Keywords:End milling; Parameter optimization; Surface roughness; Machining time; Metaheuristics;
Many applications of metaheuristics in Electrical Discharge Machining (EDM) process paRameters optimization have been reported in liteRatures. Mukherjee, et al. [17] applied Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Sheep Flock Algorithm (SFA), ant Colony Optimization (ACO), Artificial Bee Colony (ABC) and biogeogRaphybased optimization (BBO) for single and multiobjective (material removal Rate, cutting width, surface roughness and dimensional shift) optimization of wireEDM processes. Rao and Pawar [19] applied ABC optimization to find the optimum combination of process paRameters for wireEDM with an objective of achieving maximum machining speed for a desired value of surface finish. Rao and Krishna [20] also conducted wireEDM machining experiments on Aluminum metal matrix composites reinforced with silicon carbide particulate and developed some empirical models with Response Surface Methodology (RSM) for Surface Roughness (SR), Metal Removal Rate (MRR), and Wire Wear Ratio (WWR) in terms of machining paRameters. They did some works on multiobjective optimization for minimizing SR, WWR and maximizing MRR, using GAII. Pare, et al. [18] explored GA, Simulated Annealing (SA), TeachingLearningBased Optimization (TLBO) and GRavitational Search (GS) algorithms to minimize the surface roughness and to determine the optimum machining conditions for the endmilling of composite materials. Teimouri and Baseri [26] also optimized EDM process paRameters. They designed ANFIS models to correlate the EDM paRameters to material removal Rate (MRR) and surface roughness (SR). Continuous ant colony optimization (ACOr) technique was used to select the best process paRameters for maximum MRR and specified SR.
Some applications of metaheuristics are found for turning and milling opeRations as well. Yildiz [27] presented an optimization approach based on Artificial Bee Colony (ABC) algorithm for optimal selection of cutting paRameters in multipass turning opeRation. Mellal and Williams [16] used a recently developed metaheuristic, called the Cuckoo Optimization Algorithm (COA) for minimization of unit production cost in multipass turning process to obtain optimum cutting paRameters. TamizhaRasan and Bamabas [25] used Particle Swarm Optimization (PSO) and Simulated Annealing (SA) algorithms to obtain the best possible values of cutting tool geometry for the minimization of flank wear in a lathe machine, considering surface roughness as constRaint. On the other hand, Kadirgama, et al. [5] optimized cutting paRameters for desired surface roughness of milling aluminum alloys with Ant Colony Optimization (ACO).
Silva, et al. [23] did some works for optimizing the production cost subjected to quality constRaints in the milling opeRations on hardened steel. They developed Artificial NeuRal Networks (ANN) model, and applied Genetic Algorithms (GA) and Mesh Adaptive Direct Search (MADS) algorithms for that purpose. Khanghah, et al. [9] presented their research on optimization of cutting tool geometry for micromilling applying simulated annealing optimization method on RSM based regression models. KaRabulut and KaRakoc [8] investigated the machinability of silicon carbide and aluminum alloybased metal matrix composite during milling opeRation. Prediction model was developed for the surface roughness through regression analysis and ANN. Some recent research works related to our current research are summarized in Table 1.
LiteRatures 
Applications 
Objectives 
Variables 
Models 
Metaheuristics 
Madic et al. (2014) 
Laser cutting of stainless steel 
Improving quality chaRacteristics 
Power, speed, pressure 
ANN 
RCGA, SA, IHSA 
Silva (2014) 
Milling of hardened steel 
Min. Prod. cost 
Cutting paRameters 
ANN 
GA, MADS 
Teimouri and Baseri (2014) 
EDM 
Max. MRR 
EDM paRameters 
ANFIS 
ACOr 
Kadirgama et al. (2010) 
Milling of aluminum alloys 
Min. SR 
Speed, Feed Rate, axial and Radial depth 
RSM 
ACO 
Yusup et al. (2014) 
AbRasive WaterJet machining 
Min. SR 
Machining control paRameters 
Regression 
ABC, GA, SA 
Yildiz (2013) 
Multipass turning 
Min. Cost 
Cutting paRameters 
Analytical 
ABC 
Mukherjee et al. (2012) 
WireEDM 
Min. MRR 
Process paRameters 
ANN 
GA, PSO, SFA, ACO, ABC, BBO 
Rao and Pawar (2009) 
WireEDM 
Max. Machining speed 
Process paRameters 
RSM 
ABC 
Mellal and Williams (2015) 
Multipass turning 
Min. Production cost 
Cutting paRameters 
Analytical 
COA 
Khanghah et al. (2015) 
Micromilling 
Cutting tool geometry 
Speed, feed, depth 
RSM 
SA 
TamizhaRasan and Bamabas (2014) 
Lathe machine 
Min. Flank wear 
Cutting tool geometry 
Regression 
PSO, SA 
Pare et al. (2015) 
Endmilling on metal matrix composites 
Min. SR 
Speed, feed, depth, stepover Ratio 
Nonlinear regression 
GA, SA, TLBO, GS 
Rao and Krishna (2014) 
WireEDM on metal matrix composites 
Min. SR, WWR Max. MRR 
Process paRameters 
RSM 
GAII 
Rong et al. (2016) 
Laser bRazing welding 
Min. Width of weld bead 
Feed Rate, speed, gap 
ELM model 
GA 
Shukla and Singh (2017) 
AbRasive WaterJet machining 
Max. kerf width 
Speed, standoff distance, flow Rate 
Regression 
PSO, FFA, ABC, SA, BH, GA 
Current work by Hossain and Liao (2017) 
End milling of Hot Die Steel 
Min. Machining Time 
Cutting paRameters 
ANFIS models 
ABC, qABC, SA, MDE, ACOr 
Many other applications of metaheuristics algorithms are found in machining opeRations. Liao [11] proposed two versions of ant colony optimization (ACOr and ACOS) based algorithms for feature selection and applied them to computeRaided weld inspections. Liao [12] also investigated feature extRaction and feature selection in sensorbased condition monitoring during grinding opeRations of ceRamic materials. He used three different feature selection methods including the ACO based metaheuristics. Zuperl and Cus [29] proposed an approach of using ANFIS to represent the manufacturer’s objective function and an Ant Colony Optimization algorithm (ACO) to obtain the optimal objective value. Besides these, Liao [12] presented hybrid differential evolution and harmony search algorithms for optimizing fourteen engineering design problems selected from different engineering fields.
