# Non-Cutting Moving Toolpath Optimization with Elitist Non-Dominated Sorting Genetic Algorithm-II
## 5 Conclusions  
This study explores an evolutionary algorithm method for a multi-objective optimal PP which minimizes the toolpath length and improves the path smoothness for CNC part machining processes, while considering statically known environments. Results from the study demonstrate the excellent characteristics of the non-dominated solutions created by the NSGA-II with elitism in the PP. The developed algorithm is able to reduce the path length and the maximum turning angle during the non-cutting movements of a CNC machine. In the NSGA-II framework, genetic operators are offered to expedite the progress of individuals, facilitating the generation of paths that are shorter and smoother. The algorithm's parameters are systematically investigated to enhance its performance. PP trajectories have been analyzed through simulations and experimental settings. The experimental outcomes show that the non-dominated solutions created by the NSGA-II are characterized by advantageous parameters, offering options for paths that are both shorter and smoother. Furthermore, the objectives, namely the path length and smoothness, are compared in the Pareto optimality of the NSGA-II and MOGA. The NSGA-II algorithm demonstrated  
Figure 11: Comparison between original Workpiece 1 and optimized Workpiece 1 considering the (a) non-cutting distance and (b) cycle time. Figure 12: Comparison between original Workpiece 2 and Optimized Workpiece 2 considering the (a) non-cutting distance and (b) cycle time. compatible results with the MOGA, indicating that both types of genetic algorithms are effective for the toolpath planning problem. However, the technique deliberated here entails an examination involving the individuals. While the MOGA approach can reduce computational costs, the solutions generally converge toward a specific point during the examination step, potentially ending up as a loss of solution diversity. Simulation results have demonstrated that the NSGA-II, verified with a MOGA based on Pareto optimality, successfully optimizes the toolpath planning for two different work-pieces, while minimizing both the path length and cycle time. According to the experimental results, the NSGA-II exhibits consistent performance across different terrain representations and achieved good performance for the multi-objective PP problem. Analyses conducted using G-code manipulation and PP optimization revealed significant improvements in the machining cycle time. The results of the experimental studies show that PP optimization using the NSGA-II highlights its shorter and smoother qualities, with the optimal trajectory leading to reductions of approximately 30% in the path length and 7% in the machining cycle time. It can be highlighted that the current algorithm's operator speed restricts its applicability to offline PP. So, in future research, exploring innovative methods for improving the execution time in the NSGA-II can be considered. Additionally, the study does not consider the robot's kinematics. The literature review provided in this study reveals the importance of PP techniques in CNC machining processes, and provides a possible roadmap for future research. Moving forward, further improvements and efficiency gains can be attained using real-time PP problems and adaptive control systems. Conceptualization, G.D. and R.A.V. ; methodology, G.D.; software, G.D.; validation, G.D. and R.A.V. ; formal analysis, G.D.; investigation, G.D.; resources, G.D.; data curation, G.D.; writing--original draft preparation, G.D. and R.A.V. ; writing--review and editing, G.D. and R.A.V. ; visualization, G.D.; supervision, G.D. and R.A.V. ; project administration, G.D. and R.A.V. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. Data are provided within the article. Author [PERSON] was employed by the company R&D Department.