Multi-fleet feeder vehicle routing problem using hybrid metaheuristic

Abstract

In this paper, the Multi-fleet feeder vehicle routing problem (Multi-Fleet FVRP) has been considered. In this problem, trucks and motorcycles have left the depot and served customers. After running out of inventory, at the joint nodes with the trucks, the motorcycles have been reloaded as many as the customers need and finally, returned to the depot. After modeling this problem as a mixed-integer linear programming model, a particle swarm optimization algorithm, as well as a hybrid of particle swarm optimization-simulated annealing (PSO-SA) algorithm, is also proposed. The PSO-SA algorithm employs both PSO and SA sequentially and combines the advantages of PSO’s good exploration capability and SA’s good local search properties. Extensive comparisons have been made to evaluate the performance of the mathematical model and the proposed algorithms using two data groups. The results of small-size instances showed that the outputs of the PSO and PSO-SA algorithms are close to the outputs of the GAMS. Furthermore, these algorithms compared to the ant colony optimization (ACO) and variable neighborhood search (VNS) algorithms in terms of objective function value and runtime have satisfactory results for both data groups. In large-size instances, after tuning the parameters of the hybrid algorithm with the Taguchi method, the results of the proposed algorithm are compared with the PSO, ACO and VNS algorithms. The results and statistical analysis show that the PSO and VNS algorithms have better performance compared to the PSO-SA and ACO algorithms in terms of solution quality. Also, according to the average runtime, the performance of the algorithm PSO-SA is more efficient than that of other algorithms. In general, it can be concluded that the hybrid algorithm has better performance with respect to both time and solution quality criteria.