One of the important topics that has been widely used in smart cities in the last few decades is the transportation system routing problem. The vehicle and drone routing problem seeks to operate with mathematical models and optimization in such a way that the distance traveled, the total travel time, and ultimately the transportation cost function are minimized, and ultimately the energy consumption is minimized. In this problem, first a formal mathematical model of the dynamic optimal route objective function is examined and an optimization criterion for the system is presented. Mathematical programming approaches, maximizing or minimizing an objective function to improve the process, act to ensure operational efficiency. The vehicle routing problem for big data faces limitations. To increase the efficiency of vehicle routing systems, further studies should be conducted on all network constraints such as service time interval and carrying capacity constraints in routing. In this research, the problem of routing drones and vehicles for relief and with the aim of minimizing the total service time to demand nodes has been carried out, and the operational constraints of drones such as capacity and energy consumption have been considered.

The essence of the transportation management problem as well as drone routing is the VRP problem. Heuristic and meta-heuristic methods are suitable for small problems. In problems larger than 100 demands, the need for automatic machine learning algorithms is proposed. The results show the scalability and flexibility of the proposed approach with a model trained on large and out-of-distribution test data compared to the two meta-heuristic algorithms.