# Mobile Robot Path Planning Algorithm Based on NSGA-II
## 5 Conclusions  
To address the issues of local optima and non-smooth paths in mobile robot path planning, this paper proposed a path planning method based on NSGA-II. In the path planning algorithm designed in this paper, the concept of a search window was introduced to optimize the population initialization process. This ensures that during population initialization, the algorithm avoids unnecessary nodes and excessive paths, thereby reducing the computational overheads and improving the path planning efficiency. Additionally, this prevents randomly generated paths from being concentrated near local optima, thus guiding the algorithm away from local optimal solutions. Furthermore, a selection operator was designed using a probability-based approach, to optimize the selection process. This enables the algorithm to select a diverse range of individuals during the selection process, thereby increasing the population diversity and positively impacting the subsequent crossover and mutation operations. The path planning algorithm designed in this paper demonstrated robustness and convergence. By simultaneously selecting individuals with both high and low selection probabilities during the selection process, the algorithm maintains good diversity within the population, while ensuring that excellent individuals smoothly transition to the next generation, thus possessing the ability to escape local optima effectively.  
Moreover, a path smoothing algorithm was developed in this paper, which utilizes multi-segment Bezier curves to fit the optimal path. This approach ensures that the fitted path is free from abrupt corners, thereby guaranteeing path smoothness. The extensive experimental simulations conducted using the proposed algorithm demonstrated its effectiveness in addressing the problem of easily falling into local optima in path planning. The  
Figure 10: Path of smoothing algorithm. (**a**) Smoothed path of simple map; (**b**) smoothed path of complex map.  
planned paths were smooth and continuous, indicating the practical applicability of the proposed method in real-world scenarios.  
The research in this paper focused on studying the path planning problem for mobile robots; however, there are still some shortcomings. Therefore, there is room for improvement in this work, and the future directions for this research are outlined as follows: (1) Consideration of Multi-Robot Coordination or Swarm Robotics: Future research will explore the path planning problem for multiple robots operating collaboratively or in formation. This involves developing algorithms that enable coordination among multiple robots, to achieve collective objectives efficiently. (2) Extension to Dynamic Environments: While this paper primarily addressed path planning in static environments, real-world scenarios often involve dynamic elements such as moving obstacles, humans, or other robots. Therefore, future work will focus on studying path planning for mobile robots in dynamic environments, where the environment is subject to changes over time.  
Conceptualization, S.L. and Q.T.; methodology, S.L.; software, S.L.; validation, S.L., Q.T. and C.T.; formal analysis, S.L.; investigation, S.L.; resources, S.L.; data curation, S.L.; writing--original draft preparation, S.L.; writing--review and editing, S.L.; visualization, S.L.; supervision, S.L.; project administration, S.L.; funding acquisition, Q.T. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Beijing University of Civil Engineering and Architecture Science Research Foundation under Grant No.00331614021, the BUCEA Post Graduate Innovation Project, and the Practical Training Plan of Beijing College High Level Talents Cross Developing Project.  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding authors.  
The authors declare that they have no conflicts of interest.