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 biogeogRaphy-based optimization (BBO) for single and multi-objective (material removal Rate, cutting width, surface roughness and dimensional shift) optimization of wire-EDM processes. Rao and Pawar [19] applied ABC optimization to find the optimum combination of process paRameters for wire-EDM with an objective of achieving maximum machining speed for a desired value of surface finish. Rao and Krishna [20] also conducted wire-EDM 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 GA-II. Pare, et al. [18] explored GA, Simulated Annealing (SA), Teaching-Learning-Based Optimization (TLBO) and GRavitational Search (GS) algorithms to minimize the surface roughness and to determine the optimum machining conditions for the end-milling 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 multi-pass 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 micro-milling applying simulated annealing optimization method on RSM based regression models. KaRabulut and KaRakoc [8] investigated the machinability of silicon carbide and aluminum alloy-based 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 Water-Jet machining |
Min. SR |
Machining control paRameters |
Regression |
ABC, GA, SA |
Yildiz (2013) |
Multi-pass turning |
Min. Cost |
Cutting paRameters |
Analytical |
ABC |
Mukherjee et al. (2012) |
Wire-EDM |
Min. MRR |
Process paRameters |
ANN |
GA, PSO, SFA, ACO, ABC, BBO |
Rao and Pawar (2009) |
Wire-EDM |
Max. Machining speed |
Process paRameters |
RSM |
ABC |
Mellal and Williams (2015) |
Multi-pass turning |
Min. Production cost |
Cutting paRameters |
Analytical |
COA |
Khanghah et al. (2015) |
Micro-milling |
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) |
End-milling on metal matrix composites |
Min. SR |
Speed, feed, depth, step-over Ratio |
Non-linear regression |
GA, SA, TLBO, GS |
Rao and Krishna (2014) |
Wire-EDM on metal matrix composites |
Min. SR, WWR Max. MRR |
Process paRameters |
RSM |
GA-II |
Rong et al. (2016) |
Laser bRazing welding |
Min. Width of weld bead |
Feed Rate, speed, gap |
ELM model |
GA |
Shukla and Singh (2017) |
AbRasive Water-Jet 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 ACO-S) based algorithms for feature selection and applied them to computeRaided weld inspections. Liao [12] also investigated feature extRaction and feature selection in sensor-based 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 Hill-descent 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 Hill-descent 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 (fx mm), feed Rate (fy 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, fx is the amount of indentation of the tool into the machining surface, while feed Rate, fy 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 Ra (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 Ra, where machining paRameters are taken as inputs.
So the optimization problem becomes,
Minimize, Machining time (T) (1)
Subject to, 0.4 ≤ Ra ≤ 0.6
φ = [0, 30]°, d ={6, 7, 8, 9, 10} mm, S = {316, 520, 715} rpm,
fx=[0.2, 0.4] mm, fy = [22, 44] mm/min, and t =[0.1, 0.3] mm,
This is a mixed discrete-continuous 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 near-optimum 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, Hill-descent 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 modifying all of the codes and the codes are run on a desktop computer with Intel® Core™2 Duo 3.33GHz processor, 4GB RAM and 64-bit windows-7 enterprise opeRating system.
Statistical analysis with Student’s t-test also shows that feed Rate (fy) and Radial depth (fx) 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 (fy) and Radial depth (fx) as input paRameters, seveRal ANFIS models are developed with different architectures. The corresponding leave-one-out 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 leave-one-out RMSE |
||||||
fx |
fy |
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 t-test shows that speed, feed Rate and axial depth of cut are non-significant (with higher p-value). So it is wise to select cutter axis inclination angle (φ), tool diameter (d) and Radial depth of cut (fx) as the most influential input paRameters for Ra prediction.
Variable |
Parameter Estimate |
Standard Error |
t-value |
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 leave-one-out RMSE |
|||||||
φ |
d |
fx |
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 ≤ Ra ≤ 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 Radepends 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 identify the statistical significance of the metaheuristics and the Local Search (LS) stRategy. The experiments are independent and the experimental data satisfy 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 one-way ANOVA is prepared for testing the hypothesis that, “all ten algorithms provide the same mean best objective value”. Very low p-value 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 |
1.39276e-76 |
Error |
252.015 |
290 |
0.869 |
|
|
Total |
925.229 |
299 |
|
|
|
On the other hand, in Table 10, a one-way ANOVA is prepared for testing the hypothesis that “all of the ten algorithms take same mean elapsed time”. Very low p-value 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 two-way ANOVA is also developed [shown in Table 11]. This two-way ANOVA test informs that there are significant effects of local search stRategy (p-value = 0.0163), metaheuristics (p-value = 0) as well as their inteRactions (p-value = 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 |
6.75886e-133 |
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, fx |
Feed Rate, fy |
|||
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 self-set-up 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.
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