Advanced Optimization of Surface Characteristics and Material Removal Rate for Biocompatible Ti6Al4V Using WEDM Process with BBD and NSGA II

Machining titanium alloy (Ti6Al4V) used in orthopedic implants via conventional metal cutting processes is challenging due to excessive cutting forces, low surface integrity, and tool wear. To overcome these difficulties and ensure high-quality products, various industries employ wire electrical discharge machining (WEDM) for precise machining of intricate shapes in titanium alloy. The objective is to make WEDM machining parameters as efficient as possible for machining the biocompatible alloy Ti6Al4Vusing Box–Behnken design (BBD) and nondominated sorting genetic algorithm II (NSGA II). A quadratic mathematical model is created to represent the productivity and the quality factor (MRR and surface roughness) in terms of varying input parameters, such as pulse active (Ton) time, pulse inactive (Toff) time, peak amplitude (A) current, and applied servo (V) voltage. The established regression models and related prediction plots provide a reliable approach for predicting how the process variables affect the two responses, namely, MRR and SR. The effects of four process variables on both the responses were examined, and the findings revealed that the pulse duration and voltage have a major influence on the rate at which material is removed (MRR), whereas the pulse duration influences quality (SR). The tradeoff between MRR and SR, when significant process factors are included, emphasizes the need for a reliable multi-objective optimization method. The intelligent metaheuristic optimization method named nondominated sorting genetic algorithm II (NSGA II) was utilized to provide pareto optimum solutions in order to achieve high material removal rate (MRR) and low surface roughness (SR).


