# Mobile Robot Path Planning Algorithm Based on NSGA-II
## 1 Introduction
They systematically studied the parameters of the algorithm and compared it with an effective multi-objective evolutionary algorithm. The comparative results indicated that the improved NSGA-II generated non-dominated solutions with excellent characteristics in the solution space. [PERSON] [18] proposed a new method for global time-varying path planning (GTVP). This method obtains center points based on the real-time shape and position information of obstacles, and extracts feature points representing obstacle information. Then, it scales up the obstacle surface to generate center points and Bezier curve feature points. Finally, it outputs curves corresponding to the real-time motion trajectory of the robotic arm. The Non-dominated Sorting Genetic Algorithms II (NSGA-II) [19] improves upon the limitations of traditional genetic algorithms, which are primarily designed for single-objective problems. Derived from genetic algorithms, NSGA-II introduces the concept of Pareto optimality and incorporates an elitist selection strategy, making it one of the most popular multi-objective genetic algorithms. It offers advantages such as a fast execution speed and good convergence of solutions, enabling it to compute better solution strategies for complex problems. As a result, this paper designed a path planning algorithm based on this method. Bezier curves possess excellent geometric properties and find widespread application in computer graphics. They succinctly and accurately describe free-form curves and surfaces, serving as effective curve-fitting tools. Therefore, this paper proposed to utilize Bezier curves in designing a smooth path algorithm. Addressing the challenges of mobile robot path planning, namely the tendency to fall into local optima and the issue of non-smooth paths. This study improved the NSGA-II algorithm and used this method to solve the mobile robot path planning problem. The contributions of this paper are as follows:  
* This paper presents a mobile robot path planning algorithm based on NSGA-II. The initialization of the population is improved by limiting the generation positions of path nodes using a search window, thereby enhancing the quality of the initial path population. Practical selection operators are proposed, and optimization is performed on two objective functions: path length and path smoothness. This optimization enhances the algorithm's ability to escape local optima. * This study systematically investigated the conditions that smooth paths need to satisfy. It employed Bezier curves to smooth the planned paths, and the experimental results indicated that this approach could enhance the smoothness of the paths. * Experimental comparisons were conducted between the proposed algorithm and different algorithms. The results of the comparisons demonstrated that the paths obtained by the proposed algorithm were shorter and smoother. The rest of this work is outlined below. Section 2 introduces the improved mobile robot path planning algorithm based on the NSGA-II algorithm. Section 3 introduces the path smoothing algorithm based on a Bessel curve. Section 4 details the simulations, and Section 5 summarizes this article.