Parameter optimization of advanced machining ... - Semantic Scholar

Parameter optimization of advanced machining processes using cuckoo optimization algorithm and hoopoe heuristic Mohamed Arezki Mellal & Edward J. Williams

Journal of Intelligent Manufacturing ISSN 0956-5515 J Intell Manuf DOI 10.1007/s10845-014-0925-4

1 23

Accepted and published manuscript http://link.springer.com/article/10.1007/s10845-014-0925-4

Parameter optimization of advanced machining processes using cuckoo optimization algorithm and hoopoe heuristic Mohamed Arezki MELLAL1*, Edward J. WILLIAMS2, 3 Faculty of Engineering Sciences (FSI), M’Hamed Bougara University, Boumerdes 35000, Algeria;

1

2

Industrial and Manufacturing Systems Engineering Department, College of Engineering and Computer Science, University of Michigan, Dearborn 48126, USA; 3

Decision Sciences, College of Business, University of Michigan, Dearborn 48126, USA; *E-mail: [email protected]

[email protected]

Abstract Unconventional machining processes (communally named advanced or modern machining processes) are widely used by manufacturing industries. These advanced machining processes allow producing complex profiles and high quality-products. However, several process parameters should be optimized to achieve this end. In this paper, the optimization of process parameters of two conventional and four advanced machining processes is investigated: drilling process, grinding process, abrasive jet machining (AJM), abrasive water jet machining (AWJM), ultrasonic machining (USM), and water jet machining (WJM), respectively. This research employed two bio-inspired algorithms called the cuckoo optimization algorithm (COA) and the hoopoe heuristic (HH) to optimize the machining control parameters of these processes. The obtained results are compared with other optimization algorithms described and applied in the literature.

Keywords: Advanced machining processes; Process parameters; Cuckoo optimization algorithm (COA); Hoopoe heuristic (HH) 1.

Introduction Many modern manufacturing industries, such as aircraft, automobile, and shipbuilding,

involve several machining processes. These machining processes can be divided into two major groups which are (i) cutting process with traditional/conventional machining (e.g., turning, milling, drilling and grinding) and (ii) cutting process with advanced/unconventional machining (e.g., ultrasonic machining (USM) and water jet machining (WJM)) [1].

1


The high performance of a machining process depends on handling the process parameters. In general, a machining process model is a mathematical expression representing the relationship between two terms, process parameters and machining performance. This mathematical model can be solved using three categories of techniques [2, 3]: experimental, analytical techniques (e.g., Statistical Regression technique), and Soft Computing techniques also referred to as Artificial Intelligence (e.g., Genetic algorithm (GA) [4], Artificial Neural Network (ANN) [4], Particle Swarm Optimization (PSO) [5], Cuckoo Search (CS) [68], Glowworm Swarm Optimization (GSO) [9], Firefly Algorithm (FA) [10], and Fuzzy Logic (FL) [11]). The techniques of soft computing showed their effectiveness in solving this kind of problem [1119]. They allow finding good results and avoiding the disadvantages of experimental and analytical techniques which are [20]: costly, time-consuming, and tedious. The present work deals with the machining parameters of two traditional machining processes (drilling process and grinding process) and four advanced machining processes (abrasive jet machining (AJM), abrasive water jet machining (AWJM), ultrasonic machining (USM), and water jet machining (WJM)) by resorting to two recently developed bio-inspired optimization algorithms, namely the cuckoo optimization algorithm (COA) and the hoopoe heuristic (HH). A comparison between the results obtained by these algorithms and those obtained by different optimization algorithms applied in the literature is highlighted. The paper is organized as follows. In Section 2, the principles of the cuckoo optimization algorithm are presented. In Section 3, the main idea behind the hoopoe heuristic is presented. Section 4 presents the optimization problems of the selected machining processes. Finally, in Section 5 some conclusions and indications for further work are provided. 2.

Cuckoo optimization algorithm The cuckoo optimization algorithm (COA) was developed by Ramin Rajabioun [21] in

2011 to solve optimization problems. The main idea behind the COA is the inspiration from the behavior of a bird called the cuckoo for laying eggs in the nests of other species. From the literature, it has been proven that the COA is a powerful algorithm for solving different engineering optimization problems, such as multivariable controller design [21], replacement of obsolete components in industrial plants [22, 23], statistical process control [24], job scheduling [25], analyzing the electro-chemical machining process, fractional-order hyperchaotic system [26], and determination of the warranty period [27]. Furthermore, it has

2


been proven that the global optimum is globally guaranteed with a proper and rapid convergence after a few iterations. First, an initial population of mature cuckoos starts to lay eggs in their habitat area:

Habitat =[x1, x2 ,..., xNCOA ]

(1)

where x1, x2, …, x NCOA are the design variables of the problem. Therefore, the optimization algorithm starts with a candidate habitat matrix Npop×NCOA. The cuckoos carefully mimic the pattern and color of the eggs of the host nests. However, some eggs are dissimilar and will be destroyed by the parasitized birds. The eggs are laid within an egg-laying radius (ELR): ELR= 

Number of current cuckoos ' eggs  (varhi  varlow ) Total number of eggs

(2)

where α is a positive integer implemented for the value of ELR, varhi and varlow are the upper limit and the lower limit for variables, respectively. The cuckoos’ eggs will hatch and some chicks will starve. The goal of the cuckoos is to maximize the profit of the habitat. Hence, the minimizing problem will be written as follows:

Cost =  Profit =  fCOA (Habitat) =  fCOA ( x1, x2 ,..., xNCOA )

(3)

The survival and mature cuckoos will migrate toward the best habitat for reproduction. The cuckoos’ groups are recognized using K-means clustering. During the migration, each cuckoo flies only λ% of the way toward its goal with a deviation φ (rad) given by:

  U (0,1)     U ( , )

(4)

6 6

where λ is a random number uniformly distributed between 0 and 1. The cuckoo optimization algorithm can be summarized as follows [21]: Step 1: Initialize the habitats with some random points on the profit function; Step 2: Dedicate some eggs to each cuckoo; 3


Step 3: Define ELR for each cuckoo; Step 4: Let cuckoos lay eggs inside their corresponding ELR; Step 5: Destroy those eggs that are recognized by host birds; Step 6: Let eggs hatch and chicks grow; Step 7: Evaluate the habitat of each newly grown cuckoo; Step 8: Limit cuckoos’ maximum number in environment and kill those who live in the worst habitats; Step 9: Cluster cuckoos, find best group and select goal habitat; Step 10: Let new cuckoo population migrate toward goal habitat; Step 11: If stop condition is satisfied, stop; otherwise, go to Step 2. Figure 1 shows the flowchart of the COA. Insert: Figure 1  Flowchart of COA [21] 3.