From the liteRature survey it is evident that many researchers have been conducted with different metaheuristics for optimizing the machining paRameters in order to achieve different stated objectives. The advanced algorithms namely, ABC, qABC, ACOr, MDE and SA are widely applied in different field of manufacturing and proved to be efficient and effective. However, the specific applications and comparisons of ABC, qABC, ACOr, MDE, SA and their hybrids (with Hilldescent local search) in milling process optimization for hot die steel machining, based on ANFIS models, is very limited. An extensive research in this direction still needs careful attention. Considering this fact, this research presents five different metaheuristics (ABC, qABC, ACOr, SA, MDE) and their hybrids with Hilldescent local search in order to minimize the machining time subject to surface roughness constRaints. The objective is to obtain optimum machining paRameters for hot die steel machining with a ball end milling cutter. The optimization processes is conducted based on two ANFIS models—one for aveRage surface roughness (Ra) and another for machining time (T).
The paper is organized in a sequential order. The problem is described in problem description section. Methodology section illustRates the method of research. Input Parameter (Variable) Selection Section describes the selection of ANFIS models. The optimization of the problem and the results are discussed in optimization Section. At the end of the article, some concluding remarks are noted in conclusion Section.
This research involves the experiments [see Figure 1] conducted by Hossain and Ahmad [4] on a die material Hot die steel (H13) for ball end milling opeRation. There were six machining paRameters concerned with that experiments—cutter axis inclination angle (φ degree), tool diameter (d mm), spindle speed (S rpm), Radial depth of cut (f_{x} mm), feed Rate (f_{y} mm/min), and axial depth of cut (t mm). The inclination angle, φ represents the angle of the cutter axis with respect to normal direction to the machining surface. On the other hand, Tool diameter results the maximum width of the machined surface in a single pass of the cutter. Spindle speed, S is defined as the aveRage number of rotations of the spindle per minute. Radial depth of cut, f_{x} is the amount of indentation of the tool into the machining surface, while feed Rate, f_{y} is the amount of linear movement of the cutting tool along a paRallel direction to the machining surface. Two dependent variable were measured—surface roughness R_{a} (μm) and machining time T (min). Each specimen surface area was 1cm×1cm. Total 74 experiments were conducted (results are listed in Appendix). Based on these data two, ANFIS models are developed in order to predict T and R_{a}, where machining paRameters are taken as inputs.
So the optimization problem becomes,
Minimize, Machining time (T) (1)
Subject to, 0.4 ≤ R_{a} ≤ 0.6
φ = [0, 30]^{°}, d ={6, 7, 8, 9, 10} mm, S = {316, 520, 715} rpm,
f_{x}=[0.2, 0.4] mm, f_{y} = [22, 44] mm/min, and t =[0.1, 0.3] mm,
This is a mixed discretecontinuous constRaint optimization problem. The global optimum solution for the above problem is computationally prohibitive to obtain. One of the reasons for the computational difficulty involves the undefined relationships of machining paRameters with T and Ra. Suitable data driven models for predicting T and Ra are needed to be developed first. Then those models can be used to find at least some nearoptimum solutions using available metaheuristic algorithms.
In this research, the stated optimization problem is solved with five different metaheuristic algorithms: Artificial Bee Colony (ABC) developed by KaRaboga and Basturk [6], quick Artificial Bee Colony (qABC) proposed by KaRaboga and Gorkemli [7], Ant Colony Optimization for real numbers (ACOr) developed by Socha and Dorigo [24], Modified Differential Evolution (MDE) developed by AngiRa and Babu [1], and a Simulated Annealing (SA) algorithm proposed by Bohachevsky, et al. [2]. A geneRalized discrete variables handling method that was proposed and implemented by Liao [13], is incorpoRated in all the algorithms in this research. Deb [3] Parameter less penalty methods are consistently used in all metaheuristics for handling the constRaints. Each of the algorithms are run for 30 times allowing 100,000 number of function evaluations (only one stopping criteria) in each run. The best objective values (machining time, T) and elapsed times are recorded from each run and each algorithm. The minimum function value among all of the runs and all of the five metaheuristics is found as 6.2106537581413 (minutes).
In the second step of the research, Hilldescent local search is incorpoRated in all of the five metaheuristics to make their hybrids. These hybrid metaheuristics are also run for 30 times. The stopping criteria are set with maximum number of function evaluation (maxnfe). Thus, the algorithm continues until the number of function evaluation (nfe) reaches to the maximum limit (maxnfe = 100,000). The best function values (here it is machining time T), and the elapsed time (et) are recorded for each of the 30 runs for each of the ten algorithms (five metaheuristics and their hybrids with local search). Analysis of variances (ANOVA) and pairwise comparison are performed to determine the significant differences between the results obtained from different metaheuristic algorithms (Li, et al. [10]). Based on the analysis ABC with local search (ABC+LS) is chosen as the most suitable metaheuristic algorithm for solving this problem.
In the third step of the research ABC+LS algorithm is run for 5 times, allowing 1 million number of function of evaluation (maxnfe = 1,000,000) in each run. This maxnfe is set as the only stopping criteria. The intention of this final run is to find more precise result, and to check if further improvement of the result can be possible. Matlab R2014b (Matlab 2014) is used for modif_{y}ing all of the codes and the codes are run on a desktop computer with Intel® Core™2 Duo 3.33GHz processor, 4GB RAM and 64bit windows7 enterprise opeRating system.
Statistical analysis with Student’s ttest also shows that feed Rate (f_{y}) and Radial depth (f_{x}) are significant factors for machining time (T) (refer to Table 2). As a result feed Rate and Radial depth are selected as the most influential input paRameters for T prediction.
Now, setting feed Rate (f_{y}) and Radial depth (f_{x}) as input paRameters, seveRal ANFIS models are developed with different architectures. The corresponding leaveoneout RMSE in machining time (T) predictions are summarized in Table 3. From this table it can be noticed that smallest size ANFIS architecture
Variable 
Parameter 
Standard 
t value 
Pr > t 
Angle 
0.00109 
0.01975 
0.06 
0.9563 
Speed 
0.00211 
0.00150 
1.41 
0.1635 
Tool diameter 
0.03113 
0.14631 
0.21 
0.8322 
Feed Rate 
0.42916 
0.02645 
16.23 
<.0001 
Radial Depth 
45.50742 
2.87257 
15.84 
<.0001 
Axial Depth 
1.30584 
3.18993 
0.41 
0.6836 
Number of membership functions for two input paRameters 
Type of Input Membership Functions and corresponding leaveoneout RMSE 

