Multi-Objective Variable Neighborhood Strategy Adaptive Search for Tuning Optimal Parameters of SSM-ADC12 Aluminum Friction Stir Welding

: This research presents a novel algorithm for ﬁnding the most promising parameters of friction stir welding to maximize the ultimate tensile strength (UTS) and maximum bending strength (MBS) of a butt joint made of the semi-solid material (SSM) ADC12 aluminum. The relevant welding parameters are rotational speed, welding speed, tool tilt, tool pin proﬁle, and rotation. We used the multi-objective variable neighborhood strategy adaptive search (MOVaNSAS) to ﬁnd the optimal parameters. We employed the D-optimal to ﬁnd the regression model to predict for both objectives subjected to the given range of parameters. Afterward, we used MOVaNSAS to ﬁnd the Pareto front of the objective functions, and TOPSIS to ﬁnd the most promising set of parameters. The computational results show that the UTS and MBS of MOVaNSAS generate a 2.13% to 10.27% better solution than those of the genetic algorithm (GA), differential evolution algorithm (DE), and D-optimal solution. The optimal parameters obtained from MOVaNSAS were a rotation speed of 1469.44 rpm, a welding speed of 80.35 mm/min, a tool tilt of 1.01 ◦ , a cylindrical tool pin proﬁle, and a clockwise rotational direction.


Introduction
Cast aluminum has been used in innovative creations such as auto engines, turbine engines, etc., because it has good mechanical properties and easy fabrication. However, the problems with cast aluminum are defects in the structure such as porosity, cracking, and different gains that are difficult to control when cooling down after the casting process. Therefore, cast aluminum use has been reduced in auto engines and turbine engines. SSM (semi-solid material) aluminum was generated to compensate for the problems of cast aluminum because SSM aluminum is fabricated by a process that controls the different gains and defects within the structure. Therefore, semi-solid metal aluminum has been widely used in engine parts in aerospace, automobile, and marine products. The welding process is important to the engine part joint. Fusion welding has been the conventional way of metal welding, but it is a difficult process for aluminum welding. As aluminum material has a low melting point, the fusion welding process generates too high heat for welding. After welding, the welded seam temperature is reduced rapidly by ambient air that affects welded seam through cracking, porosity, distortion, and different gains [1][2][3][4].
Solid-state welding joints are used to reduce problems of distortion, cracking, and metallurgical changing. Friction stir welding (FSW) generates welding temperatures lower than the melting point temperature of materials, resulting in less gain changing and favorable joints after material welding [5][6][7][8][9][10]. Therefore, the friction stir welding process produces a welded seam with sufficient mechanical properties and structure [11,12]. Several works have studied the relative process parameters of mechanical properties and metallurgical structure. The parameters measure influences on welded seam quality, including rotation speed, welding speed, tilt angle, tool geometries, and the ratio shoulder to pin diameter (D/d), that affect heat generation, material deformation, material flow, material mixing, defects, strength, and metallurgical changing in weld line structure [13][14][15][16][17][18][19]. The parameters of the friction stir welding process have been studied by optimized methods such as factorial design [20], Taguchi design [21,22], grey relational method [23,24], response surface method [13,25], and combined methods [26][27][28][29]. The optimized methods can effectively control the mechanical property and defects of the weld line [30][31][32]. The weld line performance depends on many properties, such as tensile strength, hardness, impact, corrosion resistance, etc. A survey of the literature found that several kinds of research have emphasized that the main property target is tensile strength, in that it affects weld line usability performance. Consequently, tensile testing is used for quality measurements of weld line structures, being the main performance indicator of materials [33]. Thus, tensile strength has not been neglected in considering the mechanical property of the weld line. The hardness property is the second mechanical property of interest to study. Both hardness and tensile properties have a direct relationship with the material's exhibited high hardness value, and the tensile strength will increase in value, according to the reports of Khodabakhshi and Gerlich [34], and Chen and Cai [35]. Thus, hardness and other mechanical properties are ignored in the many studies shown in Table 1. Moreover, the mechanical property study of weld seams depends on weld line usability. However, bending is the weld line mechanical property that has not been studied for quality improvement in the automotive or marine industries. Therefore, the bending property should be studied together with the other properties. Several studies on aluminum alloy welding have presented optimization of the multi-objective strategy for many properties together in one welding condition because it provides desirable property parameters for the target requirement [29,[36][37][38].  [39] Taguchi GRA and TOPSIS Tension and Hardness 3.43 Goyal and Garg (2018) [40] RSM ANOVA Tension and Hardness 2. 6 Wakchaure et al. (2018) [29] Taguchi GRA [43] Taguchi GRA Elongation and Tension 11.25 Roshan et al. (2013) [44] RSM However, although the optimized method gives prediction results for target satisfaction, it shows a high error percentage average between 2% and 15% [38,39,44]. Improve-ment of the optimized method is important for response prediction accuracy. Furthermore, this approach to optimized parameter finding was developed based on the heuristic approach. Optimization predictions in many studies have used heuristic methods for problem solving that displayed accurate success and fast response times. Several heuristic approaches displayed high effectiveness, such as the technique for order of preference by similarity to ideal solution (TOPSIS), differential evolution algorithms (DEs), artificial neural networks (ANNs), genetic algorithms (GAs), adaptive large neighborhood search (ALNS), etc., and these methods have been used to optimize tour routing, transportation, agriculture, welding, and manufacturing processes [39,[45][46][47][48][49][50][51]. The optimization finding for welding conditions is especially important because inappropriate welding conditions deteriorate the quality of the weld line. Therefore, the heuristic approach is used as an optimized parameter in the FSW process because the result of the optimized welding parameter exhibited a low range error of approach of 0.5-3% [30,42,45,52], as shown in Table 1. The heuristic approach is highly effective for optimized parameter prediction. Moreover, the Pareto optimization is used for optimal parameter finding together with a heuristic approach. This increases the exactness of optimal parameter prediction, especially in multi-objective optimization [29,37,43].
Therefore, in this work, we present the variable neighborhood strategy adaptive search (VaNSAS) and Pareto optimal for finding the optimal parameters in the FSW process. The welding feature is the butt joint for SSM ADC 12 aluminum material. The welding optimization parameters are rotation speed, welding speed, tool tilt angle, and tool geometry. The two optimization responses are the tensile and bending strengths of the weld line. The weld line structure is studied by scanning electron microscope (SEM) to determine the weldability characteristics and defects.

