عنوان مقاله [English]
نویسندگان [English]چکیده [English]
One of the key processes in a banking system is the money transfer process from the depot (i.e., treasury) to customers (i.e., branches) and returns it in the limited time. A number of factors (e.g., the number and location of treasury, allocation of branches to treasury, security problem, fleet and routes of transmission and geographical distribution of branches) are effective in the optimal or appropriate performance of the money transfer process. However, the key parameter to be successful in such a process is to choose the correctness path so that the money transfer process ends in the lowest time with the lowest risk. In this paper, a bi-objective model for a multi-depot vehicle routing problem is designed. The value of path risk is depended on some measures, such as type of street (a major or minor street), permitted traffic type (one-way and two-way), street width and average of street traffic can be used. Other measures, such as traffic moment and suddenly events (e.g., accidents) can be ignored. Since the vehicle routing problem (VRP) is NP-hard, a multi-objective bat algorithm (MOBA) is proposed and the associated results are compared with the well-known multi-objective evolutionary algorithm, namely non-dominated sorting genetic algorithm-II (NSGA-II). Despite the continuous nature of the proposed MOBA and the complexity of the proposed model, a simple efficient solution representation is used, in which feasible solutions are produced in each step. Because of the continuous nature of the proposed MOBA algorithm, new coding and decoding representations are designed that result in decreasing the computational time. The comparison of the proposed MOBA results in terms of the objective function value is illustrated in order to show the efficiency of the proposed MOBA.