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. © 2011 Springer Science+Business Media B.V.
- Hybrid algorithms
- Probabilistic algorithms
- Variable Neighborhood Search
- Vehicle Routing Problem
Guimarans, D., Herrero, R., Riera, D., Juan, A. A., & Ramos, J. J. (2011). Combining probabilistic algorithms, Constraint Programming and Lagrangian Relaxation to solve the Vehicle Routing Problem. Annals of Mathematics and Artificial Intelligence, 62(3-4), 299-315. https://doi.org/10.1007/s10472-011-9261-y