Multi-Objective Optimization of Friction Stir Processing Tool with Composite Material Parameters

Abstract

Compared to base aluminum alloys, the surface composites of aluminum alloys are more widely used in the automotive, aerospace, and other industries. The ability to yield enhanced physical properties and a smoother microstructure has made friction stir processing (FSP) the method of choice for developing aluminum-based surface composites in recent times. In this work, the Goal Programming (GP) approach is adopted for the Multi-Objective Optimization of FSP processes with three Artificial Intelligence (AI)-based metaheuristics, viz., Artificial Bee Colony (ABC), Particle Swarm Optimization (PSO), and Teaching–Learning-Based Optimization (TLBO). Three parameters, copper percentage (Cu%), graphite percentage (Gr%), and number of passes, are considered, and multi-factor non-linear regression prediction models are developed for the three responses, Tool Vibrations, Power Consumption, and Cutting Force. The TLBO algorithm outperformed the ABC and PSO algorithms in terms of solution quality and robustness, yielding significant improvements in tool life. The results with TLBO were improved by 20% and 14% compared to the PSO and ABC algorithms, respectively. This proves that the TLBO algorithm performed better compared with the ABC and PSO algorithms. However, the computation time required for the TLBO algorithm is higher compared to the ABC and PSO algorithms. This work has opened new avenues towards applying the GP approach for the Multi-Objective Optimization of FSP tools with composite parameters. This is a significant step towards toll life improvement for the FSP of composite alloys, contributing to sustainable manufacturing.

1. Introduction

Aluminum alloys are widely used in many different industries, including manufacturing, shipbuilding, automotive, aerospace, and maritime. This is because of their excellent resistance to corrosion, high strength-to-weight ratio, and high electrical and thermal conductivity. Aluminum alloys can be made into surface composites with ceramic reinforcements, such as TiO₂, Al₂O₃, TiC, etc., to overcome the inferior surface wear resistance of aluminum alloys [1]. These surface composites maintain the bulk material’s modest weight while exhibiting outstanding surface hardness and wear behavior. Aluminum-alloy-based composites with reinforcements for improved surface qualities are produced using friction stir processing (FSP). Through localized plastic deformation, FSP can alter the characteristics of the material [2]. Friction Stir Welding (FSW) is the procedure from which it is derived. The particular tool that is not consumed during the process and utilized in FSP/FSW is fabricated as a cylindrical shape, referred to as a shoulder, with a needle-like-shaped profile, often having a 3:1 shoulder-to-pin diameter. The FSP tool is moved closer to the workpiece until the shoulder surface passes over it laterally in a route and the pin enters the workpiece’s surface. The material surrounding the tool pin is stirred, which improves the mechanical characteristics and uniformly refines the grains [3]. When aluminum matrices are filled with the appropriate reinforcements, surface composites are created. Following this, FSP is applied to the strengthened surfaces [4].