Hoopoe heuristic The hoopoe heuristic (HH) was developed in 2012 [28]. The HH algorithm is inspired by

the lifestyle of a bird family called hoopoe. Notably, the ground-probing behavior of certain hoopoe species was investigated. The hoopoes dig into trees or rocks to lay their eggs in different areas. Hence, they try to find the optimum position. On the other hand, they explore the landscape, make short probes into the ground and insert the bill fully for searching edible objects. The HH algorithm works with only one hoopoe and several nests. Therefore, the function evaluations are determined from the number of nests and generations of hoopoes. The hoopoe explores the landscape randomly by performing a Lévy flight:

S (t 1)  S (t )    Lévy( )

(5)

where α>0 is the step size, α = O(1). The Lévy flight obeys a Lévy distribution: Lévy  u  t  , (1    3)

(6)

The area is probed by the hoopoe by penetrating its bill, with a success probability to find a worm:

ps  0, 1

4

(7)


It is also assumed that the hoopoe digs the area perfectly as well as greater than a predefined threshold of success probability. It can be noted that the ground probing and the Lévy flight are the intensification and diversification of the HH, respectively. The hoopoe heuristic can be summarized as follows [28]: Step 1: Create a random set of points; Step 2: Perform the ground-probing with a fixed value of digging radius; Step 3: Perform a Lévy flight; Step 4: Evaluate the fitness values; Step 5: Classify the fitness values; Step 6: Identify the best fitness value; Step 7: If stop condition is satisfied, stop; otherwise, go to Step 2. Figure 2 shows the flowchart of the HH. Insert: Figure 2  Flowchart of HH 4.

Optimization models of selected machining processes This section includes two traditional and four advanced machining processes. The

optimization models of these machining processes are presented, the COA and the HH are applied to find the optimal parameters, and the results are compared to previous works. The two algorithms have been run on Intel Pentium Processor G620 (3Mo Cache, 2.60GHz, Sandy Bridge) PC with 4GB memory (Windows 7, 64 bits). 4.1. Traditional machining processes 4.1.1. Grinding process 4.1.1.1. Model The grinding process model presented by Gopal and Rao [29] is adopted in this paper. The goal is to maximize the material removal rate (MRR) of the ceramic grinding process. The MRR mathematical problem involves the feed rate fr (m/min), depth of cut dc (μm), and grit size (M) as decision variables of the model.

Maximize MRR  ( f r )*(dr ) The MRR represented by Eq. (8) is subject to the maximum allowable values of surface

5

(8)


roughness SRmax (μm) and number of flaws NDmax, respectively:

0.145(dc )0.1939 ( f r )0.7071 ( M )0.2343  SR max

(9)

where the SRmax = 0.3, 0.35 or 0.4 (μm) for the respective experiments.

29.67(dc )0.4167 ( f r )0.8333  NDmax

(10)

where the NDmax = 7, 9, or 11 for the respective experiments. The parameter bounds (search space) for the three process parameters (decision variables) are given as:

8.6 (m/min)  f r  13.4 (m/min)

(11)

5 (μm)  dc  30 (μm)

(12)

120  M  500

(13)

4.1.1.2. Results and discussion The grinding process formulated by the above optimization problem has been solved using the COA and the HH which were presented in Section 2 and Section 3, respectively. Table 1 presents a statistical comparison of the results obtained by both algorithms with other techniques proposed by the previous researchers for different combinations of constraints. Better values and constraint violations in each category are highlighted in bold type. Insert: Table 1  Comparison of the optimum results for grinding process From Table 1, it can be seen that the HH has outperformed the GA. The COA has outperformed all other techniques for the experiments 2, 3, 6, and 9 in terms of maximizing the MRR value and reducing the number of function evaluations. The TLBO, ARQiEA, and NMPSO increased the MRR value of some experimental cases. However, the constraints have been violated. From Table 2, it can be observed that the COA has converged very fast. The information about the total execution time of other algorithms reported in Table 1 is unavailable in the literature. However, for all the cases, the results of the COA are obtained in a lower number of function evaluations, which clearly indicates that the execution time is shorter compared to other optimization algorithms.

6


Insert: Table 2  CPU time for the grinding process 4.1.2. Drilling process 4.1.2.1. Model The goal considered here is to minimize the surface roughness in the drilling process [35]. The optimization problem involves three machining parameters, namely the cutting speed A (m/min), feed rate B (mm/rev), and cutting environment C:

Minimize Ra  4.115  0.82767A+8.225B+0.135C+0.0538A2

(14)

The boundary conditions for the parameters are:

5 (m/min)  A  15 (m/min)

(15)

0.1 (mm/rev)  B  0.3 (mm/rev)

(16)

1 C  3

(17)

4.1.2.2. Results and discussion In [35], Kilickap et al. applied the genetic algorithms (GA) for solving the above optimization problem, whereas Rao and Kalyankar in [34] used the teaching-learning based optimization. Table 3, Figures 3 and 4 summarize the statistical comparison across all the algorithms. The HH and COA have been run for 1800 and 50 function evaluations, respectively. Furthermore, the execution time was 21.5437 s and 0.39 s, respectively. Insert: Table 3  Comparison of the optimum results for drilling process Insert: Figure 3  Optimal values for drilling process Insert: Figure 4  Number of function evaluations for drilling process From Table 3, it can be observed that the HH has outperformed the GA in terms of surface roughness value and number of function evaluations. Rao and Kalyankar [34] reveal that the results obtained by the TLBO were at the third iteration. However, the total number of function evaluations has not been provided. The COA provided similar surface roughness value (1.8892 μm) with the TLBO, but the COA converged at the second iteration and the total number of function evaluations was 50.

7


4.2. Advanced machining processes 4.2.1. Water jet machining 4.2.1.1. Model The water jet machining (WJM) uses the kinetic energy of water jet for precision cutting of several materials, such as Kevlar®, asbestos, graphite, glass epoxy, and leather [20]. Jain et al. [20] presented the WJM optimization problem for maximizing the material removal rate MRR (mm3/s) and used genetic algorithms. It involves four decisions variables: water jet pressure at the nozzle exit Pw (MPa), diameter of water jet nozzle dwn (mm), traverse rate of the nozzle fn (mm/s), and stand-off-distance X (mm). C fw Pw    yw   2256.76  f  0.297 1.5 0.5 (2/3)  w n Maximize MRR  d wn f n X  1   1  e  C fw 2 P  w    

(18)

where:



2 0.5  0.57  0.2 2    K

 1  cw K   1  Pw 2  K

  

X Xi

(19)

(20)

(21)

The maximizing of the MRR is subject to the power consumption constraint:

1

2 1.5 0.777 101.5 d wn Pw 0 Pmax

(22)

The values of the constants are presented in Table 4 and the variable bounds are:

1(MPa)  Pw  400 (MPa)

(23)

0. 05 (mm)  dwn  0. 5 (mm)

(24)

1 (mm/s)  f n  300 (mm/s)

(25)

2. 5 (mm)  X  50 (mm)

(26)

8


Insert: Table 4  Values of the constants used in the optimization problem of water jet machining (WJM) [20] 4.2.1.2. Results and discussion The optimization problem of the water jet machining described above has been solved using the COA and HH. The obtained results by both algorithms and the GA used by Jain et al. [20] are presented in Table 5. It should be noted that Jain et al. [20] reported that the optimal obtained value of MMR using GA was 139.79 mm3/s. However, if one replaces the optimal cutting parameters, then, we find 134.2452 mm3/s. The execution time of the COA and HH was 0.39 s and 21.8245, respectively. The HH improved the MRR value over the GA with 0.1305 mm3/s, but needed 1,000 supplementary function evaluations. Table 5  Comparison of the optimum results for water jet machining From Figures 5 and 6, it can be observed that the COA has outperformed the GA and HH by increasing the value of MRR and decreasing the number of function evaluations. Insert: Figure 5  Optimal values for water jet machining Insert: Figure 6  Number of function evaluations for water jet machining 4.2.2. Abrasive jet machining The abrasive jet machining (AJM) uses velocity jet of abrasive particles and carrier gas. It is an efficient machining process for ductile/brittle metals/alloys, ceramics, and semiconductors [20]. In this paper, the models of Jain et al. [20] for the brittle and ductile materials are adopted, where the goal is to maximize the material removal rate MRR (mm3/s). 4.2.2.1. Process for brittle materials a) Model The optimization problem of the abrasive jet machining for brittle materials involves three decision variables: mass flow rate of abrasive particles Ma (kg/s), mean radius of abrasive particles rm (mm), and velocity of abrasive particles va (mm/s). The objective function for maximizing the MRR is given by Eq. (27) and the surface roughness constraint is given by Eq. (28).