Literature Survey
The FSW process has several important parameters, but we found that two parameters mainly affect weld joint performance, namely, rotation speed and welding speed. These parameters indicate the heat generation deformation of the material and material flow in welding [12,[52][53][54], so that both the rotation speed and welding speed parameters cannot be ignored in the FSW process. Other parameters that are supported to improve the weld joint quality are tilt angle, tool geometries, the ratio of shoulder to pin diameter (D/d), and tool material. Some FSW cases could be omitted in advocated parameter studies, but the weld line quality gives a highly effective performance, as shown in Table 2. Nevertheless, these advocated parameters are given importance to increase the weld line performance. Both tilt angle and tool geometries are especially influential parameters for effective material flow when fulfilling and mixing the material within the weld joint, which decreased or eliminated defects in the structure [55][56][57][58][59].
For the parameters of the ratio of shoulder to pin diameter (D/d) and the axial force affected by the heat generation and process force in the initial welding, the influence of two parameters was reduced for weld line creation [60][61][62]. However, the tool loading force showed a significant effect on the initial welding. The tool loading force parameter expedited high heat generation for the plastic deformation of the material and reduced axial force after material deformation. The tool loading force parameter does not affect the weld movement [63] because the heat in the welding process is controlled by two parameters, rotation speed and welding speed. Therefore, the tool axial force parameter has been ignored in many previous studies, as shown in Table 2.  [36] FEM and ANN AA 5083 The tool material was a low effect parameter of whether material hardness selection was suited to the material type of the workpiece. The weld joint was unaffected by tool material [66,67]. The literature review emphasized the two main parameters, namely, rotation speed and welding speed of FSW, that affected heat generation deformation and microstructure changing. The other parameter was secondary in that it could help to improve avocation of the weld line quality and decrease defects in the structure. Therefore, parameter selection for studies on FSW depended on consideration of the consequences of the parameter, such that much research on the effects of welding parameter control was carried out with diverse approaches to many responses. Several experimental design methods for optimized parameters were used, such as factorial design, response surface method, Taguchi design, and D-optimal. Each experimental design method showed differences in the number of experiments and design steps that depended on the number of parameters and level values. However, when comparing the experimental design methods with many mixed levels from similar factor numbers, the D-optimal design approach exhibited a low number of experiments and many level values of parameters [68][69][70]. Thus, D-optimal design was used as an experimental design in much research.
Many optimal approaches to finding parameters of the welding process were used to predict the response to the development of the weld line quality. The local search approach was often used to optimize parameter conditions owing to its uncomplicated and desirable results. In 2020, Senthil et al. [37] presented the response surface method for optimization of the FSW parameters of aluminum pipe. Two welding parameters were rotation speed and welding speed, which was a main parameter of FSW. The two types of mechanical property objectives for optimization were tensile strength and elongation percentage, which was multi-objective in one condition. The optimized condition for FSW displayed improvement in the two properties to increase tensile strength and suitable elongation percentage. The error of the prediction method was 3.7% when compared with the confirmed result. Accordingly, Goyal and Garg [40] and Shanavas and Dhas [25] used the RSM method and ANOVA approach to find optimal parameter conditions of marine-grade aluminum. The focus of the study was tensile strength elongation percentage and hardness of the weld line. This method showed high effectiveness of result prediction because it indicated an improvement in the mechanical property and desired quality of weld line usability. In addition, the Taguchi design was used for experimental design and optimal parameter conditions with grey relation analysis (GRA) or analysis of variance (ANOVA) in FSW. Ramesha et al. [53] and Prasad and Namala [71] used the Taguchi design and ANOVA approach for multi-objective optimization of dissimilar aluminum welding. Both tensile strength and hardness were used for one optimal parameter prediction. The result of the optimal parameter displayed high weld joint performance of the properties of tensile strength and hardness together. Although the optimum welding condition showed good mechanical property of the weld line, a tunnel defect appeared in the structure. Therefore, the GRA approach was developed to increase the effectiveness of the optimized parameter prediction method and reduce defects in the structure, which offered a good solution and reduced defects in the weld joint. Shaik et al. [32] studied multi-objective optimization on three properties, namely, tensile, elongation, and impact of the weld joint. The Taguchi design and GRA approach were used to design an experiment and optimal parameter condition prediction. The weld line of optimal parameter welding conditions exhibited a satisfying performance and no defect in the weld joint. However, the effectiveness of the prediction approach gave a high prediction error when comparing the result confirmation, ranging from 11-15%, as reported by Gupta et al. [38] and Kesharwani et al. [43].
The heuristic approach was used to develop the solution prediction method of the FSW process. Sharma et al. [39] presented the Taguchi design and TOPSIS approach to find the optimal parameter in a multi-objective response. The performance prediction for the weld joint showed increased accuracy in the multi-response of one optimal welding parameter that reduced the method error to 3.42%. Accordingly, Siva et al. [65] used the Taguchi experimental design and combined both GRA and TOPSIS in their improvement of the optimal welding parameters in multi-response. The prediction method showed satisfactory results and effectively controlled defects of the weld seam. Wakchaure et al. [29] presented the combined method of GRA and an artificial neural network (ANN) for optimized welding parameters of tensile strength and impact. The error of the prediction process was 3.25% of the confirmed result, and the weld line displayed high effective strength. The heuristic method of an ANN and genetic algorithm (GA) was used to optimize welding process conditions of mechanical and corrosion properties in cryorolled aluminum welding. The experiment followed the Taguchi design approach for collection of mechanical and corrosion response data. After that, the experiment data were used for the optimized prediction of the parameter process. The weld joint showed high effective mechanical and corrosion properties with an optimized welding parameter that was presented by Babu et al. [41]. However, the prediction method error was not acceptable because it was high when compared to the confirmed result. Tamjidy et al. [42] presented the prediction development for FSW using a biogeography-based optimization algorithm, including the Pareto optimal frontier approach for optimal result selection and TOPSIS and Shannon's entropy approach for decision making in solution accepting. The Pareto optimal approach offered the choice of several optimal solution predictions, which contained too many values for the desire response. However, the several optimal results could not satisfy decision making for the determinative target. The heuristic approach of TOPSIS and Shannon's entropy selected the best optimal solution in the group, resulting in a low error of 0.59%. Accordingly, Shojaeefard et al. [28] used the Pareto optimal frontiers method together with other heuristic methods in FSW, which provided highly effective optimal solution generation for multi-objective response.
Therefore, development of the heuristic method is important for decreasing error prediction. An accuracy prediction method depends on the characteristics of the heuristic algorithm. Several approach generations in one heuristic algorithm have displayed the high infallibility of the prediction method. One heuristic algorithm has exhibited very accurate solution finding, namely, the variable neighborhood strategy adaptive search (VaNSAS) approach. The VaNSAS algorithm has shown prominent solution finding on several algorithms in the improvement box. Therefore, the precision of the VaNSAS algorithm has been demonstrated by several researchers. Jirasirilerd et al. [45], Pitakaso et al. [51], and Pitakaso et al. [50] studied problem solving in production and planning with the VaNSAS algorithm. The improvement box operations to process the VaNSAS algorithm were the differential evolution algorithm, iterated local search, swap method, modified differential evolution algorithm, large neighborhood search, and shortest processing time-swap. The prediction accuracy result of the VaNSAS algorithm showed a high precision up to 99.99%, such that the error rate was 0.01% for predicted solutions. Therefore, the VaNSAS algorithm is a high accuracy approach and offers excellent result prediction. In this paper, the VaNSAS is firstly extended for use with the multi-objective decision making. The main mechanism of VaNSAS remains the same when it is applied to solving the multi-objective problem. The general procedure of VaNSAS is composed of four steps: (1) generate the initial set of solutions; (2) perform the track touring process; (3) update the heuristics information, and (4) re-do steps (2) and (3) until a termination condition is met. In the track touring process, the best solution will survive to tour in the next iteration. The weighted sum method is used to select the survival track to use in the next iteration. Then, the Pareto front is collected during the simulation, and TOPSIS is used to select the promising solution The multi-objective variable neighborhood strategy adaptive search is called MOVaNSAS.