Introduction
Ti6Al4V or Titanium Grade 5 is biocompatible, which means that it is well tolerated by the human body, making it suitable for medical implants such as orthopedic implants [1], dental implants [2], and prosthetics [3]. The superior corrosion resistance, formability, and weldability lead to the extensive use of titanium alloys in a wide range of industries such as the aerospace [4], automotive [5,6], chemical [7], and marine industries [8]. Titanium and its alloys are difficult to machine/process and expensive when utilized in conventional machining methods because of their high chemical reactivity (causing tool deformation) [9,10] and poor thermal conductivity [11,12]. In several industries, wire electric discharge machining (WEDM), which utilizes thermo-mechanical energy, can process with excellent accuracy [13] and provide a good surface finish [14,15]; thus, it is often employed to deal with such highstrength materials. In the WEDM process, a conductive wire (electrode) travels continually, and the heat results in an electric spark that erodes the conductive work material [16,17]. During the process, dielectric fluid is utilized as a medium for ionization to create the electrical arc across the workpiece and the wire (electrode). The steady flow of dielectric fluid acts as a cooling agent and helps in flushing the removed material away. The heat energy from these electrical sparks removes material in the form of micro-debris.
The WEDM equipment's conservative technical data or the operator's expertise was traditionally used to choose the appropriate parameters for the maximum material removal rate and minimum surface roughness during the EDM process, which resulted in inconsistent machining performance. Devarasiddappa et al. [18] focused on reducing the surface roughness of Ti6Al4V alloy processed using WEDM. They obtained a 2.6% reduction in SR for ideal process variables of the WEDM process. Muhammad Umar Farooq et al. [19] manufactured convex and concave shapes in Ti6Al4V using the WEDM technique and found that servo voltage, wire feed, pulse-on time, and pulse-off time affect the precision of geometrical profiles and the diameter of corners. The pulse duration was shown to be the most important variables driving overcut in convex profiles. Chaudhari et al. [20] employed Taguchi's L9 array to machine Ti6Al4V alloy using the WEDM technique and found that pulse duration and current have an impact on MRR and SR. Lin et al. [21] emphasized the benefits of using the gray Taguchi technique to optimize a number of quality variables such as electrode depletion, MRR, and overcut for micro-EDM finish quality of the Ti6Al4V alloy. According to the experimental findings, the peak current and pulse duration play a key role in the micro-EDM of Ti6Al4V alloy. Priyadarshini et al. [22] studied the use of Ti6Al4V alloy using EDM for various pulse parameters and chose MRR, SR, and TWR (tool wear rate) as output factors utilizing a Taguchi orthogonal array for the experiment.
Material removal rate and surface roughness were the output parameters utilized by Gupta et al. [23] while using the WEDM process to machine a Ti6Al4V alloy, whereas the process parameters were pulse duration, wire speed, servo voltage, wire tension, pulse current, and feed rate. They observed that pulse duration has a significant effect on MRR and SR. When using the WEDM method to cut Ti6Al4V alloy, Mouralova et al. [24] evaluated the current, voltage, pulse duration, and wire speed as the process parameters. They determined using experiments that a quicker pulse-on time and longer pulse-off time resulted in a better surface quality. Ti6Al4V was studied as a work material by Pramanik et al. [25] and machined utilizing the WEDM method while taking the effect of wire tension, pulse-on time, and pulse-off time as process parameters into consideration. They reached the conclusion that shorter pulse-on times and longer pulse-off times produced better results. Bisaria and Shandilya [26] studied the influence of pulse duration and spark gap voltage on MRR (material removal rate) and SR (surface roughness). They discovered that, although MRR and SR values decreased with a rise in voltage and pulse-off time, they increased drastically with a rise in pulse-on time. Many experimental investigations have sought to investigate the impact of various process factors on the performance of the WEDM machining. The majority of the experiments, however, had limitations on the variety of process variables they were able to investigate or the range of values they could investigate, and it can be suggested that there is still scope for improvement in terms of collecting data by piloting an in-depth and comprehensive investigation of the impact of a wide variety of WEDM process variables and their levels on the productivity and surface quality generated when processing Ti6Al4V alloy.
The appropriate process parameters is to be selected carefully for sustainable production, and the parameters associated with WEDM for the machining of the Ti6Al4V alloy have been optimized by a number of researchers [27,28]. To collect data from experiments with the minimum waste of time, money, raw materials, etc., systematic experiment design is crucial. Among the tools for designing experiments are Taguchi techniques employing an orthogonal array, response surface methodology (RSM), and fractional factorial design. A comprehensive review of the literature revealed that several researchers from all over the world have contributed to the process parameter optimization of the WEDM method for the machining of titanium-based alloys. WEDM is a process with multiple inputs and multiple outputs that has complex relationships on each parameter and how they interact with each other. When multiple objectives are dealt with, numerous conflicting situations arise that require a resolution. The best representation of this tradeoff is optimum pareto points obtained through evolutionary optimization which finds the solution near the global optimum with less time and computing effort. Thus, there arises a need for multiresponse optimization [29], including gray relational analysis (GRA) [30,31], heat transfer search (HTS) algorithm [32,33], teacher learning-based algorithm [34], particle swarm algorithm [35], genetic algorithm [36], and artificial neural networks [37], which have been tested in order to find the tradeoff solution in terms of optimized process parameters.
Deb et al. [38] implemented NSGA II (non-sorted genetic algorithm II), a newly developed approach that was designed to handle multi-objective problems and search for a variety of solutions that efficiently reflect the tradeoff between contrasting objectives. NSGA II can effectively explore the solution space, maintain diversity, and provide optimum or near-optimal solutions for the optimization of two conflicting objectives, namely, maximum material removal rate (MRR) and minimal surface roughness in WEDM. AISI 5160 steel [39], high-speed steel [40], and AISI D3 tool steel [41,42] are a few materials that are processed in WEDM whose results are optimized using NSGA II. In the literature, limited studies can be found on minimizing SR and maximizing MRR in WEDM of Ti6Al4V alloy using the NSGA II algorithm, which can select the most dominant solution.
The goal of this study was to optimize the machining settings in order to maximize MRR while minimizing SR. Accordingly, this study can be broken into three sections. The first section involves conducting experiments based on Box-Behnken design and collecting data regarding the responses of MRR and SR to various input parameters, including pulse active (T on ) time, pulse inactive (T off ) time, peak amplitude of current (A), and applied servo voltage (V). In the second section, the effect and influence of the parameters on the responses are examined and discussed. The third section develops the multi-objective metaheuristic NSGA II algorithm, which can search for the most optimal parameter for the conflicting objective, i.e., maximizing MRR and minimizing SR. Comparisons are made between the results obtained using these different methods, and validation is carried out via the use of confirmation tests.