Maximize MRR  0.0035

9

a M a v1.5 a 0.75 0.25  fw a

(27)


Surf ace roughness constraint:

18.26 1 ( Ra )max

 a      fw 

0.5

rmva  0

(28)

The values of the constants are presented in Table 6 and the variable bounds are given below:

0.0000167(kg/s)  M a  0.0005 (kg/s)

(29)

0.005 (mm)  rm  0 .075 (mm)

(30)

150000 (mm/s)  va  400000 (mm/s)

(31)

Insert: Table 6  Values of the constants used in the optimization problem of abrasive jet machining in brittle materials [20] b) Results and discussion Table 7 summarizes the results available in the literature and those obtained in the present work. Jain et al. [20] used generic algorithms with 7,600 function evaluations and obtained the maximum MRR of 8.2423 mm3/s, whereas Rao et al. [36] used simulated annealing and improved the value of MRR (8.2525 mm3/s). Leter, Rao and Kalyankar [37] tried increasing the value of MRR using teaching-learning based optimization and obtained 8.797 4mm3/s. However, the constraint of surface roughness has been violated. Thus, the result of the TLBO is not competitive. The values of MRR obtained by the HH and COA are 8.2481 mm3/s and 8.2528 mm3/s, respectively. The execution time was 0.8112 s for the COA and 40.2795 s for the HH. Insert: Table 7  Comparison of the optimum results for abrasive jet machining process in brittle materials Figure 7 shows that the HH has increased the value of MRR over the GA, and the COA over all the algorithms. Furthermore, the COA needed the lowest number of function evaluations (Figure 8). This shows the superiority of COA over all the algorithms applied to solve the optimization problem of AJM in brittle materials. Insert: Figure 7  Optimal values for abrasive jet machining in brittle materials

10


Insert: Figure 8  Number of function evaluations for abrasive jet machining in brittle materials 4.2.2.2. Process for ductile materials a) Model The optimization problem of the abrasive jet machining for ductile materials involves the same decision variables as those for brittle materials. However, the mathematical expressions of the objective function and the surface roughness constraint are different.

Maximize MRR  1.0436 106

w 2 1.5 0.5  cw H dw a

M a va3

(32)

Surf ace roughness constraint:

25.82 1 ( Ra )max

 a     H dw 

0.5

rmva  0

(33)

The values of the constants are presented in Table 8. and the variable bounds are given as the same as in the case of brittle materials (Eq. (29)(31)). Insert: Table 8  Values of the constants used in the optimization problem of abrasive jet machining (AJM) for ductile materials [20] b) Results and discussion The HH and COA are applied to this model. The execution time of each algorithm was 54.8344 s and 1.0296 s, respectively. As for brittle materials, the results are compared with the GA used by Jain et al. GA [20], the simulated annealing used by Rao et al. [36], and the teaching-learning based optimization used by Rao & Kalyankar [37]. The comparison of the results is given in Table 9 which shows that the TLBO has violated the constraint limitation. Thus, the result of the used TLBO is not competitive. The HH has given the maximum MRR of 0.605371 mm3/s as compared to 0.6035 mm3/s given by the GA [20] and 0.6053 mm3/s given by the SA [36]. The COA has given 0.605637 mm3/s with only 480 function evaluations. Insert: Table 9  Comparison of the optimum results for abrasive jet machining process in ductile materials Figures 9 and 10 show the MRR value obtained by each algorithm and the required 11


number of function evaluations, respectively. Therefore, the COA has proved its superiority over all the applied algorithms for AJM in ductile materials. Insert: Figure 9  Optimal values for abrasive jet machining in ductile materials Insert: Figure 10  Number of function evaluations for abrasive jet machining in ductile materials 4.2.3. Abrasive water jet machining 4.2.3.1. Model The abrasive water jet machining (AWJM) uses a high-velocity water jet in combination with abrasive particles. It is an efficient machining process for cutting different types of materials, such as copper, lead, tungsten carbide, composites, steel, titanium, graphite, and ceramics [38]. The AWJM optimization problem considered in this work is to compute a minimum Ra value [39]:

Minimize Ra  5.07976+0.08169 V  0.07912 P  0.34221 h  0.08661 d  0.34866 m  0.00031 V 2  0.00012 P 2  0.10575 h2  0.00041 d 2 (34) 2  0.07590 m  0.00008 Vm  0.00009 Pm  0.03089 hm  0.00513 dm The variable bounds are:

50(mm/min)  V  150 (mm/min)

(35)

125 (MPa)  P  250 (MPa)

(36)

1 (mm)  h  4 (mm)

(37)

60 (μm)  d  120 (μm)

(38)

0. 5 (g/s)  m  3.5 (g/s)

(39)

where V is the traverse speed, P is the water jet pressure, h is the standoff distance, d is the abrasive grit size, and m is the abrasive flow rate. 4.2.3.2. Results and discussion Table 10 summarizes and compares the results obtained by the HH, COA and other techniques applied in the literature. The minimum Ra obtained by the HH is 1.5230 μm with 20,000 function evaluations in 42.2451 s of time execution, whereas the COA provided 1.5222 μm of Ra and required 290 function evaluations in 0.7956 s. 12


Insert: Table 10  Comparison of the optimum results for abrasive water jet machining From Table 10 and Figure 11, it can be observed that the HH has outperformed eight techniques. The integrated artificial neural networksimulated annealing of type 1 [2] has given the same value with the HH 1.5230 μm, but required 7,1100 additional function evaluations. The COA (1.5222 μm, 290 function evaluations) has outperformed all the algorithms, except that the artificial bee colony [17] has given the same value with 500 function evaluations. Figure 12 shows the number of function evaluations required by each algorithm. Insert: Figure 11  Optimal values for abrasive water jet machining Insert: Figure 12  Number of function evaluations for abrasive water jet machining

4.2.4. Ultrasonic machining 4.2.4.1. Model The ultrasonic machining process (USM) uses high-frequency electrical energy which is converted into mechanical vibrations. These mechanical vibrations are transmitted to the abrasive grains in the slurry. It is an efficient machining process for ceramics, inorganic glasses, quartz, etc [20, 42, 43]. The optimization model for the USM process which is adopted in the present work is based on the model considered by Jain et al. [20], Rao et al. [44], Rao [38], and Rao & Kalyankar [37]. The objective is to maximize the MRR (mm3/s) under the surface roughness constraint. The optimization problem involves five decision variables: amplitude of vibration Av (mm), frequency of vibration fv (Hz), mean diameter of abrasive grain dm (mm), volumetric concentration of abrasive particles in slurry Cav, and static feed force Fs (N).

