A new hybrid matheuristic of GRASP and VNS based on constructive heuristics, set-covering and set-partitioning formulations applied to the capacitated vehicle routing problem

Abstract This paper develops a hybrid matheuristic in two stages to solve Capacitated Vehicle Routing Problem (CVRP) by applying Greedy Randomized Adaptive Search Procedure (GRASP), mathematical models and Variable Neighborhood Search (VNS). The CVRP consists of designing a set of routes for a fleet of identical vehicles to attend a set of customers at shortest distance traveled. In the proposed method, a routing is performed using constructive heuristics and the Set-covering problem (SCP). SCP employs local optima solutions found in previous iterations of VNS to create a partial tour which is filled by a constructive heuristic if needed. Then, the built solution undergoes a local search phase by VNS. This process is repeated as the main loop of the GRASP. As last step of the method, the Set-partitioning problem (SPP) provides a new improved solution with regard to solutions found in the GRASP. We tested our algorithm with seven benchmarks and compared it with some other heuristics in the literature. Computational experiments showed that the proposed algorithm is competitive in terms of the quality of the solutions reported in recent works.