Materials and Methods
The general steps in our proposed method include (1) identifying the number, types, and levels of the interested parameters from a literature survey and using the D-optimal experimental design to reveal the regression model to predict the target parameters for friction stir welding; (2) using MOVaNSAS to find the optimal set of parameters; and (3) performing an experiment to confirm the result obtained from (2), which is explained stepwise in the following subsection.
3.1. Identifying the Number, Types, and Levels of the Interested Parameters Using D-Optimal Experimental Design to Find the Regression Model to Predict the Target Parameters for Friction Stir Welding Table 3 shows the chemical composition of the workpiece used in our experiment. The previous research is shown in Tables 1 and 2, and the target parameter types and levels used in this research are shown in Table 4. The interested parameter types were separated into two groups: (1) continuous and (2) categorical. Each continuous parameter shows a value between code −1 and 1, as shown in Table 4. There were three continuous variables: (1) rotational speed, 1100-2200 rpm (S); (2) welding speed, 80-200 mm/min (F); and (3) tool tilt angle, 0 • -6 • (T). The two categorical variables were set as (1) tool pin profiles of cylindrical shape and hexagon shape and (2) different tool rotations of clockwise and counterclockwise directions.
The experiments were carried out according to a D-optimal experimental design (D-opt). D-opt was used to select h design points from value sets of each interested parameters by the embedding algorithm, resulting in 19 minimum model points, 5 points for estimation of the lack-of-fit, and 5 points for replicates. Finally, an experimental plan with a total of 29 points was created.
The upper and lower limits of the parameters in the statistical software Design-Expert (Stat-Ease, Inc., Minneapolis, MN, USA) were set to −1 and 1.
The intermediate coded values were calculated using Equation (1): where Scaled is the required coded value of a variable X; X is any value of the variable from X min to X Max ; and X min and X Max are the lowest and highest predefined values of the parameter, respectively. Table 4 provides the details of each uncoded parameter, which includes the upper and lower bounds of these parameters.
D-optimal software was used to design and create the experimental models and problem analysis. The quadratic model shown in Equation (2) is obtained from the experiment: where y is the ultimate tensile strength (response), x i is the uncoded levels of the variables, ε is the fitting error, the coefficient b 0 is the constant value or intercept and coefficients, and b i , b ii , and b ij represent the linear, quadratic, and interaction terms of the variables, respectively [72].