Maximize MRR 

0.75 4.963 At0.25 K usm

 fw (1   )   

0.75

0.25 Fs0.75 Av0.75Cav dm fm

(40)

Surface roughness constraint:

1

1154.7  At fw (1   )   

0.5

( Ra )max

13

 Fs Av d m     Cav 

0.5

0

(41)


The values of the constants are presented in Table 11 and the variable bounds are given below:

0. 005(mm)  Av  0 .1 (mm)

(42)

10000 (Hz)  fv  40000 (Hz)

(43)

0. 007 (mm)  dm  0.15 (mm)

(44)

0.05  Cav  0 . 5

(45)

4. 5 (N)  Fs  45 (N)

(46)

Insert: Table 11  Values of the constants used in the optimization problem of ultrasonic machining (USM) [20] 4.2.4.2. Results and discussion Jain et al. [20] used genetic algorithms for achieving maximum MRR (3.553 mm3/s) with 12,600 function evaluations. Rao et al. [44] solved the same problem by using the artificial bee colony, modified harmony search, and particle swarm optimization. Rao [38] used the simulated annealing and the shuffled frog leaping. Rao and Kalyankar [37] used the teachinglearning based optimization. The maximum MRR reported by these algorithms are given in Table 12. Insert: Table 12  Comparison of the optimum results for ultrasonic machining The HH and COA have been applied for maximizing the MRR value in USM. The obtained values were 3.7415 mm3/s and 4.0064 mm3/s, whereas the execution times were 36.9254 s and 0.7644 s, respectively. From Table 12, it can be observed that the HH has outperformed the GA (3.553 mm3/s) and the SA (3.660 mm3/s) by requiring fewer function evaluations. A maximum MRR of 4.0064 mm3/s is given by the COA, which is better than that given by all the other algorithms. Furthermore, the COA required only 225 function evaluations, which is the lowest number. Figures 13 and 14 show the increasing of the MRR value and the number of function evaluations required by each algorithm, respectively. Insert: Figure 13  Optimal values for ultrasonic machining Insert: Figure 14  Number of function evaluations for ultrasonic machining

14


5.

Conclusions and future research In this paper, two traditional machining processes (drilling and grinding) and four

advanced machining processes (AJM, WJM, AWJM and USM) were considered for computing their respective machining parameters using two modern optimization algorithms named “hoopoe heuristic” and “cuckoo optimization” algorithm. It was their first implementation in the literature for solving the above machining processes. The same optimization models were earlier solved by other researchers using various techniques. The implemented HH and COA were successfully applied to all the considered optimization models in the current work and they have given considerable improvement in terms of results. It should be noted that the both applied algorithms (COA and HH) have been run for different functions of evaluations in order to check whether either is getting trapped at a local optimum solution or not. Comparisons between the results clearly show that the COA algorithm has outperformed the other algorithms in terms of better results with fewer function evaluations. Therefore, the COA showed its effectiveness in solving this kind of problem and can be considered as a powerful optimization algorithm. The scope of future work is how to conduct the hybridization of the cuckoo optimization algorithm and hoopoe heuristic in order to render the computation more efficient and deal with the multiobjective problems.

REFERENCES 1.

Yusup N.; Zain, A.M.; Hashim, S.Z.M. Evolutionary techniques in optimizing

machining parameters: Review and recent applications (2007–2011). Expert Systems with Applications 2012, 39(10), 9909–9927. 2.

Zain, A.M.; Haron, H.; Sharif, S. Estimation of the minimum machining performance in

the abrasive waterjet machining using integrated ANN-SA. Expert Systems with Applications 2011, 38(7), 8316–8326. 3.

Baraskar, S.S.; Banwait, S.S.; Laroiya, S.C. Multiobjective optimization of electrical

discharge machining process using a hybrid method. Materials and Manufacturing Processes 2013, 28(4), 348–354.

15


4.

Wang, G.; Wang, Y.; Zhao, J.; Chen, G. Process optimization of the serial-parallel

hybrid polishing machine tool based on artificial neural network and genetic algorithm. Journal of Intelligent Manufacturing 2012, 23(3), 365–374. 5.

Chu, C.H.; Hsieh, H.T. Generation of reciprocating tool motion in 5-axis flank milling

based on particle swarm optimization. Journal of Intelligent Manufacturing 2012, 23(5), 1501–1509. 6.

Yang, X.S. Cuckoo Search, in Nature-Inspired Optimization Algorithms. Elsevier,

2014, ch. 9, 129–139. 7.

Azizah, M.; Zain, A.M.; Bazin, N.E.N; Udin, A. Cuckoo search algorithm for

optimization problems - A literature review. Applied Mechanics and Materials 2013, 421, 502–506. 8.

Kamaruzaman, A.F.; Zain, A.M.; Yusuf, S.M.; and Udin, A. Levy flight algorithm for

optimization problems - A literature review. Applied Mechanics and Materials 2013, 421, 496–501. 9.

Zainal, N.; Zain, A.M.; Haizan, N.; Radzi, M.; Udin, A. Glowworm swarm optimization

(GSO) algorithm for optimization problems: A state-of-the-art review. Applied Mechanics and Materials 2013, 421, 507–511. 10.

Johari, N.F.; Zain, A.M.; Mustaffa, N.H.; Udin, A. Firefly algorithm for optimization

problem. Applied Mechanics and Materials 2013, 421, 512–517. 11.

Adnan, M.R.H.; Sarkheyli, A.; Zain, A.M.; Haron, H. Fuzzy logic for modeling

machining process: a review. Artificial Intelligence Review 2013, DOI: 10.1007/s10462-0129381-8. 12.

Mohamad, A.; Zain, A.M.; Bazin, N.E.N.; Udin, A. A process prediction model based

on cuckoo algorithm for abrasive waterjet machining. Journal of Intelligent Manufacturing 2013, DOI: 10.1007/s10845-013-0853-8. 13.

Yusup, N.; Zain, A.M.; Hashim, S.Z.M. Overview of PSO for optimizing process

parameters of machining. Procedia Engineering 2012, 29, 914–923.

16


14.

Zain, A.M.; Haron, H.; Sharif, S. An overview of GA technique for surface roughness

optimization in milling process, in ITSim 2008: International Symposium on Information Technology. Kuala Lumpur, Malaysia, 2008. 15.

Zhang, J.Y.; Liang, S.Y.; Yao, J.; Chen, J.M.; Huang, J.L. Evolutionary optimization of

machining processes. Journal of Intelligent Manufacturing 2006, 17(2), 203–215. 16.

Liu, X.J.; Yi, H.; Ni, Z.H. Application of ant colony optimization algorithm in process

planning optimization. Journal of Intelligent Manufacturing 2013, 24(1), 1–13. 17.

Yusup, N.; Sarkheyli, A.; Zain, A.M.; Hashim, S.Z.M.; Ithnin, N. Estimation of optimal

machining control parameters using artificial bee colony. Journal of Intelligent Manufacturing 2013, DOI: 10.1007/s10845-013-0753-y 18.

