# Non-Cutting Moving Toolpath Optimization with Elitist Non-Dominated Sorting Genetic Algorithm-II
## 1 Introduction
In contrast to single-purpose improvements, studies concerning multi-objective optimization that simultaneously consider both the minimum toolpath length and the collision avoidance are limited and need to be explored for efficient and high-speed CNC systems. [PERSON] and [PERSON] [37] focused on a new optimization model that considers these constraints for drilling processes only. The NSGA-II is recognized for its robust optimization capabilities and successfully handling of various optimization problems [38; 39; 40]. The NSGA-II is a robust multi-objective evolutionary algorithm approach that has been tested across various real and simulated problems [41; 42]. Research comparing the path smoothness between the NSGA-II and GA is provided in [43]. In a different study, [PERSON] et al. [44] analyzed the PP problem on a path, focusing on two different objectives, which were difficulty and path length. The authors applied a user-defined weight to path segments relying on the NSGA-II. NSGA-II and GA optimization methods are performed on the path clearance and path length. The NSGA-II model has been utilized to address the challenges presented in the models [45]. The contribution of this paper is to propose an evolutionary algorithm approach for a multi-objective optimal PP which minimizes the toolpath length and improves path smoothness for CNC part machining processes, while considering both simulation and experimental results. This study explores the advantages of efficiently using the NSGA-II to solve the PP problem of CNC machines. The developed algorithm is able to minimize path length and decrease the maximum turning angle of the non-cutting moves generated by the CNC machine. In this paper, PP trajectories are obtained in both simulation and experimental environments. The experimental results show that the non-dominated solutions obtained through the NSGA-II exhibit favorable parameters, revealing a shorter and smoother path option. The NSGA-II offers significant advantages over single-objective optimization methods due to its robust multi-objective problem-solving capabilities. Furthermore, this study distinguishes itself from others in the literature via implementing PP optimization processes on actual CNC machining data. MOGAs are also performed to evaluate the efficiency and suitability of the non-dominated sorting nature of the NSGA-II for this problem. Since the aim is to optimize paths for multiple objectives, it is preferred to find a solution in the framework of Pareto optimality between the objectives. However, the MOGA heavily relies on selecting shared functions, which can create significant selection pressure and ultimately result in premature convergence [46; 47]. After introduction, details of the equations of the PP optimization problem in CNC systems from a design perspective are presented in Section 2. Section 3 describes the multi-objective PP optimization using the NSGA-II model. Comparative Pareto graphs, with the MOGA and the analysis of the effect of the NSGA-II on the travel distance and machining cycle time on the workpieces, are presented in both the simulation and experimental environments in Section 4. Lastly, the benefits and remarks of the offered method are presented and discussed in this paper.