Using the Multi-Objective Variable Neighborhood Strategy Adaptive Search (MOVaNSAS) to Find the Optimal Parameters
The multi-objective variable neighborhood strategy adaptive search (MOVaNSAS) approach is a new metaheuristic to search for a solution in a large searching area. Several approaches are gathered into one method in an improvement box to search for the best solution. MOVaNSAS is composed of four steps [45], as follows.

Generate a Set of Initial Tracks
The initial set of tracks is the real number that is uniformly randomly generated from Equation (3).
where Y ij1 is the value in track i, position j at iteration 1. j is the number of interest parameters, i is the number of tracks, which is a predefined number. Y ijt is decoded as the value of rotational speed, welding speed, tool tilt angle, tool pin profile, and rotational direction using Equation (4).
where R is value of the parameter, L is the lowest allowed value of the parameter, U is the highest allowed value of the parameter, and e is the value in position (Y ijt ). For example, if Y 111 (rotation speed) is 0.36, the value of the real rotation speed is 1100 + [(0.36) × (2200 − 1100)] = 1496. The next step of MOVaNSAS is the track touring process, which is explained as follows.

Perform Track Touring Process (TTP) in a Specified Improvement Box
MOVaNSAS will use the track touring process to improve the current solution quality. In the track touring process, all tracks will independently select an improvement box to improve their quality. The improvement boxes used in this section are: (1) differential equation method (DEM), (2) best track transition method (B-TTM), track transition method (TTM), and random track transition method (R-TTM). The roulette wheel selection is used to select the improvement box with specified probability function Equation (5).
where P bt is the probability of the selection of an improvement box in iteration t; N bt−1 is the number of tracks that selected an improvement box in the previous iteration; A bt−1 is the average objective value of all tracks that selected an improvement box in the previous iteration; and I bt−1 is a reward value, increased by 1 if an improvement box finds the best solution in the last iteration, but set to 0 if this is not the case. Additionally, W bt is the weight of the improvement box, F is the scaling factor, which is set to 0.5, and K is the parameter factor, which is set to 0.3 [45]. The improvement boxes are revealed in the next section.

Improvement Box Operation
The improvement box operation step allows finding a solution from three selected approaches in each improvement box. These are as follows: This method employs the basic idea of the differential evolution algorithm. The update of Y ijt can be executed by Equation (6).
when Y ijt is the value in element of track i, position j, subiteration q. Subiteration q is the iteration that is used inside DEM at iteration t (main iteration of MOVaNSAS). Let us divide the tracks into two sets. The first set is set Z and the others are set A and set I = Z ∪ A when I is the total number of tracks. Z is the set of tracks that selects DEM as the improvement box; normally, Z has only one track, but it can also randomly pick more than one track in iteration t. A is the set of tracks that does not select DEM as the improvement box. Y njt ∈ A and Y mjt ∈ A while Y rjt ∈ Z. These vectors are randomly picked from their set of tracks. The decoding method is executed every Y ijq . Weight sum objective functions are used to select the survival track (Equation (7)).
The update of Y ijq+1 will be executed using Equation (8).
In this research, two objectives are presented; thus, there are two weight values needed for each objective in each iteration. w 1 is a randomly chosen number from 0 to 1, and w 2 is (1 − w 1 ). q is a predefined parameter that is set to 100 iterations [51]. The Pareto front is used to keep the nondominated solution from the selection process of DEM. Let us denote f 1 (y r ) and f 2 (y r ) as objective functions of objectives 1 and 2 of track r, respectively. Let R represent a set of feasible solutions, y = (y 1 , y 2 , . . . , y i ), which is the set of decision vectors, and f v (y) = ( f 1 (y), f 2 (y), . . . , f V (y)) is the set of objective functions of vector y. y will dominate y' if and only if f v (y) ≤ f v (y') for all v = 1, 2, 3, . . . , V.

Random Track Transition Method (R-TTM)
This method employs the basic idea of the transition algorithm. R-TTM uses Equation (9) to transform, while rand i is a random number from 0 to 1.
when Y hjq is a new random track (track h, position j, subiteration q) when Y hjq = U(0, 1) and CR is set to 0.9 [51].

Track Transition Method (TTM)
The existing tracks will be used to transit with the Y ijq ∪ Z while Y mjq ∪ A. Equation (10) is used to operate the TTM.
Best Track Transition Method (B-TTM) B-TTM uses Equation (11) to transform from the current solution to the new solution. Y pjt is the best track (track p) position, iteration t. The best solution is updated every time f iq is updated.
RTM, TTM, and B-TTM use the weighted sum objective function to select the survival track for subiteration q + 1 and use the Pareto front procedure to collect the nondominated solution. The number of Q (maximum number of subiterations) is set to 50-100 iterations as suggested by Pitakaso et al. [51]. After the Pareto front is obtained, TOPSIS selects the most promising set of parameters to test the performance of the heuristics compared with the D-optimal solution.
The technique for order preference by similarity to ideal solution (TOPSIS) is a technique that is widely used to select the most promising solution among all Pareto solutions. TOPSIS was first presented by Hwang and Yoon in 1981 [73]. TOPSIS starts by constructing the normal decision matrix that will transform various attribute dimensions into nondimensional attributes using Equation (12).
where I is the number of points in the Pareto front, j is a set of positive objective functions, and j is a set of negative objective functions. The next step is to calculate the normalized decision matrix using Equation (13).
where w j is the predefined parameter for the weight of each objective function. The positive (A*) and negative (A') solution matrix will be constructed using Equations (14)- (17).

Positive Ideal Solution
Negative Ideal Solution The next step is to calculate the separation measure for each alternative from both positive and negative ideal solutions using Equations (18) and (19).
Finally, the relative closeness to the ideal solution will be calculated using Equation (20), and the solution closest to 1 will be selected as the most promising solution from the Pareto front.