f_{x} 
f_{y} 
Gbellmf 
gaussmf 
gauss2mf 
pimf 
psigmf 
dsigmf 
1 
2 
1.1762 
1.1155 
1.1155 
1.1155 
1.1762 
1.1762 
1 
3 
1.1155 
1.1155 
1.1155 
1.1155 
1.1155 
1.1155 
1 
4 
1.1155 
1.1155 
1.1155 
6.0826 
1.1155 
1.1155 
2 
1 
1.1222 
1.1113 
1.1112 
1.1112 
1.1019 
1.1019 
2 
2 
0.5161 
0.5161 
0.5161 
0.5161 
0.5161 
0.5161 
2 
3 
0.5161 
0.5161 
0.5161 
0.5161 
0.5161 
0.5161 
2 
4 
0.5161 
0.5161 
0.5161 
0.5161 
0.5161 
0.5161 
3 
1 
1.1112 
1.1112 
1.1112 
1.1112 
1.1112 
1.1112 
3 
2 
0.5161 
0.5161 
0.5161 
0.5161 
0.5161 
0.5161 
3 
3 
0.5161 
0.5161 
0.5161 
0.5161 
0.5161 
0.5161 
3 
4 
0.5161 
0.5161 
0.5161 
1.6005 
0.5161 
0.5161 
4 
1 
1.1112 
1.1112 
1.1112 
1.1112 
1.1112 
1.1112 
4 
2 
0.5161 
0.5161 
0.5161 
0.5161 
0.5161 
0.5161 
4 
3 
0.5161 
0.5161 
0.5161 
0.5161 
0.5161 
0.5161 
4 
4 
0.5161 
0.5161 
0.5161 
0.5161 
0.5161 
0.5161 
For simplicity the ANFIS model with dsigmf type of membership function has been chosen for machining time prediction. So, as shown in Figure 3, an ANFIS model with (2, 2) number of dsigmf type membership functions is used for machining time prediction for the optimization problem.
At the same time, in Table 4, a statistical analysis withstudents ttest shows that speed, feed Rate and axial depth of cut are nonsignificant (with higher pvalue). So it is wise to select cutter axis inclination angle (φ), tool diameter (d) and Radial depth of cut (f_{x}) as the most influential input paRameters for R_{a} prediction.
Variable 
Parameter Estimate 
Standard Error 
tvalue 
Pr > t 
Angle 
0.01823 
0.00276 
6.61 
<.0001 
Speed 
0.00012180 
0.00020932 
0.58 
0.5626 
Tool diameter 
0.05289 
0.02043 
2.59 
0.0118 
Feed Rate 
0.00340 
0.00369 
0.92 
0.3608 
Radial Depth 
3.61971 
0.40117 
9.02 
<.0001 
Axial Depth 
0.01237 
0.44549 
0.03 
0.9779 
Number of membership function for three input paRameters 
Type of Input Membership Functions and corresponding leaveoneout RMSE 

