## 3 Multiple Destination Global Path Planning Strategy Based on Improved Q-Learning Algorithm
### Multi-Destination Simulation Experiment  
In order to verify the feasibility and effectiveness of the multi-destination path planning method in this article, a multi-destination path planning simulation experiment was designed. For the convenience of comparative research, it is assumed that the grid side length of the mobile robot working environment is 1 m. On this basis, in MATLAB modeling and simulation experiment of multi-destination global path planning is carried out. Aiming at verifying the adaptability of the multi-destination path planning algorithm to the environment, the experimental environment is set up in layers. The environment map model is 40 \(\times\) 40. At the same time, to verify the adaptability, the algorithm can improve the transportation efficiency of mobile robots. This experimental environment has 8 sets of simulation experiments. The number of destinations in each group of experiments gradually increased. The length of the moving path obtained by the experiment is shown in Figure 11. The comparison of the planned routes for the eight destinations is shown in Figures 12 and 13. In the two figures, point \(S\) represents the starting point of the mobile robot. Point set \(\mathbf{T}_{i}\) (\(i=1,2,3,4,5,6,7,8\)) represents the destination of transportation. The black grid area represents 1 obstacle. The solid line represents the planning route of the mobile robot. Figure 11: Comparison of single and multi-destination path lengths. Figure 12: Single-destination path planning. Figure 13: Multi-destination path planning. path of multi-destination planning can reach all destinations at one time. It reduces the number and time of calculation paths. From the path length comparison chart in Figure 11, as the number of destinations increases, the path length planned by the single-destination path planning algorithm increases rapidly. However, the path length planned by the multi-destination path planning algorithm designed in this article grows smoothly. Compared with the ground path planning algorithm, the average length of this article is reduced by 22%. It improves the work efficiency of the mobile robot. Comparison of MD-Q-Learning (Multi-Destination-Q-Learning) Based on the Fewest Obstacles and NSGA_II  
NSGA_II is one of the most popular multi-destination genetic algorithms at present. It reduces the complexity of non-inferior ranking genetic algorithms. It has the advantages of fast running speed and good solution set convergence. It has become the benchmark for the performance of other multi-destination optimization algorithms based on heuristics. MD-Q-learning algorithm based on passing through the fewest obstacles is based on heuristics. Therefore, this article compares the multi-destination method of this article with the previous NSGA_II algorithm in two test cases. This selection of test cases is relatively difficult, comparing with other previous simulation experiments. The obstacle percentages for these test cases are 18% and 34%. In order to compare these two algorithms, theoretical analysis and experimental analysis is undertaken in this article. In the theoretical analysis of these algorithms, this article estimated their time complexity. Definition: O (M\({}^{\text{M}}\)N\({}^{\text{b}}\)) is a function describing the space complexity of the algorithm. The smaller the values of a and b, the more concise the algorithm is. Meanwhile M is the number of iterations, N is the overall size of population. The time complexity of algorithm in this article is O (M\({}^{2}\)N\({}^{2}\)), when the time complexity of the NSGA_II algorithm is O (MN\({}^{2}\)). The additional complexity of multi-destination path planning based on MD-Q-learning with minimal obstacles is caused by the map reconstruction and the nature of the Q-learning algorithm. However, since the overall and iteration values are small, the running time of the algorithm will not increase.