Update the Heuristics Information
Some heuristic information needs to be updated in order to be used in the next iterations. The update rule is shown in Table 5. Table 5. Update rule for heuristics information.

Variables
Update Procedure

N bt
Total number of tracks that select improvement box b from iteration 1 to iteration t.

A bt
Average profit value generated from improvement box b from iteration 1 to iteration t.
Update the best set of tracks if there is a better solution.

Repeat the Steps in TTP and Update the Heuristics Information until the Number of Termination Conditions Is Met
The stopping criterion here is the maximum number of iterations, which was set to 1000 (resulting from the preliminary test). The pseudocode of MOVaNSAS is shown in Algorithm 1.

The Compared Method
In this section, two well-known metaheuristics are compared with the proposed method. We used (1) a genetic algorithm (GA) and (2) a differential evolution algorithm (DE) to compare with the proposed method. We modified the DE proposed by Srichok et al. [26]. It is composed of four general steps: (1) generate an initial solution, (2) perform a mutation process, (3) perform a recombination process, and (4) perform a selection process. The second compared method is a GA, and we modified the GA proposed by Metchell and Melanie [62]. Generally, the GA is composed of four steps: (1) generate an initial solution, (2) perform a mutation procedure, (3) perform a crossover procedure, and (4) perform a selection procedure. The DE and GA that are applied with the weighted sum method for the selection process and use the Pareto front to collect the nondominated set of solutions and TOPSIS to select the most promising set of parameters are called MODE and MOGA, respectively.

Experimental Framework and Results
The computational results are divided into three parts: the result from the D-optimal experimental design, the results for the proposed problem using MOVaNSAS, and other compared methods. The results of the experiment using the parameter levels determined in the second part confirmed the reliability of the theoretical levels of the parameters.

Optimization Process by D-Optimal Experimental Design
We designed the experiment using Design-Expert software. Five controlled parameters were set: rotational speed (S), welding speed (F), tool tilt angle (T), tool pin profile, and type. We used different rotation details for the specimens, as listed in Table 6. The D-optimal experimental design produced 29 experiments, as shown in Table 7; thus, 29 specimens were prepared, as shown in Figure 1.
After the welding process was finished, the ultimate tensile strength (UTS) and maximum bending strength (MBS) were measured using a tensile test machine (model NRI-TS501-300, Narin Instruments Co. Ltd., Bangmueng Mueng, Samutprakarn, Thailand; Figure 2). The welded specimens were tested until broken, and then the UTS and MBS were recorded, as shown in Table 7.  After the welding process was finished, the ultimate tensile strength (UTS) a imum bending strength (MBS) were measured using a tensile test machine (mo . The welded specimens were tested until broken, and then the UTS and M recorded, as shown in Table 7.     Based on the experimental results in Table 7, the D-optimal experimental design software produced a regression equation showing the relationship between the variable values. The ANOVA results for the UTS showed that the model forms were acceptable as mathematical models because the p-values of the quadratic model were lower than 0.05, and the model was statistically significant with a 95% confidence interval. The mathematical model had a coefficient of determination (R 2 ) from the influence of variables equal to 95.26%, and the revised coefficient (adjusted R 2 ) was greater than 86.73%, which confirmed that the regression model obtained the right format for the above UTS response, as shown in Table 8. Four models for the UTS were formulated as follows:  The ANOVA results for the MBS are shown in Table 9. The mathematical model had a coefficient of determination (R 2 ) of 95.26% and the revised coefficient (adjusted R 2 ) from the influence of variables was equal to 86.73%. The developed mathematical model for the MBS includes four models as follows: where S, F, and T represent the rotational speed, welding speed, and tool tilt angle, respectively. The D-optimal experimental design software was used to determine the optimal solution using the regression model in Equations (21)

Results Using Multi-Objective Variable Neighborhood Strategy Adaptive Search (MOVaNSAS)
The proposed VaNSAS was coded in PyCharm (JetBrains Americas, Inc., Marlton, NJ, USA) using a PC with an Intel Core i7 3.70 GHz CPU and 8 GB DDR4 RAM. The objective function of the model was given by the D-optimal experimental design (Equations (21)-(24)) and we used VaNSAS to find the optimal solution to the problem subject of Equations (25)- (28). The ranges of the parameter values that can be applied using the D-optimal experimental design are shown in Table 10. The range of the ultimate tensile strength is not limited because it is the response of the input parameters that we aim to determine. this solution were as follows: rotational speed of 1893.30 rpm, welding speed of 167.26 mm/min, tool tilt angle of 1.610°, cylindrical pin profile, and clockwise rotation. Resulting multi-responses were UTS of 183.59 MPa and MBS of 141.71 MPa. The parameters generating this solution were as follows: rotational speed of 1995.75 rpm, welding speed of 90.72 mm/min, tool tilt angle of 4.94°, cylindrical pin profile, and counterclockwise rotation.  1100 rpm ≤ S ≤ 2200 rpm, 0 degrees ≤ T ≤ 6 degrees (31) In our experiment, the computational time was set to be the termination condition. It was set to 10 min for all proposed MOVaNSAS and compared methods (GA and DE). The Pareto fronts of all heuristics are shown in Figure Table 10 shows the compared performances of MODE, MOGA, and MOVaNSAS in finding the Pareto front. We tested the proposed methods by constructing the solution using a different number of iterations. All proposed methods used the same number of  Table 10. From the computational result, we found that MOVaNSAS gave the highest ratio, which means when we used equal iteration, MOVaNSAS gave the highest number of points in the Pareto front. The Pareto front in Table 10 was applied with TOPSIS to find the promising solution.
TOPSIS was applied to find the promising parameters using w1 and w2 = 0.5 (expertise suggestion). The results of TOPSIS for all methods are shown in Table 11, and the level of parameters obtained from the promising solution is shown in Table 12. From the computational results shown in Tables 11 and 12, the UTS and MBT of MOVaNSAS were 202.45 and 148.58 MPa, respectively. The UTS was better than MODE, MOGA, and D-opt by 5.58%, 5.15%, and 10.27%, respectively, and the MBS was better than MODE, MOGA, and D-opt by 2.23%, 2.13%, and 4.84%, respectively.