Materials and Methods
In this work, a CNC wire-cut EDM DK7732C-C manufactured by Suzhou Baoma Numerical Control Equipment Co., Ltd. (Suzhou and China) with 3 kVA power and a BMW 3000 controller ( Figure 1) was used to cut the profile shown in Figure 2 on a commercial titanium Ti6Al4V alloy of 5 mm thickness. Table 1 presents a list of the chemical components of the titanium Ti6Al4V alloy utilized in this investigation. Deionized water was utilized to eject the waste particles produced during the machining process, and a φ 0.25 mm zinc-coated brass wire was utilized as the electrode for cutting purposes. RSM is an abbreviation for response surface methodology, which is a powerful mathematical and statistical tool that can investigate and optimize complicated systems. Researchers have extensively utilized the Box-Behnken design (BBD), which is a form of response surface methodology (RSM), in order to optimize experimental trials [43]. The Box-Behnken design is advantageous since it does not contain any points at the extremities of the cubic region produced by the two-level factorial combinations that are either costly to test or difficult to test due to physical restrictions in experimentation [44]. It is widely used in a variety of sectors, including agrochemicals, pharmaceuticals, and bioprocessing [45].  RSM is an abbreviation for response surface methodology, which is a powerful mathematical and statistical tool that can investigate and optimize complicated systems. Researchers have extensively utilized the Box-Behnken design (BBD), which is a form of response surface methodology (RSM), in order to optimize experimental trials [43]. The Box-Behnken design is advantageous since it does not contain any points at the extremities of the cubic region produced by the two-level factorial combinations that are either costly to test or difficult to test due to physical restrictions in experimentation [44]. It is widely used in a variety of sectors, including agrochemicals, pharmaceuticals, and bioprocessing [45].
The experiments used a two-level design with four parameters, namely, pulse active time (Ton) ranging from 110 to 120 µs, pulse inactive time (Toff) ranging from 50 to 60 µs, applied servo voltage (V) ranging from 40 to 50 V, and peak amplitude of current (A) ranging from 40 to 42 A. The Box-Behnken design was employed to generate a total of 29 experiments, and the corresponding values of the response characteristics were determined. Table 2 depicts the range of input parameters that were chosen on the basis of preliminary pilot experiments and an extensive investigation of the literature.  RSM is an abbreviation for response surface methodology, which is a powerful mathematical and statistical tool that can investigate and optimize complicated systems. Researchers have extensively utilized the Box-Behnken design (BBD), which is a form of response surface methodology (RSM), in order to optimize experimental trials [43]. The Box-Behnken design is advantageous since it does not contain any points at the extremities of the cubic region produced by the two-level factorial combinations that are either costly to test or difficult to test due to physical restrictions in experimentation [44]. It is widely used in a variety of sectors, including agrochemicals, pharmaceuticals, and bioprocessing [45].
The experiments used a two-level design with four parameters, namely, pulse active time (Ton) ranging from 110 to 120 µs, pulse inactive time (Toff) ranging from 50 to 60 µs, applied servo voltage (V) ranging from 40 to 50 V, and peak amplitude of current (A) ranging from 40 to 42 A. The Box-Behnken design was employed to generate a total of 29 experiments, and the corresponding values of the response characteristics were determined. Table 2 depicts the range of input parameters that were chosen on the basis of preliminary pilot experiments and an extensive investigation of the literature. The experiments used a two-level design with four parameters, namely, pulse active time (T on ) ranging from 110 to 120 µs, pulse inactive time (T off ) ranging from 50 to 60 µs, applied servo voltage (V) ranging from 40 to 50 V, and peak amplitude of current (A) ranging from 40 to 42 A. The Box-Behnken design was employed to generate a total of 29 experiments, and the corresponding values of the response characteristics were determined. Table 2 depicts the range of input parameters that were chosen on the basis of preliminary pilot experiments and an extensive investigation of the literature. Table 2. Control factors and their levels.