Numerous researchers have employed various methodologies to analyze factors while fabricating surface composites. A few writers [5] looked into how the Al6061 alloy was made during FSP. The number of FSP passes, the kinds of reinforcements, and the material’s post-treatments were discovered to have an impact on the microstructural and physical properties of the manufactured surface composites. The maximum hardness, tensile strength, and elongation percentage were optimized by the authors using the Taguchi method. ANOVA was also used to determine which parameter had the biggest impact on the output answers. It was determined that the use of Al₂O₃ as reinforcement increases the surface hardness and tensile strength of surface composites. Furthermore, the hardness was enhanced by the third-pass FSP and the post-heat-treated Al6061 (T6). Using the Taguchi approach, the researchers enhanced the friction stir processing parameters—such as the feed rate, number of FSP passes, and tool rotation speed—to increase the composites’ hardness. The effects on the composites’ properties, such as microstructure and wear rate, based on aluminum alloys with varying percentages of reinforcement (by volume), were examined in a distinct study [6]. SEM, XRD, hardness testing, and wear testing were used to assess the composite materials. It was found that the hardness, density, and wear resistance of the resulting composites are all increased by the quantity of reinforcement incorporated into the aluminum alloy matrix. A few studies looked into how process factors affected processed (FSP)MgAZ31B sheets’ formability with the tensile testing environment. The settings were tuned with the ANOVA approach [7]. Furthermore, the researchers created an empirical model to evaluate the link between the parameters and formability. A similar effort was attempted to optimize the input parameters of the Friction-Stir-Processed Al6061/TiB2. That study investigated how input parameters such as reinforcement percentage, speed, RPM, and lodgings impact FESEM image and surface attributes. Taguchi (one variable) and Grey Relational Analysis (multivariable) were adopted to optimize process parameters [8]. For the composites’ wear, parameter optimization was also carried out. A team of researchers applied a wear test for a composite of epoxy resin with fly ash, adopting the Taguchi method [9]. The DoE approach was studied to investigate the influence of the factors of lowest wear and frictional force. The tool RPM, feed, tilt angle, and depth of penetration of the hardness of the Mg alloy were found to be significant parameters using the Taguchi optimization approach and signal-to-noise (S/N) ratio analysis [10]. The optimization of process parameters for the FSP of alloys has been a topic of research recently [11,12,13,14]. Furthermore, the optimization of FSP with the effect of adding nano particles was investigated in [15,16].

It is evident from the literature that research is concentrated on the wear analysis of composites and their microstructural analysis, as well as process parameter optimization in FSP. Nevertheless, there is little research on the parametric optimization of hybrid surface composites made with in situ and ex situ reinforcements and the microstructural characterization of the reinforcements, which are produced utilizing the FSP technique to enhance tool life. This work focuses on adopting the Goal Programming (GP) approach for the Multi-Objective Optimization of cutting tool life for the FSP process with three Artificial Intelligence (AI)-based metaheuristics, namely Artificial Bee Colony (ABC), Particle Swarm Optimization (PSO), and Teaching–Learning-Based Optimization (TLBO), for the FSP of Al6061-based hybrid composites reinforced with copper and graphite microparticles mixed in different weight percentages (1:1 by weight).

Goal Programming (GP) is a mathematical modeling technique which is based on minimizing deviations from the set goals. Initially, GP is introduced as an extension of Linear Programming (LP) problems for handling multiple objectives; however, over the past years, GP has evolved for solving non-linear problems as well. It is based on the philosophy of satisficing. The concept of satisficing was coined by Herbert Simon in 1957 [17]. It is based on two verbs, viz., ‘satisfy’ and ‘suffice.’ It is also a goal-based approach wherein Decision Maker (DM) is aimed to achieve set targets/goals. If these goals are achieved, then it would be a sufficient condition for the DM, hence satisfying DM as well. The handbook of GP was published by Jones and Tamiz in 2010 [18], which presented a complete summary of GP work. Generally, three types of analysis are performed with GP, such as resource planning, allocation, and leveling, wherein the focus is on controlling the required resources to achieve the set goals, marking the accomplishment of goals with the available resources, and achieving the satisficing solution with uncertainty and goal priorities. In the GP approach, every individual objective function is considered as a goal, and target values are defined. Further, deviation from each of the goals is fixed, and the sum of deviations is defined. GP takes this sum of deviations as an objective function in the context of the GP problem formulation and tries to minimize it. The conceptual difference between the classical optimization approach and the GP approach is that, in GP, the focus is on satisfying the deviations for every goals rather than minimizing the individual objective function. It is evident from the literature that a variety of problems, such as non-convex, linear, non-linear, etc., are effectively formulated with the GP approach [19,20,21]. Hence, the GP approach is adopted in the current work.

In this work, the GP approach is adopted for the Multi-Objective Optimization of the FSP process with three AI-based metaheuristics, viz., ABC, PSO, and TLBO. Three parameters, such as copper percentage (Cu%), graphite percentage (Gr%), and number of passes, are considered, and multi-factor non-linear regression prediction models are developed for the three responses—Tool Vibrations, Power Consumption, and Cutting Force.