Verifying the Results by Testing Optimal Parameters with Actual Specimens
After we obtained the promising parameters from MOVaNSAS, as shown in Table 12, we performed a test and compared the results of confirmed experiments with the calculated MOVaNSAS results in order to check if the parameter values generated by VaNSAS could form a welded material with the UTS and MBS. Twelve replications were conducted, and the average ultimate tensile strength and average maximum bending strength were recorded, as shown in Table 13. In addition, the high performance of the weld line could be observed from the relationship between tensile strength and ductile property. The ductile property is considered from the elongation percentage by tensile testing. The elongation percentage or ductile value of the weld line shows a maximum elongation of 14.4% before damaging the weld line, as shown in Figure 7. 14.4% before damaging the weld line, as shown in Figure 7. The difference in verifying the result and prediction value can be calculated by Equation (32): where / is the UTS or MBT generated by the experiment and / MOVaNSAS is the UTS or MBT generated by MOVaNSAS. The average UTS and MBT obtained from our experiment were 0.208% and 0.324% better, respectively, than the original values. Next, we explain the microstructure of the material from the experiment specimens.

Microstructure Analysis
The defect formation and microstructure were analyzed by three approaches: optical microscope (OM), scanning electron microscope (SEM), and EDX-ray spectroscopy. For the welding, the optimized parameter conditions were rotation speed of 1469.44 rpm, welding speed of 80.35 mm/min, tilt angle of 1.01°, cylindrical tool, and clockwise direction, which resulted in no groove defects or discontinuity. The full weld seam of the welding parameters from MOVaNSAS shows the weld line without defects, as shown in Figure  8a, due to the optimal welding conditions of MOVaNSAS, including suitable relational parameters during tool rotation speed and welding speed at a ratio of 18.62. This relational ratio is not over a ratio of 50 and not over a heat level in FSW, showing smooth-surface weld joints without groove defects on the surface [8,[74][75][76][77].
The microstructural result of the optimized welding parameters exhibited a changing structural deformation in the weld joint area that was transferred from the FSW process The difference in verifying the result and prediction value can be calculated by Equation (32): where UTS/MBT Exp is the UTS or MBT generated by the experiment and UTS/MBT MOVaNSAS is the UTS or MBT generated by MOVaNSAS. The average UTS and MBT obtained from our experiment were 0.208% and 0.324% better, respectively, than the original values. Next, we explain the microstructure of the material from the experiment specimens.

