem. Ann Math Artif Intell 62, 299–315 (2011). https://doi.org/10.1007/s10472-011-9261-y

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