Parameters and Their Levels −1 Level +1 Level
Pulse active (T on ) time (µs) 110 120 Pulse inactive (T off ) time (µs) 50 60 Servo voltage (SV) (V) 40 50 Peak amplitude of current (PC) (A) 40 42 The response characteristics evaluated in the present study were the MRR and average SR. The arithmetic average roughness, i.e., the average deviation of the surface profile from the mean line within the evaluation length was considered for measuring surface roughness, expressed in micrometers. An SJ-210-Mitutoyo surf test equipped with a 2 µm stylus tip diamond indenter was used to measure the SR at three different locations. The average of all three values was then selected. Equation (1) was used to determine the MRR after the machining time was measured using a stopwatch [46,47].
where L is the cutting length is constant (45 mm), H is the height of the workpiece (5 mm), and t is the machining time (recorded using stopwatch in min).

Response Surface Methodology (RSM)
A statistical and mathematical approach called response surface methodology (RSM) can be used to optimize and investigate the interaction between a number of input variables (factors) and one or more output variables (responses). It is commonly used in the field of experimental design and process optimization, which is particularly useful when the association between the input variables and the response variables is intricate and nonlinear. By systematically varying the levels of the input variables and measuring the corresponding response, RSM helps to model and understand the relationship and, subsequently, determine the optimal values of the input variables to achieve desirable responses. Table 3 depicts the BBD and experimental findings of the machining capabilities characterizing the WEDM process. For a 5% significance level (α = 0.05), the "p-value" must be less than or equal to 0.05 to be considered significant, and the backward elimination method excludes irrelevant factors. The model's potential for predicting an optimal response value for correlation coefficient R was evaluated in the most favorable conditions possible. Regression analysis was used to determine the optimum region to investigate the responses under study by fitting mathematical models to the experimental data. The data from the experiment runs were analyzed and obtained with the use of Design expert software V 13.0, and the significance of each coefficient for MRR and SR is depicted in Tables 4 and 5.   An experimental relationship expressed by a second-order polynomial equation with interaction terms was utilized to fit the data from the BBD model. The final result of coded factors is shown in (Equations (2) and (3)).

Multivariate Analysis (ANOVA)
(2) Analysis of variance (ANOVA) was implemented to analyze the data, and Tables 4 and 5 show the significance of the experimental findings for different models along with the related p-values. Four linear correlation coefficients (A, B, C, and D), six interaction coefficients (AB, AC, AD, BC, BD, and CD), and four quadratic coefficients (A 2 , B 2 , C 2 , and D 2 ) were found to be substantial. The p-values of each model term were investigated to depict the interaction patterns between the variables; for p < 0.0001, the model's F-value of 18.5 for MRR and 10.02 for SR showed that it was very significant. Due to the relative pure error, the lack of fit F-value of 0.8983 for MRR and 0.5147 for SR was not significant (p = 0.0702).
Overall, unless the model is adequately fit to validate its suitability for use, inadequate or inaccurate results may be obtained through the investigation and optimization of the fitted response surface [48,49]. The p-value is used to determine the significance of each coefficient and the degree of interaction between variables. Effects characterized by p < 0.05 are considered significant. The degree of correlation between the values observed and predicted is better when the significance level is greater [50]. The "Pred R-squared" of 0.9175 and the "Adj R-squared" of 0.9342 for MRR and the "Pred R-squared" of 0.9021 and the "Adj R-squared" of 0.9278 for SR were reasonably compatible in the current examination. In addition, the correlation coefficients with a high value (R 2 for MRR of 0.9687 and for SR of 0.9542) showed a significant relationship between the values of the anticipated and experimental responses. The low CV value (5.42% for MRR and 4.52% for SR) made it evident that there were minor deviations between the predicted and experimental results, and it also demonstrated that the experiments were very precise and reliable. The adequate precision ratio in the current investigation was determined to be 14.91 for MRR and 12.13 for SR, indicating a sufficient indicator, and the present model may be utilized to move about the design space.

