# Non-Cutting Moving Toolpath Optimization with Elitist Non-Dominated Sorting Genetic Algorithm-II
## 1 Introduction
Additional research introduced an algorithm that minimized the amount of non-cutting time in the milling process via optimally dividing the toolpaths [4]. Consequently, GAs are recommended for optimizing the cutting parameters during machining processes [16; 17]. The traveling salesman problem (TSP), used with the sequential ordering problem (SOP) to establish generalized precedence constraints, can also be found in the literature. The validation of toolpath optimization through the use of the TSP confirmed for the multi-cavity machining of intricate parts [18]. In the drilling process, it is demonstrated that many studies have utilized the TSP model to find an optimal path solution [19]. This leads to the minimization of path length during movement, which has been shown to be an effective strategy for sequencing issues in manufacturing [20]. However, numerous studies in the field of drilling toolpath optimization have mostly focused on simple shapes and hole arrangements [21]. Another study utilized AISs to enhance the surface smoothness of milling operations through determining optimal parameters and focusing on various factors such as the cutting depth, feed rate, and cutting speed [22]. Numerous studies have been performed in attempts to apply ant colony optimization (ACO). For instance, [PERSON] et al. [23] aimed to minimize non-cutting airtime during hole-making processes, applying the ant colony algorithm. In addition, [PERSON] et al. [24] adopted a modified ACO to achieve optimal machining parameters that help to reduce production costs. Drilling operations modeled as a TSP have been addressed through the use of PSO on CNC machines. In [25], the PSO model was implemented with only a few control variables, providing a user-friendly and applicable model that contributed to reducing manufacturing costs. In another study, the applicability of PSO in defining the optimal process parameters for turning the machining is investigated. This analysis aimed to detect the best feed rate and tooling speed that would enhance the machining accuracy while simultaneously reducing the machining time and costs [26]. In the context of CNC end milling optimization, the use of the PSO method is recommended to improve surface roughness [27]. Furthermore, PSO is utilized to choose the optimal parameters for reducing both the machining cycle time and the production costs [28]. In another study, a comparison of unit production cost reductions is performed between the PSO, GA, and SA methods [29]. Additionally, fully informed and advanced PSOs are introduced to the optimization of the toolpath planning of a five-axis milling machine process. The findings indicated that fully informed PSO is more effective in reducing the errors when compared to the PSO method [30]. Researchers have proposed various methodologies to improve the cycle time and energy consumption in order to achieve optimal trajectories for a high-speed CNC system design. [PERSON] and [PERSON] [31] presented a method for time-optimal feed rate scheduling, specifically tailored for the quantic spline toolpath. [PERSON] et al. [32] introduced a time-optimal path planning technique that considers the second-order dynamics of feed drives during the traversal of contour curves. [PERSON] et al. [33] suggested an algorithm to optimize the time allocation for jerk-limited feed rates along the parametric curves. [PERSON] and [PERSON] [34] proposed an approach aimed at minimizing feed rate fluctuations and modulating the feed continuously through optimizing NURBS toolpaths. Generating toolpaths for complex geometries requires additional caution to prevent collisions between the tool and workpiece, especially in high-speed multi-axis machines [35]. Therefore, it is crucial to explore the methods to optimize the toolpaths analytically [36].