The remainder of this paper is organized as follows: Section 2 describes the mathematical modeling for the three responses—Tool Vibrations, Power Consumption, and Cutting Force. The GP problem formulation is discussed in Section 3. Three algorithms, such as ABC, PSO, and TLBO, are presented in Section 4. Section 5 discusses the results, and the conclusions are presented in Section 6.

2. Mathematical Modeling

The Al6061 alloy is used as the matrix material in the surface composite fabrication process. Microparticles of graphite and copper are combined to prepare the reinforcement for the manufacturing of hybrid composites. The literature states that copper and the Al6061 alloy combine to generate a potent intermetallic combination. For this reason, it is chosen as the in situ reinforcement for composites based on Al6061. Graphite, on the other hand, is chosen as the ex situ reinforcement for the surface composite fabrication because it functions as a solid lubricant and gives the composite its lubricating qualities, minimizing wear. A specific amount of ethanol is added to the mixture of ground copper and graphite particles to create a slurry. The Al6061-T6 alloy plates of a size of 100 mm × 30 mm × 20 mm are purchased from Shree Balaji Steel House, Bhosari, Pune, India. The reinforcement for hybrid composite fabrication is prepared by mixing copper and graphite microparticles. The Al6061 matrix plates have holes drilled in them, and this slurry is used to fill them in at three different weight percentages—2%, 4%, and 6%. H13 tool steel was chosen as the tool material for FSP based on the literature review. A VMC machine of the Symbiosis Institute of Technology in Pune, India, is used for FSP. One by one, the FSP tools are placed on a tool holder to create the composites. The composites are manufactured using a milling machine with the following set parameters for each reinforcement weight percentage (2%, 4%, and 6%) and tool: 1400 rpm, 40 mms—1 linear speed, 5 mm depth of cut which is equal to the pin length, and path = 80 mm. These parameters are set based on the literature review, trial experimentations, and machine specifications. The FSP set-up photograph is shown in Figure 1a, and an AutoCAD drawing of the set-up is shown in Figure 1b with the three tool diameters. The photograph of the friction-stir-processed samples is shown in Figure 1c.

For the experimentation, the copper percentage (Cu%), graphite percentage (Gr%), and number of tool passes are considered as parameters. In total, 27 combinations of parameters are experimented. Vibrations generated on spindle (in dB), current (in amperes), and cutting forces (in N) generated in three directions, viz., x, y, and z, are measured with in-built sensors such as load sensors and piezo electric sensors. Figure 2 presents the force measurement coordinate system. The resultant cutting force is calculated as a Root Mean Square (RMS) of cutting forces as per the industry standard.

Table 1. Experimental results.

Sr. No.	Cu%	Gr%	Number of Passes	Vibration_Spindle	Current	Load_X	Load_Y	Load_Z	Resultant Force
1	1	1	2	4.545	4.568	0.552	0.205	0.261	0.644
2	1	1	2	4.545	4.561	0.13	2.959	0.035	2.962
3	1	1	2	4.261	0.231	0.093	0.005	0.001	0.094
4	1	2	3	4.616	0.226	2.325	0.003	0.63	2.409
5	1	2	3	4.616	0.184	0.179	2.88	0.357	2.907
6	1	2	3	4.617	0.206	2.333	0.003	1.002	2.539
7	1	3	4	4.447	0.232	0.585	0.004	0.184	0.613
8	1	3	4	4.447	0.231	1.46	1.535	0.113	2.121
9	1	3	4	4.448	0.232	1.071	0.02	0.248	1.1
10	2	1	3	4.619	0.19	1.012	0.003	1.838	2.098
11	2	1	3	4.618	0.202	0.49	2.315	0.918	2.538
12	2	1	3	4.617	0.207	0.56	0.004	0.749	0.935
13	2	2	4	4.542	4.576	0.891	0.003	0.675	1.118
14	2	2	4	4.541	4.564	0.081	2.24	0.348	2.268
15	2	2	4	4.543	4.572	1.413	0.012	0.496	1.498
16	2	3	2	4.45	4.587	0.233	0.003	1.385	1.405
17	2	3	2	4.543	4.57	0.003	0.003	0.998	0.998
18	2	3	2	4.543	4.57	0.494	2.339	0.445	2.432
19	3	1	4	4.624	4.643	0.35	0.52	0.431	0.761
20	3	1	4	4.624	4.651	0.3	2.238	0.213	2.268
21	3	1	4	4.624	4.645	1.063	0.003	0.662	1.252
22	3	2	2	4.45	4.53	0.556	1.141	0.713	1.456
23	3	2	2	4.51	4.531	0.003	0.045	1.524	1.525
24	3	2	2	4.499	4.531	0.153	3.024	0.267	3.039
25	3	3	3	4.62	0.192	0.087	0.003	0.722	0.727
26	3	3	3	4.621	0.198	2.4	1.337	0.635	2.82
27	3	3	3	4.546	4.577	2.85	1.197	0.842	3.204