Diagnostic Graphs
The data statistics are shown in Figures 3 and 4; analyzing the experimental and the model observation diagnostic plots enabled the determination of the models' accuracy. Figures 3A and 4A show the residual plots for the responses, which exhibited a normal% probability distribution, whereby the points were logically closer to the straight line, with no significant deviations; thus, the current model significantly improved the interaction between the response and the process variables. The data statistics are shown in Figures 3 and 4; analyzing the experimental and the model observation diagnostic plots enabled the determination of the models' accuracy. Figures 3a and 4a show the residual plots for the responses, which exhibited a normal% probability distribution, whereby the points were logically closer to the straight line, with no significant deviations; thus, the current model significantly improved the interaction between the response and the process variables.       The predicted values were extremely similar to the observed values, as shown in Fi ures 3B and 4B. By establishing a satisfactory fit of the model, the externally studentiz residuals vs. experimental runs were examined, and the results showed that all of the da points fit inside the limits (Figures 3C and 4C). For each run, the values of the predict and actual responses were regularly distributed with almost straight lines, as shown Figures 3D and 4D. Figures 3E,F and 4E,F show the Box-Cox plots (for power transfo mations of variables), indicating that the perturbation of variables was within the specifi range.

3D Response Surface Plot
In order to understand the major impacts of the two variables, as well as their inte actions, it is useful to compare the effects of the two components using 3D surface plot The predicted values were extremely similar to the observed values, as shown in Figures 3B and 4B. By establishing a satisfactory fit of the model, the externally studentized residuals vs. experimental runs were examined, and the results showed that all of the data points fit inside the limits (Figures 3C and 4C). For each run, the values of the predicted and actual responses were regularly distributed with almost straight lines, as shown in Figures 3D and 4D. Figures 3E,F and 4E,F show the Box-Cox plots (for power transformations of variables), indicating that the perturbation of variables was within the specified range.

3D Response Surface Plot
In order to understand the major impacts of the two variables, as well as their interactions, it is useful to compare the effects of the two components using 3D surface plots. Figure 5 illustrates the 3D response surface plot for the MRR, from which it can be observed that the maximum MRR (6.62 mm 3 /min) was recorded for maximum T on (120 µs) and T off (60 µs) but medium voltage (45 V) and current (41 A). When the titanium (Ti6Al4V) alloy was processed using WEDM, the combined effects of T on with T off , T on with current, and T on with servo voltage (Figure 5A-C) resulted in better spark creation and improved characteristics, which increased workpiece vaporization and melting, thereby resulting in increased MRR. Therefore, the combination of higher values for these input parameters resulted in an increase in the EDM process's overall productivity. In the case of the interactions of T off with current and T off with voltage ( Figure 5D,E), it is evident that there was little variation in these two factors, along with a gradual increase in MRR. The interaction of current and voltage ( Figure 5F) had a negligible impact on the WEDM productivity. improved characteristics, which increased workpiece vaporization and melting, thereby resulting in increased MRR. Therefore, the combination of higher values for these input parameters resulted in an increase in the EDM process's overall productivity. In the case of the interactions of Toff with current and Toff with voltage ( Figure 5D,E), it is evident that there was little variation in these two factors, along with a gradual increase in MRR. The interaction of current and voltage ( Figure 5F) had a negligible impact on the WEDM productivity. From the 3D response surface plot of SR (Figure 6), it can be observed that the surface roughness was minimum (3.18 µm) for maximum voltage (50 V), minimum Toff (50 µs), and medium Ton (115 µs) and current (41 A). In general, it can be observed that interactions among the various machining parameters were much simpler than the simple rule of thumb, and their combined impact on the process response was quite ambiguous. Figure  6A-C show how roughness varied with Ton and Toff, Ton and current, and Ton and servo voltage. According to the figure, superior quality (i.e., smaller SR values) could essentially be achieved by combining lower values of Ton and Toff, Ton and current, and Ton and servo voltage in contrast to their impact on process productivity (MRR). In the case of the interaction of Toff with current and Toff with voltage ( Figure 6D,E), it is evident that there was little variation in these two factors, along with a gradual decrease in SR for decreasing inputs. The interaction of current and voltage ( Figure 6F) had a negligible impact on the roughness. From the 3D response surface plot of SR ( Figure 6), it can be observed that the surface roughness was minimum (3.18 µm) for maximum voltage (50 V), minimum T off (50 µs), and medium T on (115 µs) and current (41 A). In general, it can be observed that interactions among the various machining parameters were much simpler than the simple rule of thumb, and their combined impact on the process response was quite ambiguous. Figure 6A-C show how roughness varied with T on and T off , T on and current, and T on and servo voltage. According to the figure, superior quality (i.e., smaller SR values) could essentially be achieved by combining lower values of T on and T off , T on and current, and T on and servo voltage in contrast to their impact on process productivity (MRR). In the case of the interaction of T off with current and T off with voltage ( Figure 6D,E), it is evident that there was little variation in these two factors, along with a gradual decrease in SR for decreasing inputs. The interaction of current and voltage ( Figure 6F) had a negligible impact on the roughness. From the 3D response surface plot of SR ( Figure 6), it can be observed that the surface roughness was minimum (3.18 µm) for maximum voltage (50 V), minimum Toff (50 µs), and medium Ton (115 µs) and current (41 A). In general, it can be observed that interactions among the various machining parameters were much simpler than the simple rule of thumb, and their combined impact on the process response was quite ambiguous. Figure  6A-C show how roughness varied with Ton and Toff, Ton and current, and Ton and servo voltage. According to the figure, superior quality (i.e., smaller SR values) could essentially be achieved by combining lower values of Ton and Toff, Ton and current, and Ton and servo voltage in contrast to their impact on process productivity (MRR). In the case of the interaction of Toff with current and Toff with voltage ( Figure 6D,E), it is evident that there was little variation in these two factors, along with a gradual decrease in SR for decreasing inputs. The interaction of current and voltage ( Figure 6F) had a negligible impact on the roughness.

