# Application of Angle Related Cost Function Optimization for Dynamic Path Planning Algorithm
## 3 Problem Analysis  
The design motive behind our SODPP algorithm is presented in this section. We chose three commonly used and representative algorithms, namely the Dijkstra algorithm, A* algorithm and ant colony algorithm, to illustrate the motive. The Dijkstra algorithm was proposed by Professor [PERSON] to solve the shortest path problem [12]. It can be used to solve the shortest path from source point to other nodes in directed graph. It is also the theoretical basis of the routing algorithm and optimal path algorithm in many systems at present [13]. The main idea of the Dijkstra algorithm is to carry out a breadth-first search from the source point and expand to the outer layer from the starting point to the end point. The Dijkstra algorithm is guaranteed to find the optimal path in the given network, but for larger scale road networks, the processing efficiency is lower [14], and thus, it is not suitable for real-time and high accuracy dynamic path planning. There are two main issues for the Dijkstra algorithm, as follows:  
1. Because of the strategy of global search, it is necessary to search all the nodes in the network. The search space is shown in Figure 1--it takes a lot of computation time and the time efficiency of the algorithm is low;
2. Because of the need to store intermediate results, when the network is large, it uses a lot of storage space. The ant colony algorithm is also a heuristic algorithm that takes advantage of nature law. The ant colony algorithm is a kind of bionic algorithm which is proposed to simulate the behavior of an ant colony searching for optimal path after studying the real behavior of ant colony foraging [15]. The ant colony algorithm is often used to solve complex combinatorial optimization problems, such as the traveling salesman problem and the optimal path problem. In solving the optimal path problem, the ant colony algorithm (ACA) leads the behavior of searching for the optimal path by pheromones when simulating the foraging process of an ant colony in the biological world. The ant colony algorithm is an iterative algorithm based on empirical control. Its search space decreases with the number of iterations (increasing or decreasing), as shown in Figure 2. The search process of the ant colony algorithm does not depend on any mathematical theory, and it has a strong ability to find the global optimal solution. In the ant colony algorithm, ants tend to choose the path with more pheromones, and the selection of a path by ants will enhance the pheromone concentration of these paths so that the positive feedback of information can be realized. Although ants will choose the path with high pheromone concentration, the probability-based state transfer strategy still gives ants a certain probability of choosing a path a with low pheromone concentration so that the algorithm can try more paths to find the shortest path. However, the ant colony algorithm is still an iterative algorithm based on experience, which is prone to local convergence and slow convergence speed [16]. At the same time, it takes a long time to construct the solution which results in a long search time. It is not suitable for systems with high real-time requirements. Figure 1: Search space of the Dijkstra algorithm. The A* algorithm is a simple and practical heuristic search method which was proposed by [PERSON], [PERSON], and [PERSON] in 1968. The so-called heuristic search is a knowledge-based search strategy which refers to the evaluation of all the nodes that can be searched in a search tree by evaluating the best nodes and then searching for the target nodes from the best nodes. The heuristic search can effectively reduce the search area, avoid a large number of unnecessary search paths, and improve the efficiency. Compared with blind search methods, like the Dijkstra algorithm, the heuristic search, in principle, only needs part of the search space to get the solution of the problem, and the efficiency of the search can be improved effectively [17; 18].