Combining Constraint Programming, Lagrangian Relaxation and Probabilistic Algorithms to solve the Vehicle Routing Problem

This paper presents a hybrid approach that aims at solving the Capacitated Vehicle Routing Problem (CVRP) by means of combining Constraint Programming (CP) with Lagrangian Relaxation (LR) and Probabilistic Algorithms. After introducing the CVRP and reviewing the main literature on this area, the paper proposes the use of a multistart hybrid Variable Neighbourhood Search (VNS) algorithm. This algorithm uses a randomised version of the classical Clarke and Wright savings heuristic to generate a starting solution to a given CVRP. 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. Some results on well-known CVRP benchmarks are analysed and discussed.