## 5 Conclusions  
Aiming at the multi-destination path planning scenario, this article designed a multi-destination path planning algorithm. The algorithm combines the sorting method based on the reconstructed environment grid map and the improved Q-learning algorithm. Firstly, it is necessary to calculate the environmental obstacle values between the starting location and the destination. At same time, the environmental obstacle values need to be calculated between the two destinations multiple times. Then, according to the calculated environmental obstacle value between the two locations, multiple destinations are optimized and sorted. The global destination path sequence with the smallest environmental obstacle value is selected. Finally, based on CSD's MD-Q-learning, multi-destination global path plan is obtained.  
The evaluation function based on CSD increases the possibility of the MD-Q-learning algorithm to reach the optimal Pareto front. It is used to solve the robot path planning problem. Using the proposed multi-destination path planning method, the Q-learning algorithm is extended to solve the multi-destination problem. The implementation results show that the Pareto front of the proposed multi-destination path planning method is close to the optimal Pareto front. In addition, the search operation is distributed throughout the Pareto front based on the CSD evaluation function and the sorting method with passing through the fewest obstacles. Therefore, it is not only close to the best Pareto front, but also passes through fewer obstacles. The comparison results of the MD-Q-learning and NSGA_II algorithms based on the fewest obstacles show that both algorithms are close to the best Pareto front at an acceptable level.  
The simulation results show that the multi-destination path planning method designed in this article has good adaptability in different environments. The length of path in the global planning is reduced by 22% compared with the average length of the single-destination path planning algorithm. The work efficiency of the mobile robot is improved. Comparing with other multi-destination path planning algorithms, NSGA II, the solutions obtained by the algorithm of this article are close to the best Pareto front at an acceptable level. Moreover, the mobile robot safely passes fewer obstacles.  
This article did not consider the local path planning. There is no route smoothness optimization. The detail optimization of the path is insufficient. Therefore, there is still a large space to reduce the length of path. At the same time, the greedy algorithm leads to a lot of redundant searching. These redundant searches lower the calculation speed. The algorithm in this article and NSGA_II belong to the heuristic algorithm. In some special cases, the heuristic algorithm will get very bad answers or poor efficiency. In the future, this algorithm needs to be further improved and applied to real robots.  
Conceptualization, H.Z. and K.D.; methodology, H.Z. and K.D.; formal analysis, Y.Q. and N.W.; data curation, H.Z. and K.D.; writing--original draft preparation, H.Z. and K.D.; writing--review and editing, H.Z.; visualization, K.D. and N.W.; supervision, H.Z. and L.D.; funding acquisition, H.Z. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China, grant number 51505335; the Doctor Startup Projects of TUTE, grant number KYQD 1806.  
Not applicable.  
The authors declare no conflict of interest.