Multi-Objective Optimization Using Nondominated Sorting Generic Algorithm II (NSGA II)
NSGA II is a powerful multi-objective optimization algorithm that uses nondominated sorting to find the optimal solutions that satisfy multiple objectives simultaneously. In this case, the objectives were to maximize MRR and minimize SR for WEDM parameters, which are dependent on Ton, Toff, V, and A. However, MRR and SR are conflicting objectives, and optimizing one may lead to the degradation of the other. To address this issue, NSGA II practices elitist nondominated selection to obtain a nondominated set of solutions. The nondominated solutions are selected on the basis of the ranking of the nondominated level, which is performed using the crowd comparing operator and crowd distance. These methods help to maintain population diversity and prevent the algorithm from premature convergence to a local optimum.
The NSGA II procedure is outlined below.

Multi-Objective Optimization Using Nondominated Sorting Generic Algorithm II (NSGA II)
NSGA II is a powerful multi-objective optimization algorithm that uses nondominated sorting to find the optimal solutions that satisfy multiple objectives simultaneously. In this case, the objectives were to maximize MRR and minimize SR for WEDM parameters, which are dependent on T on , T off , V, and A. However, MRR and SR are conflicting objectives, and optimizing one may lead to the degradation of the other. To address this issue, NSGA II practices elitist nondominated selection to obtain a nondominated set of solutions. The nondominated solutions are selected on the basis of the ranking of the nondominated level, which is performed using the crowd comparing operator and crowd distance. These methods help to maintain population diversity and prevent the algorithm from premature convergence to a local optimum.
The NSGA II procedure is outlined below.
Step 1: On the basis of the maximum and minimum values of the input parameters, initialize the population (N); Step 2: Determine the fitness functions for every individual, including MRR and surface roughness; Step 3: Sort the initialized population using nondominated criteria; Step 4: Choose the individuals on the basis of crowding distance and ranking, and then produce offspring via crossover operations with a factor of 0.95 and mutation operations with a factor of 0.01; Step 5: Add the populations of the parents and offspring together, and determine who belongs in the next generation according to ranking and crowding distance; Step 6: If the maximum generation (500) has been achieved, stop; if not, return to Step 4.
Due to the nature of MRR and SR conflicts and their dependence on T on , T off , PC, and SV, this can be resolved by assigning a negative sign (indicating minimization) to MRR.
ANOVA was performed using Equations (2) and (3) to obtain objective functions for MRR and SR. Table 4 represents the pareto optimal solutions obtained in a study aimed at achieving superior surface finish and increased material removal rate (MRR). The study was conducted by varying four machining parameters, namely, pulse active (T on ) time, pulse inactive (T off ) time, servo voltage, and peak amplitude of current, using a pareto fraction of 0.1 and a population size of 1000. Table 6 includes 23 solution sets, with the optimal solution being solution number 2. Each solution set was characterized by corresponding values of T on , T off , servo voltage, peak current, MRR (in mm 3 /min), and SR (surface roughness in µm). MRR and SR were the two objective functions obtained after conducting ANOVA. The table shows that the values of T on , T off , servo voltage, and peak current varied across the solution sets, leading to different values of MRR and SR. Figure 7 illustrates the 23 results of the pareto optimal front, highlighting a better convergence of the results. Depending on the specific product requirements, any solution from the set in Table 4 can be acceptable. The most desirable set, on the other hand, was chosen with the primary goal of achieving a superior productivity factor and quality factor (MRR and roughness); in this case, solution 2 was preferable to other pareto optimal solution sets.