presents the experimental results. Further, the multi-factor non-linear regression model is developed for three objectives, viz., Tool Vibrations, Power Consumption, and Cutting Force, generated while machining. Power Consumption is calculated as a product of voltage and current. In this study, the input voltage is assumed to be constant, and hence the power consumed during machining is directly corelated with the current drawn. Three independent variables such as copper percentage (Cu%), graphite percentage (Gr%), and number of passes are considered which are presented as $x_1,x_2, \mathrm{a}\mathrm{n}\mathrm{d}{x}_3$, respectively.

2.1. Modeling for Tool Vibrations

As discussed earlier, the tool is mounted on the spindle. The vibrations generated on the spindle are referred to as tool vibrations and are mathematically modeled. Equation (1) presents the mathematical equation for tool vibration. The R-Sq value obtained here is 86%. The tool vibrations are to be minimized.

$$\begin{array}{ll}Tool Vibration& =3.38+\left(0.07\right)\ast Cu+\left(0.32\right)\ast Gr+\left(0.58\right)\\ & \ast Number of Passes+\left(-0.03\right)\ast C{u}^2+\left(-0.08\right)\ast Cu\ast Gr\\ & +\left(0.08\right)\ast Cu\ast Number of Passes+\left(-0.05\right)\ast G{r}^2\\ & +\left(0.02\right)\ast Gr\ast Number of Passes+\left(-0.13\right)\\ & \ast {Number of Passes}^2\end{array}$$

(1)

2.2. Modeling for Power Consumption

The power consumption is referred to from the current generated during the machining. Generally, the power is calculated as Voltage ∗ Current. Since the voltage is constant, the power consumed is directly proportional to the current measurement. Equation (2) presents the mathematical equation for power consumption. The R-Sq value obtained here is 99%. The power consumed during machining is to be minimized.

$$\begin{array}{l}Power Consumption\\ & =26.54+\left(-6.25\right)\ast Cu+\left(0.38\right)\ast Gr+\left(-14.99\right)\\ & \ast Number of Passes+\left(1.26\right)\ast {Cu}^2+\left(3.92\right)\ast Cu \ast Gr\\ & +\left(-2.46\right)\ast Cu \ast Number of Passes+\left(0.54\right)\ast Gr2\\ & +\left(-3.95\right)\ast Gr \ast Number of Passes+\left(4.89\right)\\ & \ast { Number of Passes}^2\end{array}$$

(2)

2.3. Modeling for Cutting Force

The cutting forces generated during machining are measured along with three directions with inbuilt sensors. Further, the resultant force is calculated as an RMS value. Equation (3) presents the mathematical equation for cutting force. The R-Sq value obtained here is 88%. The cutting forces during machining are to be minimized.

