AISI 304 is the most common among grades of the austenitic stainless steel family, which accounts for roughly 72%. It has been widely used in high technology industries and chemical foods due to excellent corrosion resistance and high strength in high-temperature conditions.¹ AISI 304 austenitic stainless steel is regarded as a difficult-to-machine material due to its low thermal conductivity, toughness, gumming, easy work hardening, and high built-up edge, leading to poor surface integrity, increased tool wear and low productivity.² As a matter of fact, surface integrity is an essential criterion for evaluating a part's corrosion resistance and fatigue strength. More specifically, it is the surface roughness and residual stress which are two critical indicators of surface integrity determine the product's cost and quality.³ Improving surface integrity, therefore, is a requirement of the production and also a significant challenge for selecting technology parameters to satisfy customer requirements.⁴ Recently, researchers have been trying to develop new algorithms to optimize the machining process to ensure the above criteria simultaneously. Also, there has been a growing trend towards the application of nature-inspired algorithms to solve optimizations effectively. Yang proposed many nature-inspired algorithms, such as genetic algorithm (GA), particle swarm optimization (PSO), ant colony optimization (ACO), firefly algorithm (FA), cuckoo search (CS) and bat algorithm (BA).⁵

GA was applied to predict the surface roughness when milling and drilling. The test showed that the minimum surface roughness predicted by GA is lower than the results measured from the experiment, regression model and response surface method.^6,7 Likewise, when turning AISI 304, tool wear estimated by the utilization of GA is lower than that calculated by applying traditional optimization techniques.⁸ Zhou, et al. also used the GA-GBRT technique to predict the surface roughness and optimize Ra and MRR simultaneously during the turning of AISI 304.⁹ The results indicated that increasing the machining efficiency requires a slight rise of the cutting speed and depth of cut. Kumar deployed a Pareto optimal solution based on the GA to identify optimum real-time condition, thereby simultaneously ensuring productivity and quality.¹⁰ When comparing the optimal results of surface roughness between GA and PSO, Ahmad, et al. emphasized that PSO brought about the lower optimal surface roughness in a shorter time than GA.¹¹

On studying the algorithm used for soft computation in mechanical machining such as turning, milling, drilling and grinding, Chandrasekaran, et al. indicated that PSO with an unsophisticated mathematical structure was more efficient than GA in many circumstances.¹² Besides, PSO combined with Pareto optimal solution was employed to find the minimum surface roughness and maximum plastic deformation layer thickness.¹³

When investigating optimization algorithms applied in many fields, BA is more novel, more simple and more robust than PSO.^14,15 In multi-objective optimization, BA was also evaluated to be more effective than PSO, NSGA III.¹⁶

Based on the above literature review, it is noted that the metaheuristic algorithms have proved their superiority when solving the problem of multi-objective optimization in machining. BA has been proposed to be more effective in terms of a quick convergence rate, the optimal point's focus, and escape from local extremes. Therefore, this study focuses on two objectives. Firstly, RSM was used to develop the mathematical models of the relationship between cutting speed, feed rate, and depth of cut with two output indicators, including surface roughness and residual stress. Secondly, Pareto optimal solution based on applying BA was exploited to improve surface integrity when turning AISI 304 austenitic stainless steel. This paper’s findings were expected to help production planners choose the most suitable set of cutting parameters to meet customer requirements.

The results of surface roughness and residual stress measurement are shown in Table 4. It can be seen that surface roughness and residual stress are in the range of (0.44-1.72) μm and (125.9-240.8) MPa respectively.

3.2 Develop Regression Equations

Based on Eqs. (1), (2) and (3) for prediction for surface roughness and residual stress were respectively formed as shown below.

Ra=12.11-0.0818Vc-11.57f-3.69f+0.000149Vc2+64.68f2+1.460ap2+0.0079Vcf+0.01002Vcap+2.27fapRsquare=99.49%

(2)

σ=1559-11.99Vc-665f+1066ap+0.0260Vc2+75154f2+484ap2-2.40Vcf-4.52Vcap-1177fapRsquare=91.62%

(3)

The R_square values (91.62 and 99.49%) for the quadratic and power models are high enough to obtain reliable estimates. Fig. 4 shows the normal probability plot of the residuals with values of surface roughness and residual stresses for normal distribution. Indeed, it can be seen that the points evenly distributed are skewed towards both sides in a straight line, which demonstrates the proposed model is sufficient to show the suitability.

Fig. 4 
Normal probability plots for R_a and σ

3.3 Optimization of Responses

The objective of the present study is to minimize the surface roughness and residual stress simultaneously. The mathematical formulation of the current optimization problem can be stated as follows:

Minimize F(x) = {f₁, f₂}

f1=12.11-0.0818Vc-11.57f-3.69f+0.000149Vc2+64.68f2+1.460ap2+0.0079Vcf+0.01002Vcap+2.27fapf2=1559-11.99Vc-665f+1066ap+0.0260Vc2+75154f2+484ap2-2.40Vcf-4.52vcap-1177fap

where cutting parameters lower and upper bounds:

230m/min≤Vc≤290m/min0.08mm/rev≤f≤0.2mm/rev0.1mm≤ap≤0.5mm

To optimize the multi-objective function, the article proposes to use the BA.

