a hybrid metaheuristic algorithm for the vehicle routing problem with delivery time cost

this paper addresses the vehicle routing problem with delivery time cost. this problem aims to find a set of routes of minimal total costs including the travelling cost and delivery time cost, starting and ending at the depot, in such a way that each customer is visited by one vehicle given the capacity of the vehicle to satisfy a specific demand. in this research, a hybrid metaheuristic approach based on electromagnetism and simulated annealing algorithms is proposed. the purpose of such a combination is to have the benefits of both algorithms. simulated annealing (sa) algorithm is powerful in escaping from local optimums. on the other hand, electromagnetism (em) algorithm generates wide varieties of solution populations. the computational results of some instances are reported and then these results are compared with the lower bound of problem. the results demonstrate the effectiveness of the metaheuristic algorithm in solving this model.