Yusoff, Y.; Ngadiman, M.S.; Zain, A.M. Overview of NSGA-II for optimizing

machining process parameters. Procedia Engineering 2011, 15, 3978–3983. 19.

Grzenda, M.; Bustillo, A.; Zawistowski, P. A soft computing system using intelligent

imputation strategies for roughness prediction in deep drilling. Journal of Intelligent Manufacturing 2012, 23(5), 1733–1743. 20.

Jain, N.K.; Jain, V. K.; Deb, K. Optimization of process parameters of mechanical type

advanced machining processes using genetic algorithms. International Journal of Machine Tools and Manufacture 2007, 47(6), 900–919. 21.

Rajabioun, R. Cuckoo optimization algorithm. Applied Soft Computing 2011, 11(8),

5508–5518. 22.

Mellal, M.A.; Adjerid, S., E.; Williams, E.J.; Benazzouz, D. Optimal replacement

policy for obsolete components using cuckoo optimization algorithm based-approach: Dependability context. Journal of Scientific and Industrial Research 2012, 71(11), 715‒721. 23.

Mellal, M.A.; Adjerid, S.; Williams, E.J. Optimal selection of obsolete tools in

manufacturing systems using cuckoo optimization algorithm. Chemical Engineering Transactions 2013, 33, 355‒360.

17


24.

Addeh, J.; Ebrahimzadeh, A.; Azarbad, M.; Ranaee V. Statistical process control using

optimized neural networks: A case study. ISA Transactions 2013, DOI: 10.1016/j.isatra.2013.07.018 25.

Rabiee M.; Sajedi, H. Job scheduling in grid computing with cuckoo optimization

algorithm. International Journal of Computer Applications 2013, 62(16), 38–44. 26.

Sahab, A.R.; Ziabari, M.T.; Modabbernia, M.R. A novel fractional-order hyperchaotic

system with a quadratic exponential nonlinear term and its synchronization. Advances in Difference Equations 2012, 2012,1–21. 27.

Roozitalab, A.; Asgharizadeh, E. Optimizing the warranty period by cuckoo meta-

heuristic algorithm in heterogeneous customers’ population. Journal of Industrial Engineering International 2013, 9(27), 1–6. 28.

El-Dosuky, M.A.; Rashad, M.Z.; Hamza, T.T.; EL-Bassiouny, A.H. New hoopoe

heuristic optimization. International Journal of Science and Advanced Technology 2012, 2(9), 85–90. 29.

Gopal, A.V.; Rao, P.V. The optimisation of the grinding of silicon carbide with

diamond wheels using genetic algorithms. International Journal of Advanced Manufacturing Technology 2003, 22(7–8), 475–480. 30.

Lee, T.S.; Ting, T.O.; Lin, Y.J.; Htay, T. A particle swarm approach for grinding

process optimization analysis. International Journal of Advanced Manufacturing Technology 2007, 33(11–12), 1128–1135. 31.

Zahara, E.; Hu, C. Solving constrained optimization problems with hybrid particle

swarm optimization. Engineering Optimization 2008, 40(11), 1031–1049. 32.

Mani, A.; Patvardhan, C. Solving ceramic grinding optimization problem by adaptive

quantum evolutionary algorithm, in IEEE International Conference on Intelligent Systems, Modelling and Simulation 2010. 33.

Lee, T.S.; Ting, T.O.; Lin, Y.J. An investigation of grinding process optimization via

evolutionary algorithms, in IEEE Swarm Intelligence Symposium 2007.

18


34.

Rao, R.V.; Kalyankar, V.D. Parameter optimization of machining processes using a new

optimization algorithm, Materials and Manufacturing Processes 2012, 27(9), 978–985. 35.

Kilickap, E.; Huseyinoglu, M.; Yardimeden, A. Optimization of drilling parameters on

surface roughness in drilling of AISI 1045 using response surface methodology and genetic algorithm. International Journal of Advanced Manufacturing Technology 2011, 11(8), 79–88. 36.

Rao, R.V.; Pawar, P.J.; Davim, J.P. Optimization of process parameters of mechanical

type advanced machining processes using a simulated annealing algorithm. International Journal of Materials and Product Technology 2010, 37(1–2), 83–101. 37.

Rao R.V.; Kalyankar, V.D. Parameter optimization of modern machining processes

using teaching–learning based optimization algorithm. Engineering Applications of Artificial Intelligence 2013, 26(1), 524–531. 38.

Rao, R.V. Modeling and optimization of modern machining processes, in Advanced

modeling and optimization of manufacturing processes 2011. London: Springer-Verlag, ch. 3,177–284. 39.

Zain, A.M.; Haron, H.; Sharif, S. Genetic Algorithm and Simulated Annealing to

estimate optimal process parameters of the abrasive waterjet machining. Engineering with Computers 2011, 27(3), 251–259. 40.

Çaydas, U.; Hascalık, A. A study on surface roughness in abrasive waterjet machining

process using artificial neural networks and regression analysis method. Journal of Materials Processing Technology 2008, 202(1–3), 574–582. 41.

Zain, A.M.; Haron, H.; Sharif, S. Optimization of process parameters in the abrasive

waterjet machining using integrated SA–GA. Applied Soft Computing 2011, 11(8), 5350–5359. 42.

Kumar, J. Ultrasonic machining  A comprehensive review. Machining Science and

Technology: An International Journal 2013, 17(3), 325–379. 43.

Lalchhuanvela, H.; Doloi, B.; Bhattacharyya, B. Enabling and understanding ultrasonic

machining of engineering ceramics using parametric analysis. Materials and Manufacturing Processes 2012, 27(4), 443–448.

19


44.

Rao, R.V.; Pawar, P.J.; Davim, J.P. Parameter optimization of ultrasonic machining

process using nontraditional optimization algorithms. Materials and Manufacturing Processes 2010, 25(10), 1120–1130.

20


Table captions Table 1  Comparison of the optimum results for grinding process Table 2  CPU time for the grinding process Table 3  Comparison of the optimum results for drilling process Table 4  Values of the constants used in the optimization problem of water jet machining (WJM) [20] Table 5  Comparison of the optimum results for water jet machining Table 6  Values of the constants used in the optimization problem of abrasive jet machining in brittle materials [20] Table 7  Comparison of the optimum results for abrasive jet machining process in brittle materials Table 8  Values of the constants used in the optimization problem of abrasive jet machining (AJM) for ductile materials [20] Table 9  Comparison of the optimum results for abrasive jet machining process in ductile materials Table 10  Comparison of the optimum results for abrasive water jet machining Table 11  Values of the constants used in the optimization problem of ultrasonic machining (USM) [20] Table 12  Comparison of the optimum results for ultrasonic machining Figure captions Figure 1  Flowchart of COA [21] Figure 2  Flowchart of HH Figure 3  Optimal values for drilling process Figure 4  Number of function evaluations for drilling process Figure 5  Optimal values for water jet machining Figure 6  Number of function evaluations for water jet machining Figure 7  Optimal values for abrasive jet machining in brittle materials Figure 8  Number of function evaluations for abrasive jet machining in brittle materials Figure 9  Optimal values for abrasive jet machining in ductile materials Figure 10  Number of function evaluations for abrasive jet machining in ductile materials Figure 11  Optimal values for abrasive water jet machining

21


Figure 12  Number of function evaluations for abrasive water jet machining Figure 13  Optimal values for ultrasonic machining Figure 14  Number of function evaluations for ultrasonic machining

22


Table 1  Comparison of the optimum results for grinding process

Expt.

