In the calculations presented in the article, an artificial immune system (AIS) was used to plan the routes of the fleet of delivery vehicles supplying food products to customers waiting for the delivery within a specified, short time, in such a manner so as to avoid delays and minimize the number of delivery vehicles. This type of task is classified as an open vehicle routing problem with time windows (OVRPWT). It comes down to the task of a traveling salesman, which belongs to NP-hard problems. The use of the AIS to solve this problem proved effective. The paper compares the results of AIS with two other varieties of artificial intelligence: genetic algorithms (GA) and simulated annealing (SA). The presented methods are controlled by sets of parameters, which were adjusted using the Taguchi method. Finally, the results were compared, which allowed for the evaluation of all these methods. The results obtained using AIS proved to be the best.

The fixed fleet heterogeneous open vehicle routing problem (HFFOVRP) is one of the most practical versions of the vehicle routing problem (VRP) defined because the use of rental vehicles reduces the cost of purchasing and routing for shipping companies nowadays. Also, applying a heterogeneous fleet is recommended due to the physical limitations of the streets and efforts to reduce the running costs of these companies. In this paper, a mixed-integer linear programming is proposed for HFFOVRP. Because this problem, like VRP, is related to NP-hard issues, it is not possible to use exact methods to solve real-world problems. Therefore, in this paper, a hybrid algorithm based on the ant colony algorithm called MACO is presented. This algorithm uses only global updating pheromones for a more efficient search of feasible space and considers a minimum value for pheromones on the edges. Also, pheromones of some best solutions obtained so far are updated, based on the quality of the solutions at each iteration, and three local search algorithms are used for the intensification mechanism. This method was tested on several standard instances, and the results were compared with other algorithms. The computational results show that the proposed algorithm performs better than these methods in cost and CPU time. Besides, not only has the algorithm been able to improve the quality of the best-known solutions in nine cases but also the high-quality solutions are obtained for other instances.