$$\begin{array}{ll}Cutting Forces& =-7.36+\left(1.45\right)\ast Cu+\left(1.86\right)\ast Gr+\left(5.07\right)\\ & \ast Number of Passes+\left(-0.19\right)\ast C{u}^2+\left(-0.75\right)\ast Cu\ast Gr\\ & +\left(0.38\right)\ast Cu\ast Number of Passes+\left(-0.47\right)\ast G{r}^2\\ & +\left(0.56\right)\ast Gr\ast Number of Passes+\left(-1.26\right)\\ & \ast {Number of Passes}^2\end{array}$$

(3)

3. Goal Programming Problem Formulation

As discussed earlier, in the GP approach, the deviation from the set goal is defined, and the sum of the deviations is minimized. In this work, the penalty function approach is adopted to handle the goal constraints. In this section, the GP formulation is described. The pseudo-objective function y is defined. The goals of three objective functions, viz., Current, Tool Vibrations, and Cutting Force, are set based on the experimental results.

$$Function y=Predict\left(x\right)$$

$$\begin{array}{ll}Current=26.54& +\left(-6.25\right)\ast Cu+\left(0.38\right)\ast Gr+\left(-14.99\right)\\ & \ast Number of Passes+\left(1.26\right)\ast {Cu}^2+\left(3.92\right)\ast Cu \ast Gr\\ & +\left(-2.46\right)\ast Cu \ast Number of Passes+\left(0.54\right)\ast Gr2\\ & +\left(-3.95\right)\ast Gr \ast Number of Passes+\left(4.89\right)\\ & \ast { Number of Passes}^2\end{array}$$

$$\begin{gathered} if Current \le 0.20 \\ Current\text{\_}minus=0; \\ Currentpen=0; \\ else \\ Current\text{\_}minus=0.20-Current; \\ Currentpen={Current\text{\_}minus}^2; \\ end \end{gathered}$$

$$\begin{array}{ll}Cutting Forces& =-7.36+\left(1.45\right)\ast Cu+\left(1.86\right)\ast Gr+\left(5.07\right)\\ & \ast Number of Passes+\left(-0.19\right)\ast C{u}^2+\left(-0.75\right)\ast Cu\ast Gr\\ & +\left(0.38\right)\ast Cu\ast Number of Passes+\left(-0.47\right)\ast G{r}^2+\left(0.56\right)\ast Gr\\ & \ast Number of Passes+\left(-1.26\right)\ast {Number of Passes}^2\end{array}$$

$$\begin{gathered} if Force \ge 0.50 \\ Force\text{\_}plus=Force-0.50; \\ Forcepen= {Force\text{\_}plus}^2; \\ else \\ Force\text{\_}plus=0; \\ Forcepen=0; \\ end \end{gathered}$$

$$\begin{array}{ll}Tool Vibration& =3.38+\left(0.07\right)\ast Cu+\left(0.32\right)\ast Gr+\left(0.58\right)\ast Number of Passes\\ & +\left(-0.03\right)\ast C{u}^2+\left(-0.08\right)\ast Cu\ast Gr+\left(0.08\right)\ast Cu\\ & \ast Number of Passes+\left(-0.05\right)\ast G{r}^2+\left(0.02\right)\ast Gr\\ & \ast Number of Passes+\left(-0.13\right)\ast {Number of Passes}^2\end{array}$$

$$\begin{gathered} if Tool\text{\_}Vibrations \ge 4.2 \\ Tool\text{\_}Vibrations\text{\_}plus=Tool\text{\_}Vibrations-4.2; \\ Too{l}_{Vibrationspen}={Tool\text{\_}Vibrations\text{\_}plus}^2; \\ else \\ Tool\text{\_}Vibrations\text{\_}plus=0; \\ Tool\text{\_}Vibrationspen=0; \\ End \end{gathered}$$

$$\begin{gathered} y=Current\text{\_}minus+Force\text{\_}plus+Tool\text{\_}Vibrations\text{\_}plus+1000 \\ \ast (Currentpen+Forcepen +Tool\text{\_}Vibrationspen); \end{gathered}$$

4. Methodology

As discussed earlier, in this work, three AI-based optimization algorithms, viz., ABC, PSO, and TLBO, are adopted for solving the GP problem.