φ 
d 
f_{x} 
Gbellmf 
gaussmf 
gauss2mf 
pimf 
psigmf 
dsigmf 
2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 
2 2 2 3 3 3 4 4 4 2 2 2 3 3 3 4 4 4 2 2 2 3 3 3 4 4 4 
2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 
3.9632 0.2378 0.2578 0.3178 0.2222 0.2210 0.3502 0.2225 0.2218 0.2927 0.4398 0.4060 0.2273 0.2398 0.2353 0.2278 0.2420 0.2490 0.2791 0.3135 0.3147 0.2305 0.2432 0.2561 0.2295 0.2394 0.2481 
6.7554 0.2655 0.2654 0.4777 0.2221 0.2212 0.2537 0.2221 0.2208 0.3600 0.2558 0.2469 0.2269 0.2419 0.2459 0.2260 0.2372 0.2398 0.2654 0.3064 0.2936 0.2311 0.2359 0.2329 0.2298 0.2293 0.2271 
1.3951 0.3565 0.3566 0.3051 0.2220 0.2257 0.3052 0.2227 0.2255 0.2797 0.3470 0.3383 0.2388 0.2777 0.2777 0.2326 0.2779 0.2779 0.2735 0.2817 0.2788 0.2363 0.2648 0.2796 0.2323 0.2700 0.2792 
7.9759 0.3155 0.3155 0.3021 0.2258 0.2253 0.3021 0.2259 0.2260 0.2778 0.4155 0.4133 0.2452 0.2793 0.2793 0.2377 0.2793 0.2793 0.2726 0.2770 0.2796 0.2368 0.2788 0.2808 0.2326 0.2794 0.2794 
4.7754 0.2380 0.2379 0.4639 0.2216 0.2259 0.4638 0.2260 0.2260 0.2810 0.3505 0.3724 0.2428 0.2769 0.2779 0.2334 0.2655 0.2772 0.2746 0.3310 0.3527 0.2371 0.2483 0.2783 0.2330 0.2490 0.2790 
4.7754 0.2380 0.2387 0.4639 0.2207 0.2259 0.4638 0.2259 0.2260 0.2811 0.3261 0.3740 0.2427 0.2769 0.2779 0.2333 0.2325 0.2774 0.2746 0.3235 0.3469 0.2362 0.2493 0.2794 0.2321 0.2355 0.2790 
Another point has to be noted that, ABC and qABC are modified for handing constRaint optimization problem following the approach by KaRaboga and Akay (2011), to compute the probability of selecting a food source by the onlooker bees.
Metaheuristics 