SRmax NDmax Technique (μm)

Parameters: fr (m/min), dc (μm) and M

1

0.3

(13.37, 5.56, 471.29) 74.34 (13.3996, 5.6067, 492.472) 75.12846 (13.4, 5.607, 500) 75.1341 (13.4, 5.607, 481.0194) 75.1342 (13.4, 5.607, 500) 75.1342 (13.4, 5.607, 476.6414) 75.1342 (13.309, 6.027, 494.937) 80.2133 (13.399978, 5.60697, 476.35102) 75.1332 (13.4, 5.607027, 499.99462) 75.1342 (12.05, 8.22, 494.12) 99.05 (12.1688, 8.4520, 499.4811) 102.8518 (12.1715, 8.4557, 500) 102.9185 (12.1946, 8.4878, 500) 103.5048 (12.2, 8.488, 500) 103.5048 (12.1716, 8.4558, 500) 102.9024 (13.251, 9.955, 416.928) 131.914 (12.1702887, 8.45396, 499.7754) 102.8872 (12.171594, 8.455778, 500) 102.9203 (11.15, 11.21, 485) 124.99 (11.173, 11.5332, 499.2599) 128.8612 (11.1765, 11.5405, 500) 128.9823 (11.1977, 11.5842, 500) 129.7162 (11.2, 11.58, 500) 129.7162 (11.1766, 11.5405, 500) 128.9835 (11.527, 11.893, 197.525) 137.525 (11.1765, 11.54032, 500) 128.9803

7

2

9

3

11

GA [29] GA [30] PSO [30] NMPSO [31] ARQiEA [32] DE [33] TLBO [34] HH COA GA [29] GA [30] PSO [30] NMPSO [31] ARQiEA [32] DE [33] TLBO [34] HH COA GA [29] GA [30] PSO [30] NMPSO [31] ARQiEA [32] DE [33] TLBO [34] HH

23

MRR

Values of constraints SR (μm) 0.299 0.2975 0.2959 0.2986 0.2959 0.2998 0.2993 0.2992 0.2959 0.297 0.3 0.3 0.30000033 0.300095 0.3 0.3424 0.2993 0.2993 0.3 0.3 0.3 0.30000048 0.30002295 0.3 0.3825 0.2993

Std. Dev.

Number of function evaluations

N/A 0.0995 7.18E14 2.94E–10 1.14E13 0 N/A 8.78E16 0 N/A 0.8839 1.44E14 9.12E–06 6.42E06 7.19E06 N/A 5.13E16 0 N/A 1.0011 0 0.0001 3.73E06 1.08E05 N/A 2.05E16

9000 10000 10000 6784 3153 10000 8000 9900 950 9000 10000 10000 6812 4151 10000 8000 9900 1150 9000 10000 10000 6804 5432 10000 8000 11250

ND 6.989 7 7 7 7 7 7.2549 7 7 8.969 9 9 9.000011 9 9 9 9 9 10.89 11 11 11 11 11 10.855 11

Accepted and published manuscript http://link.springer.com/article/10.1007/s10845-014-0925-4 4

0.35

7

5

9

6

11

7

0.40

7

COA GA [29] GA [30] PSO [30] NMPSO [31] ARQiEA [32] DE [33] TLBO [34] HH COA GA [29] GA [30] PSO [30] NMPSO [31] ARQiEA [32] DE [33] TLBO [34] HH COA GA [29] GA [30] PSO [30] NMPSO [31] ARQiEA [32] DE [33] TLBO [34] HH COA GA [29] GA [30] PSO [30] NMPSO [31] ARQiEA [32] DE [33]

(11.176551, 11.540563, 500) (13.42, 5.54, 326.01) (13.3996, 5.6067, 467.0716) (13.4, 5.607, 258.2402) (13.4, 5.607, 387.2869) (13.4, 5.607, 500) (13.4, 5.607, 255.7044) (13.307, 6.184, 494.861) (13.4, 5.607016, 473.71121) (13.4, 5.607027, 500) (13.39, 10.19, 430.40) (13.3995, 10.2477, 451.8736) (13.4, 10.2484, 430.7846) (13.4, 10.2485, 493.2479) (13.4, 10.25, 500) (13.4, 10.2485, 483.4113) (13.175, 10.815, 465.792) (13.39981, 10.248, 414.32648) (13.4, 10.248456, 500) (12.76, 14.96, 490.33) (12.8662, 15.2933, 499.9865) (12.8663, 15.2934, 500) (12.8906, 15.3513, 500) (12.89, 15.35, 500) (12.8663, 15.2935, 500) (13.215, 15.639, 259.738) (12.866328, 15.292966, 500) (12.86633, 15.29345, 500) (13.40, 5.55, 144) (13.3999, 5.6069, 368.3301) (13.4, 5.6070, 238.4232) (13.4, 5.607, 436.5745) (13.4, 5.607, 500) (13.4, 5.607, 256.5515)

24

128.9837 74.35 75.1278 75.1341 75.1338 75.1338 75.1338 82.290 75.1340 75.1341 136.44 137.3147 137.3293 137.3293 137.3293 137.3293 142.488 137.3212 137.3293 190.89 196.7674 196.7694 197.8883 197.8615 196.7708 206.668 196.7643 196.7705 74.37 75.1335 75.1341 75.1338 75.1338 75.1338

0.2993 0.327 0.3012 0.3461 0.3142 0.2959 0.3470 0.3008 0.2996 0.2959 0.345 0.3412 0.3451 0.3337 0.3326 0.3359 0.3376 0.3475 0.3326 0.348 0.35 0.3492 0.35 0.35 0.3492 0.4167 0.3492 0.3492 0.396 0.3185 0.3527 0.3054 0.2959 0.3459

11 6.956 7 7 7 7 7 7.3340 7 7 8.984 9 9 9 9 9 9.3348 9 9 10.98 11 11 11.000024 11.000062 11.000028 10.858 11 11 6.97 7 7 7 7 7

0 N/A 0.557 7.18E14 4.11E–10 1.14E13 0 N/A 1.44E16 0 N/A 0.2958 8.61E14 4.07E–08 2.00E13 4.60E6 N/A 5.37E16 0 N/A 0.9251 1.44E13 0.0007 3.68E05 6.85E06 N/A 6.29E16 0 N/A 0.0505 7.18E14 2.73E–09 1.14E13 0

1050 9000 10000 10000 6812 2305 10000 4000 9600 750 9000 10000 10000 6802 3042 10000 4000 9100 650 9000 10000 10000 6792 4002 10000 4000 14000 1150 9000 10000 10000 6804 2589 10000


8

9

9

11

TLBO [34] HH COA GA [29] GA [30] PSO [30] NMPSO [31] ARQiEA [32] DE [33] TLBO [34] HH COA GA [29] GA [30] PSO [30] NMPSO [31] ARQiEA [32] DE [33] TLBO [34] HH COA