4.1. Artificial Bee Colony

The Artificial Bee Colony (ABC) optimization technique [22] solves difficult optimization problems by mimicking honeybees’ foraging behaviors. In this method, a virtual population of bees is separated into three types: employed bees, bystanders, and scouts, with each having a unique role in exploring and utilizing the solution space. Employed bees provide information about food sources, representing prospective solutions, while observers assess their quality. When a food supply is depleted, scouts seek to find new options at random, ensuring a diverse exploration. This collaborative method enables the ABC algorithm to rapidly navigate multidimensional environments, making it ideal for a variety of engineering, logistics, and machine learning applications.

In the employed bee phase, each bee explores a food source represented by a solution $x_i$ and evaluates its fitness $f \left(x_i\right)$.

The employed bees generate new solutions in the neighborhood of their current food sources using the following equation:

$$x_j=x_i+{\varnothing }_{ij} (x_i-x_k)$$

(4)

where ${\varnothing }_{ij}$ is a random number in the range [−1,1], and $x_k$ is a randomly chosen food source from the colony.

In the onlooker phase, the selection of food sources is based on their fitness, calculated as follows:

$$p_i={\displaystyle \frac{f \left(x_i\right)}{{\sum }_{j=1}^{n}f \left(x_i\right)}}$$

(5)

If a food source does not improve after a predefined number of iterations, it is abandoned, and the scout bee searches for a new food source randomly as follows:

$$x_s=xmin+r\cdot (xmax-xmin)$$

(6)

where $r$ is a random number in [0, 1], and $xmin, xmax$ define the boundaries of the search space.

This collaborative approach allows the ABC algorithm to efficiently navigate multidimensional landscapes, making it particularly effective for various applications in engineering, logistics, and machine learning. Its balance of exploration and exploitation is crucial for tackling diverse optimization challenges. Figure 3 presents the flowchart of the ABC algorithm.

4.2. Particle Swarm Optimization

The Particle Swarm Optimization (PSO) algorithm [23] is a population-based optimization technique inspired by the social behavior of birds and fish. In PSO, potential solutions, known as particles, move through the solution space, adjusting their positions based on their own experiences and those of their neighbors. Each particle maintains its velocity, which is updated using two key components: the particle’s best-known position $p_i$ and the global best position $g$ found by the swarm. The velocity update equation can be expressed as follows:

$$v_i \left(t+1\right)=\omega ·v_i\left(t\right)+c_1· r_1· (p_i-x_i (t\left)\right)+c_2· r_2· (g-x_i(t\left)\right)$$

(7)

where $\omega$ is the inertia weight, $c_1, c_2$ are cognitive and social coefficients, and $r_1, r_2$ are random numbers between 0 and 1.

The position of each particle is then updated using the following equation:

$$x_i \left(t+1\right)=x_i\left(t\right)+v_i(t+1)$$

(8)

Through iterative updates, PSO efficiently explores the solution space, converging towards optimal solutions while balancing exploration and exploitation. Its simplicity and effectiveness make it a popular choice for various optimization tasks, including engineering design, machine learning, and scheduling problems. Figure 4 presents the flowchart of the PSO algorithm.

4.3. Teaching–Learning-Based Optimization

Teaching–Learning-Based Optimization (TLBO) [24] is a metaheuristic algorithm inspired by the teaching and learning processes in a classroom. It simulates the interaction between teachers and students, where the teacher imparts knowledge to students, improving their performance. The algorithm consists of two main phases: the teacher phase, where the best solutions (students) are identified and improved based on the teacher’s guidance, and the learner phase, where students collaborate to enhance their solutions. This process continues iteratively until an optimal or satisfactory solution is found, making TLBO effective for various optimization problems across different domains. Figure 5 presents the flowchart of the TLBO algorithm.