Microstructure Analysis
The defect formation and microstructure were analyzed by three approaches: optical microscope (OM), scanning electron microscope (SEM), and EDX-ray spectroscopy. For the welding, the optimized parameter conditions were rotation speed of 1469.44 rpm, welding speed of 80.35 mm/min, tilt angle of 1.01 • , cylindrical tool, and clockwise direction, which resulted in no groove defects or discontinuity. The full weld seam of the welding parameters from MOVaNSAS shows the weld line without defects, as shown in Figure 8a, due to the optimal welding conditions of MOVaNSAS, including suitable relational parameters during tool rotation speed and welding speed at a ratio of 18.62. This relational ratio is not over a ratio of 50 and not over a heat level in FSW, showing smooth-surface weld joints without groove defects on the surface [8,[74][75][76][77].
of SSM-ADC12 aluminum material. After FSW, the grain of the weld seam showed changes in the grain size from the base material to the welding zone, as shown in Figure  8b. The grain size in the welding zone is on average 10 µ m, decreasing from the base material by 75%. The weld line structure displayed a difference in deformation in the retreating side (RS) and advancing side (AS), as shown in Figure 9. The thermomechanical affected zone (TMAZ) affected tool stirring and heat in the process. The observed characteristics of the microstructure in the TMAZ-RS and TMAZ-AS were material deformations from the mechanical force of tool stirring and the heat expanding effect in welding. The tool stirring and heat effect in the welding process incurred material flow in the rotational direction and structural deformation. Therefore, the TMAZ-RS and TMAZ-AS areas exhibited differences in the microstructure of the base material that are shown in Figure 9d,e. Whereas the stir zone (SZ) showed a sound weld joint, the interweave material flow and homogeneous material mixing led to recrystallization and structural completeness without defects in the weld joint. The SZ structures of both the top and bottom zones are shown in Figure  9b,c. The base material (BM) area exhibited slight changes in grain growth because of the heat of the welding processes that generated high heat during joint welding, and the heat extended from the TMAZ to the BM area. Therefore, some microstructures in the BM changed in the intimate zone of the TMAZ without difficulty. Characteristics of nearby structures of the original material are displayed in Figure 9a,f.
The weld line of the optimized conditions from D-optimal showed a microdefect in the TMAZ (Figure 10d,e). The SZ displayed a fine grain, but inhomogeneous material in Figure 10b,c. The greater degree of the tool tilt angle caused the material to flow and mix in the weld seam. In addition, the TMAZ of both RS and AS exhibited material deformation and extended grain following the rotational direction that effectively increased the dislocation of equiaxed grains. Although increased dislocation density increased the weld line strength, the microvoid defect appearing in the structure was a problem of reduced tensile and bending strength. Therefore, the weld seam from the D-optimal prediction gave lower tensile and bending strength than the MOVaNSAS prediction. The microstructure of the best initial experiment showed a large void and a crack defect in the SZ (Figure  11b,c). The structure in the weld line is not homogenous and has a less fine grain than The microstructural result of the optimized welding parameters exhibited a changing structural deformation in the weld joint area that was transferred from the FSW process of SSM-ADC12 aluminum material. After FSW, the grain of the weld seam showed changes in the grain size from the base material to the welding zone, as shown in Figure 8b. The grain size in the welding zone is on average 10 µm, decreasing from the base material by 75%.
The weld line structure displayed a difference in deformation in the retreating side (RS) and advancing side (AS), as shown in Figure 9. The thermomechanical affected zone (TMAZ) affected tool stirring and heat in the process. The observed characteristics of the microstructure in the TMAZ-RS and TMAZ-AS were material deformations from the mechanical force of tool stirring and the heat expanding effect in welding. The tool stirring and heat effect in the welding process incurred material flow in the rotational direction and structural deformation. Therefore, the TMAZ-RS and TMAZ-AS areas exhibited differences in the microstructure of the base material that are shown in Figure 9d,e. Whereas the stir zone (SZ) showed a sound weld joint, the interweave material flow and homogeneous material mixing led to recrystallization and structural completeness without defects in the weld joint. The SZ structures of both the top and bottom zones are shown in Figure 9b,c. The base material (BM) area exhibited slight changes in grain growth because of the heat of the welding processes that generated high heat during joint welding, and the heat extended from the TMAZ to the BM area. Therefore, some microstructures in the BM changed in the intimate zone of the TMAZ without difficulty. Characteristics of nearby structures of the original material are displayed in Figure 9a,f.
The weld line of the optimized conditions from D-optimal showed a microdefect in the TMAZ (Figure 10d,e). The SZ displayed a fine grain, but inhomogeneous material in Figure 10b,c. The greater degree of the tool tilt angle caused the material to flow and mix in the weld seam. In addition, the TMAZ of both RS and AS exhibited material deformation and extended grain following the rotational direction that effectively increased the dislocation of equiaxed grains. Although increased dislocation density increased the weld line strength, the microvoid defect appearing in the structure was a problem of reduced tensile and bending strength. Therefore, the weld seam from the D-optimal prediction gave lower tensile and bending strength than the MOVaNSAS prediction. The microstructure of the best initial experiment showed a large void and a crack defect in the SZ (Figure 11b,c). The structure in the weld line is not homogenous and has a less fine grain than both structures of the D-optimal approach and the MOVaNSAS approach in the SZ. Moreover, the material deformation from stirring appears as large equiaxed grains in the TMAZ (see Figure 11d,e), which have a low density of grain dislocation. Therefore, this welding condition gave lower tensile and bending strength than the optimal condition of the D-optimal approach and MOVaNSAS. both structures of the D-optimal approach and the MOVaNSAS approach in the SZ. Moreover, the material deformation from stirring appears as large equiaxed grains in the TMAZ (see Figure 11d,e), which have a low density of grain dislocation. Therefore, this welding condition gave lower tensile and bending strength than the optimal condition of the D-optimal approach and MOVaNSAS.   both structures of the D-optimal approach and the MOVaNSAS approach in the SZ. Moreover, the material deformation from stirring appears as large equiaxed grains in the TMAZ (see Figure 11d,e), which have a low density of grain dislocation. Therefore, this welding condition gave lower tensile and bending strength than the optimal condition of the D-optimal approach and MOVaNSAS.   The consideration of phase in structure was evaluated by SEM for each optimal welding parameter. The weld joint structure of the MOVaNSAS approach displayed an Al 5 FeSi intermetallic compound phase in the SZ that appears to be split into large particle sizes and uniform distribution. The Al 5 FeSi intermetallic compounds were separated by tool stirring and by bumping into the tool tilt angle. Regarding rotation speed and welding speed, a suitable ratio was useful in the material flow and uniform distribution of intermetallic particles. The particle size of the Al 5 FeSi phase was smaller than 10 µm and had a spiky appearance that is shown in Figure 12b,c. The β-Al 5 FeSi phase had smaller fine particles than the Al 5 FeSi phase and uniform dispersion that produced a density of dislocation. Therefore, the density of the Al 5 FeSi and β-Al 5 FeSi phases could improve the mechanical properties of tensile and bending strength. In the same way, the TMAZ indicated that the Al 5 FeSi phase had a long shape that was small, as well. The Al 5 FeSi phase in the TMAZ showed a larger size than the Al 5 FeSi phase in the SZ because of low heat energy and deformation of low material in the TMAZ (Figure 12d,e). Thus, the TMAZ areas were appearing as a weaker mechanical property than SZ. Moreover, the BM of the SSM-ADC12 aluminum alloy showed the largest Al 5 FeSi phase, which was larger than the other zones in the structural weld joint, as seen in Figure 12a,f. The arrangement of the Al 5 FeSi phase had a smooth and even distribution. The Al 5 FeSi phase was rod-shaped and arranged along the grain boundary of the material. The consideration of phase in structure was evaluated by SEM for each optimal welding parameter. The weld joint structure of the MOVaNSAS approach displayed an Al5FeSi intermetallic compound phase in the SZ that appears to be split into large particle sizes and uniform distribution. The Al5FeSi intermetallic compounds were separated by tool stirring and by bumping into the tool tilt angle. Regarding rotation speed and welding speed, a suitable ratio was useful in the material flow and uniform distribution of intermetallic particles. The particle size of the Al5FeSi phase was smaller than 10 µm and had a spiky appearance that is shown in Figure 12b,c. The β-Al5FeSi phase had smaller fine particles than the Al5FeSi phase and uniform dispersion that produced a density of dislocation. Therefore, the density of the Al5FeSi and β-Al5FeSi phases could improve the mechanical properties of tensile and bending strength. In the same way, the TMAZ indicated that the Al5FeSi phase had a long shape that was small, as well. The Al5FeSi phase in the TMAZ showed a larger size than the Al5FeSi phase in the SZ because of low heat energy and deformation of low material in the TMAZ (Figure 12d,e). Thus, the TMAZ areas were appearing as a weaker mechanical property than SZ. Moreover, the BM of the SSM-ADC12 aluminum alloy showed the largest Al5FeSi phase, which was larger than the other zones in the structural weld joint, as seen in Figure 12a,f. The arrangement of the Al5FeSi phase had a smooth and even distribution. The Al5FeSi phase was rod-shaped and arranged along the grain boundary of the material.
The weld joint structure of the D-optimal approach exhibited lower β-Al5FeSi intermetallic phase dispersion than the structure of the MOVaNSAS approach in the SZ. The Al5FeSi intermetallic compounds exhibited large particles and low distribution when compared with the MOVaNSAS approach, as shown in Figure 13b,c. Moreover, the SZ area displayed microcracking and microvoids in the TMAZ of AS, which led to weakness in the weld line. The microstructure of the best initial experiment displayed the largest void defect and cracking in the SZ and TMAZ, as shown in Figure 14. In addition, the β-Al5FeSi intermetallic phase was not uniformly dispersed, as observed in Figure 14b,c.
The concentration of the alloying elements in the SZ was evaluated by EDX-ray spectroscopy. The weld seam structure of the MOVaNSAS approach was checked for the elemental composition of the Al5FeSi phase of new crystallization and intermetallic compound formation. The Al5FeSi phase change in particle size and distribution of phase was influenced by the heat input and experimental parameters. The Al5FeSi phase formed from the Mg2Si phase because the Fe element separated the Mg2Si phase formation, as shown in Figure 15.  The weld joint structure of the D-optimal approach exhibited lower β-Al 5 FeSi intermetallic phase dispersion than the structure of the MOVaNSAS approach in the SZ. The Al 5 FeSi intermetallic compounds exhibited large particles and low distribution when compared with the MOVaNSAS approach, as shown in Figure 13b,c. Moreover, the SZ area displayed microcracking and microvoids in the TMAZ of AS, which led to weakness in the weld line. The microstructure of the best initial experiment displayed the largest void defect and cracking in the SZ and TMAZ, as shown in Figure 14. In addition, the β-Al 5 FeSi intermetallic phase was not uniformly dispersed, as observed in Figure 14b,c.        The concentration of the alloying elements in the SZ was evaluated by EDX-ray spectroscopy. The weld seam structure of the MOVaNSAS approach was checked for the elemental composition of the Al 5 FeSi phase of new crystallization and intermetallic compound formation. The Al 5 FeSi phase change in particle size and distribution of phase was influenced by the heat input and experimental parameters. The Al 5 FeSi phase formed from the Mg 2 Si phase because the Fe element separated the Mg 2 Si phase formation, as shown in Figure 15.
The heat input during FSW was in the range of 330-520 • C. Thus, it was possible for the formation of the Al 8 Fe 2 Si and Al 4 FeSi 2 phases, which had favorable solubility in solid solution at high temperature. It is worth noting that the O element occurred during welding, resulting in a new compound phase. The O element led to Al 2 O 3 and SiO 2 phase formation, which were widely dispersed according to the analysis. The Al 2 O 3 and SiO 2 phases were resistant to tensile and bending forces as well, but both phases were increasingly embedded in the material and reduced the prominence of mechanical properties such as elongation and ductile property. Therefore, a decrease in certain mechanical properties may lead to fracture of the weld seams. The heat input during FSW was in the range of 330-520 °C. Thus, it was possible for the formation of the Al8Fe2Si and Al4FeSi2 phases, which had favorable solubility in solid solution at high temperature. It is worth noting that the O element occurred during welding, resulting in a new compound phase. The O element led to Al2O3 and SiO2 phase formation, which were widely dispersed according to the analysis. The Al2O3 and SiO2 phases were resistant to tensile and bending forces as well, but both phases were increasingly embedded in the material and reduced the prominence of mechanical properties