PaRameters 
ABC:

abandoned by its employed bee 

qABC: 
Additional Parameter for quick ABC, rv=1 

ACOr:



MDE:



SA:


Minimize Machining time (T)
Subject to, 0.4 ≤ R_{a} ≤ 0.6
Angle = [0, 30], Tool Dia = {6, 7, 8, 9, 10}, Radial Depth = [0.2, 0.4],
Feed Rate = [22, 44],
where machining time T is dependent on Radial depth of cut and feed Rate; whereas R_{a}depends on angle, tool diameter and Radial depth of cut.
Results of the optimization using five metaheuristics and their hybrids are summarized in this section. The summarystatistics for the best objective value (machining time T) and the elapsed time for all of the ten algorithms are listed in Table 7. It is observed in Table 7 that qABC+LS provides the minimum mean best objective value. On the other hand, ABC+LS shows the minimum aveRage elapsed time. Before final selection of a suitable algorithm for solving the stated optimization problem, some statistical analysis is needed to be done in order to identif_{y} the statistical significance of the metaheuristics and the Local Search (LS) stRategy. The experiments are independent and the experimental data satisf_{y} the tests for normality and homogeneity of variances. Hence the data set satisfies the necessary Assumptions For Analysis Of Variance (ANOVA) test.
In Table 8, a oneway ANOVA is prepared for testing the hypothesis that, “all ten algorithms provide the same mean best objective value”. Very low pvalue indicates that this hypothesis can be rejected and can be concluded that at least one of the algorithms provides significantly different result from the others
Algorithm 
Best objective value (machining time T) 
elapsed time 

Mean 
Median 
SD 
Max. 
Min. 
Mean 
Median 
SD 
Max. 
Min. 

