# Mobile Robot Path Planning Algorithm Based on NSGA-II
## 1 Introduction  
With the development of society, mobile robot technology is increasingly prevalent in our lives, and path planning for mobile robots is a key technology enabling them to function properly. Mobile robot path planning involves finding the optimal collision-free path according to specified constraints, which may include factors such as distance, safety, and smoothness [1]. Depending on whether the environment is known, path planning for mobile robots can be divided into global path planning [2] and local path planning [3]. Currently, the commonly used traditional path planning algorithms include the A* algorithm [4], RRT algorithm [5], [PERSON]'s algorithm [6], and artificial potential field method [7]. Intelligent path planning algorithms mainly include the ant colony algorithm [8], particle swarm algorithm [9], and genetic algorithm [10]. Intelligent algorithms are designed to mimic biological principles and are widely applied. However, they often suffer from issues such as a poor convergence precision and susceptibility to falling into local optima. Therefore, scholars both domestically and internationally have conducted extensive research on the application of intelligent algorithms. [PERSON] [11] proposed a grey wolf algorithm based on the grey wolf optimizer and grey wolf optimizer with a hybrid genetic algorithm and simulated annealing algorithm. The algorithm utilizes a nonlinear convergence factor that can be adjusted to balance the early and late stages of the algorithm. Additionally, the optimization algorithm employs an adaptive genetic crossover strategy to generate new individuals with a certain probability, thereby enhancing the diversity of the grey wolf population. In the later stages of iteration, the wolf is selected using a simulated annealing operation, to avoid the algorithm falling into local optimum. [PERSON] [12] proposed an adaptive particle swarm path planning method based on regional search to address premature convergence and local optima issues. This methodpreprocesses the original map using a regional search approach and adaptively adjusts the inertia weight factor and acceleration factor, allowing particles to quickly escape from adverse regions. Additionally, a dynamic obstacle avoidance strategy is employed to ensure safe navigation for the robot. [PERSON] [13] introduced an improved genetic algorithm by incorporating insertion and smoothing operators into the traditional genetic algorithm and by further integrating it with the niche method to prevent premature convergence. [PERSON] [14] utilized NSGA-II to optimize the path length and clearance in grid environments, constructing both single and multi-objective optimization models for efficient path planning. [PERSON] [15] proposed an enhanced lion algorithm to improve the quality of initial solutions and algorithm diversity. They employed a dual-population lion structure to enhance search capabilities and utilized fourth-order Bezier curves for path smoothing. [PERSON] [16] combined third-order Bezier curves with an improved artificial fish swarm algorithm. They initially performed morphological operations such as obstacle expansion and utilized a range of artificial fish movements based on a 16-direction, 24-field Dijkstra algorithm during the path planning process. This reduced the number of turning points, while enhancing the planning accuracy. Furthermore, they reduced the computational frequency of the fusion algorithms by incorporating a sharing mechanism and employed feedback visual fields to avoid oscillations resulting from overly large visual fields in the later stages of the algorithm. Finally, they used third-order Bezier curves to ensure directional and curvature continuity. [PERSON] [17] used path length, path smoothness, and path safety as objective functions, and augmented the original NSGA-II algorithm with operators including an invalid solution operator and shortness operator.