Combining constraint programming, lagrangean relaxation and probabilistic algorithms to solve the vehicle routing problem
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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.
CitationGuimarans, D. [et al.]. Combining constraint programming, lagrangean relaxation and probabilistic algorithms to solve the vehicle routing problem. "Annals of mathematics and artificial intelligence", 2011, vol. 62, núm. 3-4, p. 299-315.