ABC 
6.211840 
6.210668 
0.005607 
6.241470 
6.210654 
124.2495 
121.7891 
5.7559 
136.3281 
118.4219 

qABC 
6.210928 
6.210656 
0.000806 
6.214078 
6.210654 
125.1839 
124.8829 
2.8585 
137.5938 
122.1406 

ACOr 
6.507356 
6.357017 
0.867013 
11.070938 
6.210654 
138.2151 
136.0703 
7.0851 
160.6563 
128.4844 

MDE 
6.227914 
6.211440 
0.025091 
6.268045 
6.210654 
171.5990 
171.3203 
2.3361 
178.2500 
167.6250 

SA 
10.669694 
11.119450 
1.373818 
11.173225 
6.390841 
187.3985 
189.7188 
12.2103 
197.5469 
124.3438 

ABC+LS 
6.210659 
6.210654 
0.000010 
6.210701 
6.210654 
123.5781 
123.2032 
2.0197 
127.7500 
120.1250 

qABC+LS 
6.210656 
6.210654 
0.000005 
6.210678 
6.210654 
129.9229 
129.3985 
4.6715 
148.1406 
123.8438 

ACOr+LS 
6.329462 
6.268029 
0.091311 
6.446005 
6.210654 
148.4802 
146.6797 
7.9111 
166.5781 
140.0781 

MDE+LS 
6.226021 
6.210661 
0.025765 
6.268030 
6.210654 
174.5307 
173.8829 
4.2660 
191.8750 
170.1406 

SA+LS 
9.143974 
10.962028 
2.457933 
13.764865 
6.265273 
182.4386 
189.6563 
20.6365 
196.6406 
122.7031 
Source 
Sum Sq. 
d.f. 
Mean Sq. 
F 
Prob>F 
Algorithms 
673.213 
9 
74.8015 
86.08 
1.39276e76 
Error 
252.015 
290 
0.869 


Total 
925.229 
299 



On the other hand, in Table 10, a oneway ANOVA is prepared for testing the hypothesis that “all of the ten algorithms take same mean elapsed time”. Very low pvalue provides sufficient evidence to reject this hypothesis and it can be concluded that at least one of the algorithms takes significantly differentelapsed time compared to others.
In order to test the significance of the metaheuristics, the local search stRategy and their inteRaction on the elapsed time, a twoway ANOVA is also developed [shown in Table 11]. This twoway ANOVA test informs that there are significant effects of local search stRategy (pvalue = 0.0163), metaheuristics (pvalue = 0) as well as their inteRactions (pvalue = 0.0001) on the elapsed time for computation.
Source 
Sum Sq. 
d.f. 
Mean Sq. 
F 
Prob>F 
Local Search 
8.741 
1 
8.741 
10.06 
0.0017 
Metaheuristics 
637.821 
4 
159.455 
183.49 
0 
Local Search*Metaheuristics 
26.651 
4 
6.663 
7.67 
0 
Error 
252.015 
290 
0.869 


Total 
925.229 
299 



Source 
Sum Sq. 
d.f. 
Mean Sq. 
F 
Prob>F 
Algorithms 
181121.1 
9 
20124.6 
258.47 
6.75886e133 
Error 
22579.5 
290 
77.9 


Total 
203700.5 
299 



Source 
Sum Sq. 
d.f. 
Mean Sq. 
F 
Prob>F 
Local Search 
454.2 
1 
454.2 
5.83 
0.0163 
Metaheuristics 
178698.9 
4 
44674.7 
573.78 
0 
Local Search*Metaheuristics 
1967.9 
4 
492 
6.32 
0.0001 
Error 
22579.5 
290 
77.9 