(13.316, 6.7, 495.196) (13.4, 5.607, 259.5362) (13.4, 5.607027, 500) (13.39, 10.21, 246) (13.9997, 10.2480, 335.3639) (13.4, 10.2484, 295.0714) (13.4, 10.2485, 388.5176) (13.4, 10.25, 500) (13.4, 10.2485, 404.9179) (13.305, 11.442, 190.029) (13.4, 10.24832, 236.378) (13.4, 10.248456, 500) (13.37, 16.49, 397.88) (13.39998, 16.5879, 373.7518) (13.4, 16.5883, 452.2157) (13.4, 16.5883, 400.0047) (13.4, 16.59, 500) (13.4, 16.5883, 381.3980) (13.378, 18.746, 406.817) (13.4, 16.58816, 343.28137) (13.4, 16.588311, 500)

89.217 75.1335 75.1341 136.71 137.3201 137.3293 137.3293 137.3293 137.3293 152.236 137.3274 137.3293 220.47 222.2769 222.2824 222.2832 222.3060 222.2832 250.784 222.2813 222.2834

0.3056 0.3450 0.2959 0.393 0.3767 0.3771 0.3529 0.3326 0.3502 0.4241 0.3964 0.3326 0.385 0.3909 0.3746 0.3848 0.3652 0.3890 0.3919 0.3988 0.3651

7.5788 7 7 8.991 9 9 9 9 9 9.4788 9 9 11 11 11 11 11.00046 11 11.590 11 11

N/A 6.18E16 0 N/A 0.2007 8.61E14 2.33E–10 2.00E13 4.60E06 N/A 6.49E16 0 N/A 0.3140 1.15E13 2.30E–08 5.14E13 1.01E03 N/A 2.00E16 0

4000 9600 550 9000 10000 10000 6798 3093 10000 4000 9600 650 9000 10000 10000 6850 3901 10000 4000 9600 650

GA: genetic algorithms; PSO: particle swarm optimization; NMPSO: Nelder Mead simplex search methodparticle swarm optimization; ARQiEA: adaptive real coded quantum inspired evolutionary algorithm; DE: differential evolution; TLBO: teaching-learning based optimization; HH: hoopoe heuristic; COA: cuckoo optimization algorithm

25


Table 2  CPU time for the grinding process

Expt.

SRmax NDmax Technique CPU time (s) (μm)

1

0.3

7

2

9

3

11

4

0.35

7

5

9

6

11

7

0.40

7

8

9

9

11

HH COA HH COA HH COA HH COA HH COA HH COA HH COA HH COA HH COA

42.9783 1.7472 44.6787 2.9952 27.0038 2.73 27.0038 2.7924 26.8946 2.2308 52.8375 3.9624 42.9003 1.2012 47.7051

1.3416 51.8547 2.106

Table 3  Comparison of the optimum results for drilling process Technique GA [35] TLBO [34] HH COA

Parameters: A (m/min), B (mm/rev) and C

Ra (μm)

(7.62, 0.1, 1) (7.6856, 0.1, 1) (7.7284803, 0.1, 1.000252) (7.6920, 0.1, 1)

1.8895 1.8892 1.8893 1.8892

Std. Dev. N/A N/A 1.85E16 0

Number of function evaluations 2000 N/A 1800 50

GA: genetic algorithms; TLBO: teaching-learning based optimization; HH: hoopoe heuristic; COA: cuckoo optimization algorithm

26


Table 4  Values of the constants used in the optimization problem of water jet machining (WJM) [20] Constants notation

Details

Units

Value

Pmax Cfw ηw

Allowable power consumption Drag friction coefficient for work material Damping coefficient of the work material Compressive yield strength of work material Tensile yield strength of the work material Length of initial region of the water jet

kW  kg mm2s1 MPa

50 0.005 2357.3 26.2

MPa mm

3.9 20

cw yw Xi

Table 5  Comparison of the optimum results for water jet machining Technique GA [20] HH COA

Parameters: Pw (MPa), dwn (mm), fn (mm/s) Constraint Number of function MRR (mm3/s) Std. Dev. and X (mm) value evaluations (397, 0.5, 214.41, 2.54) (399.3974, 0.49954, 104.988, 2.50266) (400, 0.5, 300, 2.5)

134.2452 134.3757 136.63806

0.0282 0.0211 0.0171

N/A 3.54E6 0

GA: genetic algorithms; HH: hoopoe heuristic; COA: cuckoo optimization algorithm

27

800 1800 150


Table 6  Values of the constants used in the optimization problem of abrasive jet machining in brittle materials [20]

Constants notation

Details

Units

Value

ρa ηa

Density of abrasive particles Proportion of abrasive particles effectively participating in the machining process Flow stress of work material Allowable surface roughness value

kg/mm3 

3.85 × 106 0.7

MPA μm

5000 0.8

fw (Ra)max

Table 7  Comparison of the optimum results for abrasive jet machining process in brittle materials

Technique GA [20] SA [36] TLBO [37] HH COA

Parameters: Ma (kg/s), rm (mm) and va (mm/s)

MRR (mm3/s)

Constraint value

(0.0005, 0.005, 315504.3) (0.0005, 0.005, 315764.8) (0.00049, 0.005, 333982) (0.0004999, 0.0050008, 315694.4765) (0.0005, 0.005, 315772.1247)

8.242355 8.252565 8.7974 8.248158 8.252852

8.4829E004 N/A 2.3328E005 N/A N/A 0.0577 8.6071E–005 7.94E8 1.3254E–007 0

Std. Dev.

Number of function evaluations 7600 N/A 1000 25500 240

GA: genetic algorithms; SA: simulated annealing; TLBO: teaching-learning based optimization; HH: hoopoe heuristic; COA: cuckoo optimization algorithm

28


Table 8  Values of the constants used in the optimization problem of abrasive jet machining (AJM) for ductile materials [20]

Constants notation

Details

Units

Value

ρa ρw δcw

Density of abrasive particles Density of work material Critical plastic strain or erosion ductility of work material Dynamic hardness of work material Amount of indentation volume plasticallydeformed Allowable surface roughness value

kg/mm3 kg/mm3 

2.48 × 106 2.7 × 106 1.5

MPa 

1150 1.6

μm

2

Hdw



(Ra)max

Table 9  Comparison of the optimum results for abrasive jet machining process in ductile materials

Technique

GA [20] SA [36] TLBO [37] HH COA

Parameters: Ma (kg/s), rm (mm) and va (mm/s)

MRR (mm3/s) Constraint value

(0.0005, 0.005, 333214.7) (0.0005, 0.005, 333549.08) (0.0005, 0.005, 354360) (0.0005, 0.005, 333551.6440) (0.0005, 0.005, 333600.4561)

0.6035 0.6053 0.7258 0.605371 0.605637

1.156E–003 1.5445E004 0.0622 1.4677E–004 4.5458E–007

Std. Dev.

N/A N/A N/A 1.04E6 1.83E14

Number of function evaluations 4600 N/A 1000 25000 480

GA: genetic algorithms; SA: simulated annealing; TLBO: teaching-learning based optimization; HH: hoopoe heuristic; COA: cuckoo optimization algorithm

29


Table 10  Comparison of the optimum results for abrasive water jet machining Technique Experimental [40] Regression [40] ANN [40] GA [39, 41] SA [39, 41] Integrated SAGA-type1 [41] Integrated SAGA-type2 [41] ABC [17] Integrated ANNSA-type1 [2] Integrated ANNSA-type2 [2] HH COA

Parameters: V (mm/min), P (MPa), h (mm), d (μm) and m (g/s)

Ra (μm) Std. Dev.