3.3.1 Bat Algorithm

The bat algorithm (BA) is one of the nature-inspired algorithms proposed by Yang in 2010 based on the bats’ hunting behavior.²³ In this algorithm, the bat’s position represents a solution. The algorithm’s goal is to find the best solution in all of the bat’s positions, including exploitation procedure and exploration procedure, such as:

- Exploitation procedure: The frequency f_i, velocity v_i and position x_i of the i_th bat at the iteration (t + 1) are defined by Eqs. (4), (5) and (6).

fi=fmin+fmax-fminβ

(4)

νit+1=νit+xit-x*fi

(5)

xit+1=xit+νit

(6)

where, f_min, f_max are the minimum and maximum frequency of the bat populations, β ∈ [0,1] is a uniformly distributed random value and x_* is the best location (Solution) after the t_th iteration.

Exploration procedure: Random walks among bats are created around the best optimal to prevent getting block at a locally optimal solution by Eq. (7).

xnew=xold+εAt

(7)

where, ε ∈ [-1,1] is a random number, A^t is the average loudness of all the bats at t_th iteration.

The loudness Ait and the rate rit of pulse emission have to be updated during the optimal search process, according to Eq. (8).

Ait+1=αAit,rit+1=ri01-exp⁡-τtwhere, 0<α<1, τ are constants

(8)

where, 0 < α < 1, τ are constants

3.3.2 Multi-Objective Bat Algorithm (MOBA)

This paper proposes a Pareto optimal concept, formulated by Vilfredo Pareto in the XIX century,²⁴ using the BA to simultaneously optimize surface roughness and residual stress. The flow chart of the BA is shown in Fig. 5.

Fig. 5 
Flow chart of Pareto optimal using BA

Parameters of the MOBA used in MATLAB are presented in Table 7.

Table 7 
Parameters of the MOBA

Parameters	Values
Loudness, A	0.8
Pulse rate, r	0.8
Minimize frequency, fmin	0
Maximize frequency, fmax	2
Number of iteration, t	1,000
Bat population, n	100
Number points of Pareto, N	1,000

Fig. 6 shows the formation of Pareto optimal front that consists of the final set of solutions. The final optimum (V_c, f, a_p) and their corresponding R_a and σ are shown in Table 8.

Fig. 6 
Pareto front points

Table 8 
Optimal solutions achieved by MOBA

No.	Vc [m/min]	f [mm/rev]	ap [mm]	Ra [μm]	σ [MPa]
1	252.779	0.100	0.201	0.516	117.987
2	261.006	0.080	0.258	0.430	124.112
3	258.689	0.088	0.235	0.453	120.366
4	257.074	0.092	0.226	0.468	119.189
5	254.277	0.098	0.210	0.500	118.099
6	259.661	0.085	0.243	0.443	121.630
7	256.727	0.093	0.223	0.472	118.929
8	257.665	0.090	0.229	0.461	119.616
9	255.833	0.095	0.219	0.481	118.571
10	262.242	0.080	0.302	0.427	126.941

The Pareto optimal frontier points show that for each point corresponding to one set of parameters (V_c, f, a_p), it is impossible to find another set of parameters (V_c, f, a_p) for surface roughness to reach expected value that the residual stress is lower than the value on the Pareto front or vice versa, the residual surface stress is the desired value for which the surface roughness is lower than the present value. Indeed, in Table 8, if the parameter set includes V_c = 257.665 m/min, f = 0.090 mm/rev, a_p = 0.229 mm, on the Pareto front, R_a = 0.461 μm, σ = 119.616MPa. This means that if R_a is expected to reach 0.461μm, it is impossible to choose any other sets of parameters (V_c, f, a_p) so that σ is lower than 119.616 MPa.

Hence, based on specific requirements, the appropriate machining parameters are selected. For example, when required to achieve a lower surface roughness, the cutting parameters V_c = 262.242 m/min, f = 0.080 mm/rev, a_p = 0.302 mm are chosen. The residual stress and surface roughness obtained then are σ = 126.941 MPa and R_a = 0.427 μm respectively. When a lower residual stress is required, the cutting parameters V_c = 252.779 m/min, f = 0.100 mm/rev, a_p = 0.201 mm are selected. The residual stress and surface roughness are σ = 117.987MPa and R_a = 0.516 μm respectively.

This result is significant when compared to traditional optimization methods. RSM itself also finds the optimal set of parameters. Still, RSM gives only one result which is not as good as the result found by the BA. At the same time, Pareto optimal solution based on BA provides manufacturers with countless optimizations for different requirements.

In this study, an experimental investigation was conducted to improve the surface integrity in terms of the surface roughness and residual stress when turning AISI 304 austenitic stainless steel. The following conclusions were drawn from the research.

ANOVA results showed that the feed rate had the most influence on surface roughness and residual stress.

Pareto optimal solution was employed based on the BA to optimize cutting parameters to minimize surface roughness and residual stress. Optimal results revealed the smallest roughness value is R_a = 0.427 μm; the minimum residual stress is σ = 117.987 MPa. The experimental confirmation results demonstrated that the Pareto optimal solution applying the BA was reliable and efficient.

Finding the optimal point on the Pareto front allows users to choose the optimal value for production requirements.