Total 
203700.5 
299 



It is noticeable from Figure 6 and 7 that SA and SA+LS give significantly higher results in terms of best objective value, whereas ACOr, MDE and SA (with or without LS) show significantly higher results for mean elapsed time. From Table 7, we see that the mean of best objective values and the mean of elapsed times for both SA and SA+LS are worse than any other algorithms. So, we can reject SA and SA+LS depending on our observation. Though SA improves with local search [refer to Table 7], ACOr with local search takes more time for computations. Thus the impact of local search is evident.
On the other hand, in terms of mean elapsed time measurements, ABC, qABC and their hybrids with local search give significantly faster (elapsed time) results compared to other algorithms. There is no significant difference observed during pairwise comparison between ABC, ABC+LS, qABC and qABC+LS [refer to Figures 6 and 7]. So we can chose an algorithm among these four. It has been noted earlier from Table 7 that qABC+LS provides the minimum mean of the best objective values, and ABC+LS provides the minimum aveRage elapsed time. So it would be a good choice to compare between qABC+LS and ABC+LS for the final selection of optimization algorithm. Though there is no significant difference between these two algorithms with5% level of significance, the higher elapsed time is noticeable for qABC+LS in Figure 7. So the best choice of algorithm for solving the stated optimization problem can be ABC+LS.
Run 
Best objective value 
Optimum PaRameters 
AveRage Surface Roughness, 