5. Results and Discussion

In this section, the results obtained with the ABC, PSO, and TLBO algorithms are discussed. In this work, every problem is solved 30 times, and the Standard Deviation (SD) is presented. Furthermore, the time taken by CPU for the convergence of the algorithm is also reported as the computation time. ABC, PSO, and TLBO algorithms are coded in MATLAB R2021 on Windows Platform with an Intel Core i5 processor and 4 GB RAM (Intel, Pune, India).

Table 2. Algorithm parameters and termination of algorithms.

Solution Technique	Parameters	Termination
ABC	Population size (colony size) = 5	Max generations reached or function value less than ${10}^{-16}$
	Max number of iterations = 50
	Number of onlooker bees = 5
	Abandonment limit parameter = based on population size, number of variables
PSO	Population size = 100
	Generations = 25
	Inertia weight = 1
	Inertia weight damping ratio = 0.90
	Personal learning coefficient = 1.00
	Global learning coefficient = 2.00
TLBO	Population size = 100
	Generations = 25

presents the parameters set for ABC, PSO, and TLBO for solving all the problems considered in the current work.

As discussed earlier in Section 2 and Section 3 of this manuscript, the GP approach is adopted in this work. In GP, the pseudo-objective function is formulated considering the summation of the deviation of the three goals.

Table 3. Results for pseudo-objective function.

Solution Techniques		ABC	PSO	TLBO
Variables/Goals
Best	Z	847.2	1064.2	847.2
Mean	Z	980.3218	1064.2	847.2
SD		0.5467	0.0000	0.0000
Average Run Time (Seconds)		0.06	0.03	0.38

presents the results obtained with the ABC, PSO, and TLBO algorithms for the pseudo-objective function. The best and mean solutions are presented. It is evident from Table 3 that mean solutions with the TLBO algorithm is minimal, with a practically zero SD. The results with TLBO are improved by 20% and 14% compared to the PSO and ABC algorithms, respectively. This proves that the TLBO algorithm performed better compared with the ABC and PSO algorithms. However, the computation time required for the TLBO algorithm is the highest compared to the ABC and PSO algorithms. Hence, it can be concluded that the TLBO algorithm is computationally expensive for this problem compared with the other approaches. Further, as shown in

Table 4. Solutions of ABC, PSO, and TLBO algorithms.

Solution Techniques		ABC	PSO	TLBO
Variables/Goals
Best	Tool Vibrations	4.51	4.58	4.49
	Power Consumption	0.09	0.31	0.35
	Cutting Force	1.42	1.46	1.36
	$x_1$	1.1647	2.411	1
	$x_2$	3	3	3
	$x_3$	4	4	4
Mean	Tool Vibrations	4.52	4.58	4.49
	Power Consumption	0.28	0.31	0.35
	Cutting Force	1.43	1.46	1.36
	$x_1$	1.3282	2.411	1
	$x_2$	2.9439	3	3
	${\mathit{x}}_3$	4	4	4
SD		0.5467	0.0000	0.0000
Average Run Time (Seconds)		0.06	0.03	0.38

, the solutions for the pseudo-objective function are decoded for the solutions of three goals, viz., Tool Vibrations, Power Consumption, and Cutting Force, along with the corresponding values of three independent variables such as copper percentage (Cu%), graphite percentage (Gr%), and number of passes. Moreover, as presented in

Table 5. Comparison of solutions for ABC, PSO, and TLBO algorithms.

Solution Techniques		Experimental Results	ABC	PSO	TLBO
Variables/Goals
Mean	Tool Vibrations	4.543	4.52	4.58	4.49
	Power Consumption	2.637	0.28	0.31	0.35
	Cutting Force	1.767	1.43	1.46	1.36
	$x_1$	2	1.3282	2.411	1
	$x_2$	2	2.9439	3	3
	$x_3$	3	4	4	4
SD		NA	0.5467	0.0000	0.0000
Average Run Time (Seconds)		NA	0.06	0.03	0.38

, the results are compared with the experimental results. It is evident that the TLBO results for Tool Vibrations and Cutting Force are improved by 2% and 23%, respectively. Moreover, The TLBO-optimized values of three independent variables are set on the machine and corresponding responses of Tool Vibrations, Power Consumption, and Cutting Force are measured as confirmatory experiments. The deviations are well within the range.