Optimization Validation
The final step was to validate and confirm the improvement in the performance characteristic using the optimum level of the process variables obtained using NSGA II. A confirmation experiment was performed on optimal solution set 2, and the results of the verification experiment using the optimum procedure variables are shown in Table 7, along with a comparison of NSGA II for the optimal and experimental process variables. According to Table 7, the MRR dropped by 1.06%, while the SR increased by 1.54%.

Conclusions
The current study utilized BBD/NSGA II to optimize MRR and SR in the WEDM of Ti6Al4V alloy. Mathematical equations, which were quadratic in nature, were obtained as a function of WEDM parameters for MRR and SR. On the basis of the results of the study, the following conclusions can be drawn: • This study provides valuable insights into the optimization of the WEDM process for biocompatible titanium alloy Ti6Al4V.

•
The nonlinear behavior in the responses of MRR and SR in the WEDM of Ti6Al4V alloy was found to be suitable for modeling, characterized by a quadratic model.

•
The models developed for MRR and SR were adequate with a high F-value and reasonably decent association with the trial results (R 2 of 96.87% for MRR and 95.42% for SR).

•
The pulse active (Ton) time was identified as the most influential WEDM parameter with respect to MRR and SR, achieving a maximum percentage, followed by pulse inactive time (Toff).

Optimization Validation
The final step was to validate and confirm the improvement in the performance characteristic using the optimum level of the process variables obtained using NSGA II. A confirmation experiment was performed on optimal solution set 2, and the results of the verification experiment using the optimum procedure variables are shown in Table 7, along with a comparison of NSGA II for the optimal and experimental process variables. According to Table 7, the MRR dropped by 1.06%, while the SR increased by 1.54%.

Conclusions
The current study utilized BBD/NSGA II to optimize MRR and SR in the WEDM of Ti6Al4V alloy. Mathematical equations, which were quadratic in nature, were obtained as a function of WEDM parameters for MRR and SR. On the basis of the results of the study, the following conclusions can be drawn:

•
This study provides valuable insights into the optimization of the WEDM process for biocompatible titanium alloy Ti6Al4V.

•
The nonlinear behavior in the responses of MRR and SR in the WEDM of Ti6Al4V alloy was found to be suitable for modeling, characterized by a quadratic model.

•
The models developed for MRR and SR were adequate with a high F-value and reasonably decent association with the trial results (R 2 of 96.87% for MRR and 95.42% for SR).

•
The pulse active (T on ) time was identified as the most influential WEDM parameter with respect to MRR and SR, achieving a maximum percentage, followed by pulse inactive time (T off ).

•
The NSGA II optimization technique proved to be a more effective method for optimizing multiple objectives, and the NSGA II technique provided pareto optimal solutions that offered most favorable balance between surface characteristics and material removal rate.

•
The best process variables obtained using the optimization technique NSGA II were a T on of 120 µs, T off of 57 µs, servo voltage of 50 V, and peak current of 40 A.
Author Contributions: Conceptualization, methodology, validation, investigation, resources, data curation, and writing-original draft preparation, A.N.; software, formal analysis, and writing-review and editing, V.S.; visualization, project administration, and supervision, G.J. All authors have read and agreed to the published version of the manuscript.