Conclusions
With this research, we aimed at finding the optimal welding parameters to maximize the ultimate tensile and bending strength in FSW of SSM-ADC12. The optimal welding conditions for prediction with the MOVaNSAS algorithm were a rotation speed of 1469.44 rpm, welding speed of 80.35 mm/min, tilt angle of 1.01 • , a cylindrical pin tool, and a clockwise rotational direction. This condition gave the highest UTS of 202. 45 MPa, and MBS of 148.58 MPa. The optimal welding conditions were tested for accuracy and reliability by performing the experiment, and the result showed differences of 0.203% and 0.287% for UTS and MBS, respectively. MOVaNSAS predicted UTS better than MODE, MOGA, and D-opt by 5.58%, 5.15%, and 10.27%, respectively, while it predicted MBS better than MODE, MOGA, and D-opt by 2.23%, 2.13%, and 4.84%, respectively. From this result, we can confirm that MOVaNSAS is an effective algorithm to predict the optimal parameters of the target material. The weld line structure in the optimal welding parameters showed no defect or precipitation of the small intermetallic phases Al 5 FeSi and β-Al 5 FeSi with uniform distribution. The intermetallic phase uniform dispersion led to a phenomenon of a dislocation strength mechanism, which increased both the tensile and bending mechanical properties.
However, use of the weld joint will require several properties from usable milieu. Therefore, a weld seam should have several supplementary properties in the weld joint, especially impact resistance, which is one of the most important mechanical properties of the weld line.