Furthermore, the convergence plots are plotted for the three algorithms such as PSO, TLBO, and ABC, which are presented in Figure 6a–c, respectively. The exploration as well as exploitation capabilities of all the three algorithms are evident from Figure 6. The ABC algorithm shows the better exploratory capabilities of feasible space as evident from Figure 6c. On the other hand, the TLBO algorithm shows better exploitation capabilities as evident from Figure 6b.

Confirmatory Experiments

The best optimized results with TLBO algorithms are set on the CNC vertical machining center for FSP, and the confirmatory experiments are performed. The results are presented in

Table 6. Confirmatory experiments.

	TLBO Algorithm Results	Confirmatory Results	Deviation
Tool Vibrations	4.49	5.02	12%
Power Consumption	0.35	0.37	8%
Cutting Force	1.36	1.60	18%

. The TLBO optimized values of three independent variables, viz., copper percentage (Cu%), graphite percentage (Gr%), and number of passes, are 1, 3, and 4, respectively, which are set on the machine and corresponding responses of Tool Vibrations, Power Consumption, and Cutting Force that are measured. The deviation of the actual results with the algorithmic proposed results are also presented.

6. Conclusions and Future Directions

In this work, the Multi-Objective Optimization of friction stir processing (FSP) Tool with composite material parameters for the Al6061-based hybrid surface composites is performed. In the proposed study, the Al6061 matrix is reinforced with varying copper and graphite microparticles mixture, considering it as independent parameters along with the number of passes. Hence, in total, three independent variables, i.e., copper percentage (Cu%), graphite percentage (Gr%), and number of passes, are considered. Three responses affecting the tool life, including Tool Vibrations, Power Consumption, and Cutting Force, are considered. These responses are measured online with inbuilt sensors. Moreover, multi-factor non-linear regression model is developed for these three objectives.

Furthermore, the Goal Programming (GP) approach is adopted with the penalty-function-based constraint handling method for formulating the Multi-Objective Optimization model with the aforementioned three goals. The goals/target values of each response are selected based on the experimental results. The GP approach aims to minimize the sum of deviations of each goal. The formulated GP problem is solved with the three AI-based optimization algorithms, viz., Artificial Bee Colony (ABC), Particle Swarm Optimization (PSO), and Teaching–Learning-Based Optimization (TLBO).

The best and mean solutions for the GP pseudo-objective function is presented. It is evident from the results that mean solutions with TLBO algorithm is minimal, with practically zero SD. The results with TLBO are improved by 20% and 14% compared to the PSO and ABC algorithms, respectively. This proves that TLBO algorithm performed better compared with ABC and PSO algorithms. However, the computation time required for the TLBO algorithm is the highest compared to the ABC and PSO algorithms. Further, the solutions for the pseudo-objective function are decoded for the solutions of three goals, viz., Tool Vibrations, Power Consumption, and Cutting Force, along with the corresponding values of three independent variables, i.e., copper percentage (Cu%), graphite percentage (Gr%), and number of passes. Furthermore, the results are compared with the experimental results. It is evident that the TLBO results for Tool Vibrations and Cutting Force improved by 2% and 23%, respectively. Moreover, the TLBO-optimized values of three independent variables are set on the machine and corresponding responses of Tool Vibrations, Power Consumption, and Cutting Force that are measured as confirmatory experiments. The deviations are well within the range.

This work has opened new avenues towards applying the GP approach for the Multi-Objective Optimization of FSP tool with composite parameters. This is a significant step towards toll life improvement for the FSP of composite alloys, contributing to sustainable manufacturing. In the near future, the authors intend to apply the GP approach for wear reduction during the FSP of composite alloys. Also, more realistic problems could be formulated considering real-world constraints.