University of Kashan Soft Computing Journal 2322-3707 12 2 2024 02 20 Optimization of vehicle routing based on the combination of ant colony and particle swarm algorithms with the heuristic function of the cosine of angles Optimization of vehicle routing based on the combination of ant colony and particle swarm algorithms with the heuristic function of the cosine of angles 146 164 113851 10.22052/scj.2023.248702.1118 FA Hamidreza Shafiei Department of Computer Engineering, Faculty of Engineering, Arak University, Arak, Iran. Vahid Rafe Department of Computer Engineering, Faculty of Engineering, Arak University, Arak, Iran. Maryam Amiri Department of Computer Engineering, Faculty of Engineering, Arak University, Arak, Iran. Journal Article 2022 12 17 The congestion of roads is a very important factor in urban traffic. A lot of research has tried to solve these problems using meta-heuristic algorithms. In these algorithms, firstly, routing is done randomly over large areas. This will increase the search time. In addition, these algorithms only consider the physical distance between the vehicles. Since environmental factors such as traffic are very effective in routing, these factors should be considered in routing. In this paper, to solve the problems, a dynamic path programming method based on the combination of the ant colony algorithm and particle swarm optimization, along with a cosine function of angle, has been proposed. This method takes into account various factors of roads, such as the length of the urban road and the incoming and outgoing traffic at intersections. In the method, the points that are aligned with the navigation path towards the final destination are given more chances. The results of applying the proposed model on the valid data of the TSPLIB library, which is based on the physical distance between cars, show that the search time of the proposed method has decreased by 40.74% on average compared to the results of ten other methods used for evaluation. The highest and lowest rates of decrease are 98.01% and 6.02%, respectively. The test of dynamic route planning under road traffic on some intersections of Beijing city also shows that the proposed method only causes congestion of about 1.57%. The congestion of roads is a very important factor in urban traffic. A lot of research has tried to solve these problems using meta-heuristic algorithms. In these algorithms, firstly, routing is done randomly over large areas. This will increase the search time. In addition, these algorithms only consider the physical distance between the vehicles. Since environmental factors such as traffic are very effective in routing, these factors should be considered in routing. In this paper, to solve the problems, a dynamic path programming method based on the combination of the ant colony algorithm and particle swarm optimization, along with a cosine function of angle, has been proposed. This method takes into account various factors of roads, such as the length of the urban road and the incoming and outgoing traffic at intersections. In the method, the points that are aligned with the navigation path towards the final destination are given more chances. The results of applying the proposed model on the valid data of the TSPLIB library, which is based on the physical distance between cars, show that the search time of the proposed method has decreased by 40.74% on average compared to the results of ten other methods used for evaluation. The highest and lowest rates of decrease are 98.01% and 6.02%, respectively. The test of dynamic route planning under road traffic on some intersections of Beijing city also shows that the proposed method only causes congestion of about 1.57%. https://scj.kashanu.ac.ir/article_113851_2520e61b7dbdb09a0538ccdd36d2a1e3.pdf