(50, 125, 1, 60, 0.5) (50, 125, 1, 60, 2) (50, 125, 1, 60, 2) (50.024, 125.018, 1.636, 94.973, 0.525) (50.003, 125.029, 1.486, 107.737, 0.5) (50.008, 125.02, 1.545, 102.484, 0.502) (50.003, 125.018, 1.521, 102.807, 0.5) (50, 125, 1.550, 102.521, 0.5) (50.003, 125.002, 1.476, 102.117, 0.5) (50, 125.001, 1.484, 102.107, 0.5) (50, 125, 1.5947, 101.5544, 0.5006) (50, 125, 1.545, 102.4939, 0.5)

2.124 2.6291 2.744 1.5548 1.5355 1.5242 1.5234 1.5222 1.5230 1.5229 1.5230 1.5222

N/A N/A N/A N/A N/A N/A N/A 0.0164 N/A N/A 2.57E16 0

Number of function evaluations N/A N/A N/A 6000 271100 5100 271100 500 271100 271100 20000 290

ANN: artificial neural network; GA: genetic algorithms; SA: simulated annealing; ABC: artificial bee colony; HH: hoopoe heuristic; COA: cuckoo optimization algorithm

Table 11  Values of the constants used in the optimization problem of ultrasonic machining (USM) [20]

Constants notation

Details

Units

Value

At

Kusm

Cross-sectional area of cutting tool Flow stress of abrasive particles Flow stress of the work material A constant of proportionality relating mean diameter of abrasive grains, and diameter of projections on an abrasive grain ( = Kusm d m2 )

mm2 MPa MPa mm1

20 28000 6900 0.1

(Ra)max

Allowable surface roughness value

μm

0.8

ft fw

30


Table 12  Comparison of the optimum results for ultrasonic machining

Technique

GA [20] ABC [44] HS_M [44] PSO [44] SA [38] SFL [38] TLBO [37] HH COA

Parameters: Av (mm), fv (Hz), dm (mm), Cav and Fs (N)

MRR (mm3/s)

Constraint value

(0.0263, 39333.9, 0.1336, 0.479, 10.8) (0.0167, 40000, 0.15, 0.5, 16.4) (0.0582, 40000, 0.15, 0.5, 4.5) (0.06, 40000, 0.15, 0.5, 4.5) (0.077, 40000, 0.114, 0.5, 4.53) (0.02271, 40000, 0.14, 0.5, 12.78) (0.0611, 40000, 0.15, 0.5, 4.5) (0.017553, 39941.1238, 0.115, 0.499764, 20.4331) (0.031975, 40000, 0.15, 0.5, 8.6040)

3.553 3.941 3.870 3.950 3.660 3.894 4.004 3.7415

0.0214 0.0224 0.0244 0.0095 0.0185 0.0079 0.0003 2.3355E–005

4.0064

7.5541E–006 0

Std. Dev.

N/A N/A N/A N/A N/A N/A N/A 1.40E8

GA: genetic algorithms; ABC: artificial bee colony; HS_M: modified harmony search; PSO: particle swarm optimization; SA: simulated annealing; SFL: shuffled frog leaping; TLBO: teaching-learning based optimization; HH: hoopoe heuristic; COA: cuckoo optimization algorithm

31

Number of function evaluations 12600 750 750 250 20000 1000 1000 11700 225

Accepted and published manuscript http://link.springer.com/article/10.1007/s10845-014-0925-4 Start

Initialize cuckoos with eggs

Lay eggs in different nests

Some eggs are detected and destroyed

No

Kill cuckoos in worst area

Determine egg laying radius for each cuckoo

Move all cuckoos toward best environment

Determine cuckoo societies

Population is less than maximum

Find nests with best survival rate

value? Yes Check survival of eggs in nests (get profit values)

Stop condition satisfied?

Let eggs hatch and grow No

Yes End

Figure 1  Flowchart of COA [21]

32

Accepted and published manuscript http://link.springer.com/article/10.1007/s10845-014-0925-4 Start

Create a random set of points

Perform the ground-probing with a fixed value of digging radius

Perform a Lévy flight

Evaluate the fitness values

Classify the fitness values

Identify the best fitness value

Stop condition satisfied?

No

Yes End

Figure 2  Flowchart of HH

33


Figure 3  Optimal values for drilling process 1,88955 1,88950 1,88945

Ra (μm)

1,88940 1,88935 1,88930 1,88925 1,88920 1,88915 1,88910 1,88905 1 GA

2 HH

3 TLBO

4 COA


Figure 4  Number of function evaluations for drilling process

2000

1500

1000

500

0 1 GA

2 HH

34

3 COA


Figure 5  Optimal values for water jet machining 137,00 136,50

MRR (mm3/s)

136,00 135,50 135,00 134,50 134,00 133,50 133,00 1 GA

2 HH

3 COA

Figure 6  Number of function evaluations for water jet machining


2000 1800 1600 1400 1200 1000 800 600 400 200 0 1 HH

2 GA

35

3 COA


Figure 7  Optimal values for abrasive jet machining in brittle materials 8,2540 8,2520

MRR (mm3/s)

8,2500 8,2480 8,2460 8,2440 8,2420 8,2400 1 GA

2 HH

3 SA

4 COA


Figure 8  Number of function evaluations for abrasive jet machining in brittle materials

25000 20000 15000 10000 5000 0 1 HH

2 GA

36

3 COA


Figure 9  Optimal values for abrasive jet machining in ductile materials 0,606 0,606

MRR (mm3/s)

0,605 0,605 0,604 0,604 0,603 0,603 0,602 1

2

GA

3

SA

4

HH

COA

Figure 10  Number of function evaluations for abrasive jet machining in ductile materials


25000 20000 15000 10000 5000 0 1

2

HH

GA

37

3

COA


Figure 11  Optimal values for abrasive water jet machining

2,800

1: ANN 2: Regression 3: Experimental 4: GA 5: SA 6: SAGA-type1 7: SAGA-type2 mm 8: ANNSA-type1 9: HH 10: ANNSA-type2 11: ABC 12: COA

2,600

Ra (μm)

2,400 2,200 2,000 1,800 1,600 1,400 1

2

3

4

5

6

7

8

9

10

11

12


Figure 12  Number of function evaluations for abrasive water jet machining 1: SA 2: SAGA-type2 3: ANNSA-type1 4: ANNSA-type2 5: HH 6: GA 7: SAGA-type1 8: ABC Série1 9: COA

250000 200000 150000 100000 50000 0 1

2

3

4

5

6

38

7

8

9


Figure 13  Optimal values for ultrasonic machining 1: GA 2: SA 3: HH 4: HS_M 5: SFL 6: ABC 7: PSO 8: TLBOSérie1 9: COA

4

MRR (mm3/s)

3,9 3,8 3,7 3,6 3,5 1

2

3

4

5

6

7

8

9

Figure 14  Number of function evaluations for ultrasonic machining 1: SA 2: GA 3: HH 4: TLBO 5: SFL 6: ABC 7: HS_M 8: PSOSérie1 9: COA


20000

15000

10000

5000

0 1

2

3

4

5

6

39

7

8

9