Angle, φ 
Tool dia, d(mm) 
Radial Depth, f_{x} 
Feed Rate, f_{y} 

1 
6.210653758141266 
0 
6 
0.340112541158715 
38.872261879942734 
0.600000000000000 
2 
6.210653758141338 
0 
6 
0.340112541158711 
38.872261806581925 
0.599999999999981 
3 
6.210653758141528 
0 
6 
0.340112541158702 
38.872261805633649 
0.599999999999931 
4 
6.210653758981911 
0.000000002561137 
6 
0.340112541119122 
38.872261972040320 
0.599999999994266 
5 
6.210653758141266 
0 
6 
0.340112541158715 
38.872261905683651 
0.600000000000000 
These presented approaches are applicable in metal die manufacturing industries where end milling opeRation is done on hot die steel material using ball end mill cutters. The proposed approach can enhance the artificial intelligence level of the machine tools in order to facilitate the selfsetup capabilities for machining paRameters and this will make the machine tools more versatile and intelligent. This research is indeed a little step towards the era of artificial intelligence.
 Angira R, Babu BV. Optimization of process synthesis and design problems: a modified differential evolution approach. Chem Eng Sci. 2006;61(14):47074721.
 Bohachevsky IO, Johnson ME, Stein ML. Generalized simulated annealing for function optimization. Technometrics. 1986;28(3):209217.
 Deb K. An efficient constraint handling method for genetic algorithms. Computer Methods in Applied Mechanics and Engineering. 2000;186(2–4):311338.
 Hossain MSJ, Ahmad N. Surface roughness prediction modeling for commercial dies using ANFIS ANN and RSM. IJISE. 2014;16(2):156183. DOI: 10.1504/IJISE.2014.058834
 Kadirgama K, Noor MM, Alla ANA. Response ant colony optimization of end milling surface roughness. Sensors. 2010;10(3):20542063. DOI:10.3390/s100302054
 Karaboga D, Basturk B. A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. Journal of Global Optimization. 2007;39(3):459471.
 Karaboga D, Gorkemli B. A quick artificial bee colony (qABC) algorithm and its performance on optimization problems. Applied Soft Computing. 2014;23(1):227238.
 Karabulut S, Karakoc H. Investigation of surface roughness in the milling of Al7075 and opencell SiC foam composite and optimization of machining parameters. Neural Computing & Applications. 2017;28(2):313327.
 Khanghah SP, Boozarpoor M, Lotfi M, Teimouri R. Optimization of micromilling parameters regarding burr size minimization via RSM and simulated annealing algorithm. Transactions of the Indian Institute of Metals. 2015;68(5): 897910.
 Li Z, Kucukkocb I, Nilakantanc JM. Comprehensive review and evaluation of heuristics and metaheuristics for twosided assembly line balancing problem. Computers and Operations Research. 2017;84:146161.
 Liao TW. Two hybrid differential evolution algorithms for engineering design optimization. Applied Soft Computing. 2009;10(4):11881199.
 Liao TW. Feature extraction and selection from acoustic emission signals with an application in grinding wheel condition monitoring. Engineering Applications of Artificial Intelligence. 2010;23(1):74–84.
 Liao TW, Kuo RJ, Hu JTL. Hybrid ant colony optimization algorithms for mixed discretecontinuous optimization problems. Applied Mathematics and Computation. 2012;219(6):32413252.
 Madic M, Radovanovic M, Manic M, Trajanovic M. Optimization of ANN models using different optimization methods for improving CO2 laser cut quality characteristics. Journal of the Brazilian Society of Mechanical Sciences and Engineering. 2014;36(1):9199.
 Matlab. The MathWorks, Inc. 2014. Available from: http://www.mathworks.com/
 Mellal MA, Williams EJ. Cuckoo optimization algorithm for unit production cost in multipass turning operations. International Journal of Advanced Manufacturing Technology. 2015;76(14):647656.
 Mukherjee R, Chakraborty S, Samanta S. Selection of wire electrical discharge machining process parameters using nontraditional optimization algorithms. Applied Soft Computing. 2012;12(8):25062516.
 Pare V, Agnihotri G, Krishna C. Selection of optimum process parameters in high speed CNC endmilling of composite materials using metaheuristic techniques  a comparative study. Strojniski VestnikJournal of Mechanical Engineering. 2015;61(3):176186.
 Rao RV, Pawar PJ. Modelling and optimization of process parameters of wire electrical discharge machining. Journal of Engineering Manufacture. 2009;223(11):14311440.
 Rao TB, Krishna AG. Selection of optimal process parameters in WEDM while machining Al7075/SiCp metal matrix composites. International Journal of Advanced Manufacturing Technology. 2014;73(14):299314.
 Rong YM, Zhang GJ, Chang Y, Huang, Y. Integrated optimization model of laser brazing by extreme learning machine and genetic algorithm. International Journal of Advanced Manufacturing Technology. 2016;87(912):29432950.
 Shukla R, Singh D. Experimentation investigation of abrasive water jet machining parameters using Taguchi and Evolutionary optimization techniques. Swarm and Evolutionary Computation. 2017;32:167183.
 Silva JA, AbellanNebot JV, Siller HR, GuedeaElizalde F. Adaptive control optimisation system for minimising production cost in hard milling operations. International Journal of Computer Integrated Manufacturing.2014; 27(4):348360.
 Socha K, Dorigo M. Ant colony optimization for continuous domains. European Journal of Operations Research.2008;185(3):11551173.
 Tamizharasan T, Bamabas JK. Optimization of cutting tool geometry based on flank wear  DoE, PSO and SAA approach. Indian Journal of Engineering and Materials Sciences. 2014;21(5):543556.
 Teimouri R, Baseri H. Optimization of magnetic field assisted EDM using the continuous ACO algorithm. Applied Soft Computing. 2014;14(C):381389.
 Yildiz AR. Optimization of cutting parameters in multipass turning using artificial bee colonybased approach. Information Sciences. 2013;220(1):399407.
 Yusup N, Sarkheyli A, Zain AM, Hashim SZM, Ithnin N. Estimation of optimal machining control parameters using artificial bee colony. Journal of Intelligent Manufacturing. 2014;25(6):14631472.
 Zuperl U, Cus F. Machining process optimization by colony based cooperative search technique. Strojniski VestnikJournal of Mechanical Engineering. 2008;54(11):751758.