Glowworm swarm optimization (GSO) for optimization of machining ...

J Intell Manuf DOI 10.1007/s10845-014-0914-7

Glowworm swarm optimization (GSO) for optimization of machining parameters Nurezayana Zainal · Azlan Mohd Zain · Nor Haizan Mohamed Radzi · Muhamad Razib Othman

Received: 23 October 2013 / Accepted: 12 April 2014 © Springer Science+Business Media New York 2014

Abstract This study proposes glowworm swarm optimization (GSO) algorithm to estimate an improved value of machining performance measurement. GSO is a recent nature-inspired optimization algorithm that simulates the behavior of the lighting worms. To the best our knowledge, GSO algorithm has not yet been used for optimization practice particularly in machining process. Three cutting parameters of end milling that influence the machining performance measurement, minimum surface roughness, are cutting speed, feed rate and depth of cut. Taguchi method is performed for experimental design. The analysis of variance is applied to investigate effects of cutting speed, feed rate and depth of cut on surface roughness. GSO has improved machining process by estimating a much lower value of minimum surface roughness compared to the results of experimental and particle swarm optimization. Keywords Machining · Optimization · Surface roughness · Glowworm swarm optimization · Taguchi method

Introduction Machining can be defined as a process of shaping a work piece by removing unwanted material, and cutting parameN. Zainal · A. M. Zain (B) · N. H. M. Radzi · M. R. Othman Faculty of Computing, Universiti Teknologi Malaysia (UTM), 81310 Skudai, Johor, Malaysia e-mail: [email protected]; [email protected] N. Zainal e-mail: [email protected] N. H. M. Radzi e-mail: [email protected] M. R. Othman e-mail: [email protected]

ters influenced the desired shape of work piece (Yusup et al. 2012). Machining can be divided into traditional and modern processes. Traditional processes include milling, turning, grinding, drilling and boring, while modern processes are such as electrochemical machining (ECM), electrical discharge machining (EDM), abrasive water jet (AWJ) and ultrasonic machining (USM) (Zain et al. 2011a,c). Milling is one of the most crucial and common metal machining processes used to remove materials faster with a reasonable good surface quality (Raju et al. 2011). Nowadays, the demand for high quality is focused on the surface condition and the quality of product (Nandi and Pratihar 2004). Based on previous literature, surface roughness is one of the machining performance measurements mostly studied by researchers (Raju et al. 2011; Hamdan et al. 2012; Bharathi Raja and Baskar 2012; Senthilkumaar et al. 2010; Hasçalık and Çayda¸s 2008; Markopoulos et al. 2008; Krimpenis and Vosniakos 2009; Agrawal et al. 2006; Wang et al. 2012; Zain et al. 2010a,b,c). The roughness is important to maintain the tolerance and surface roughness (Hamdan et al. 2012). Commonly, surface roughness is influenced by different cutting parameters that can be setup in advance such as cutting speed, feed rate, tool nomenclature, machining force and depth of cut (Maji and Pratihar 2011; Nandi and Pratihar 2004; Li et al. 2013; Zain et al. 2011b, 2012a,b). Cutting speed, feed rate and depth of cut are the three major cutting parameters used due to the ability of easily controlling machining process (Bharathi Raja and Baskar 2012). Recently, several researchers attempt swarm intelligence algorithms such as Cuckoo (Mohamad et al. 2013), Firefly (Johari et al. 2013) and Levy Flight (Kamaruzaman et al. 2013) for optimization process. Glowworm Swarm Optimization (GSO) is also classified as one of the swarm intelligence algorithms, proposed by Krishnanand and Ghose (2005). GSO is in the similar character to ACO and PSO

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algorithms but with some apparent differences (Krishnanand and Ghose 2006). GSO is appropriate for simultaneous capture of multiple optima of multimodal function. The optimization of multimodal function enables improving accuracy and speeding up the convergence rate (Zainal et al. 2013). This study deals with end milling process in estimating optimum machining cutting parameters. Orthogonal array, signal-to-noise (S/N) ratio and ANOVA analysis are employed to analyze the effect of all cutting parameters. Taguchi method is used for experimental design, where it is a supportive method to identify the critical parameters, increase system robustness, reduce experimental costs and improve quality product (Sahoo et al. 2008; Antony et al. 2006; Motorcu 2010). Furthermore, GSO algorithm is used to find the optimum cutting parameters that lead to the minimum surface roughness value.

i) The Lower-the-Better (LB) 

S/N L B

n 1 2 = −10 log 10 yi n

 (1)

i

ii) The Higher-the-Better (HB) 

S/N H B

n 1 1 = −10 log 10 n yi2 i

 (2)

iii) The Nominal-the-Better S/N T = 10 log 10

 ¯  y¯i s2 y

(3)

where y is the observed data (surface roughness), y¯¯ is the average of observed data, n is the number of observation and s 2 y is the variance of y.

Taguchi method Design of experiment Taguchi method is a set of methodology used in manufacturing process (Senthilkumaar et al. 2010). It is known as ”off-line quality control” of experiment since this method ensuring good performance in the design stage of products or processes at a relatively low cost (Kondapalli et al. 2013; Antony et al. 2006). Taguchi method defines the quality of product in terms of loss imparted by the product to the society from the time the products are shipped to the customer (Ghani et al. 2004). It also provides a simple, efficient and systematic approach for the optimization design for quality and cost (Hasçalık and Çayda¸s 2008; Antony et al. 2006). This study considers two major tools of Taguchi method which are orthogonal array (OA) and the signal-to-noise (S/N) ratio. OA can be defined as a fractional factorial matrix for determining a combination of factor levels for each experimental run (Tiwari et al. 2010). Taguchi design conducts the balanced (orthogonal) experimental combination method, and it is a broadly accepted method in producing high quality products at subsequently low cost (Kondapalli et al. 2013). The loss function principle is used to measure the performance characteristic deviating from the desired value (Motorcu 2010). Then, the value of the loss function is converted into S/N ratio. In Taguchi method, S/N ratio is used to indicate a response or quality characteristic (Periyanan et al. 2011). The term ‘signal’ indicates the desirable value (mean) for the output characteristic and the term ‘noise’ indicates the undesirable value for the output characteristic (Magdum and Naik 2013). There are three categories of performance characteristic of the S/N ratio as follows (Ghani et al. 2004; Senthilkumaar et al. 2010; Sibalija and Majstorovic 2012):

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Taguchi design of experiments is a simple robust technique for analyzing and optimizing the process parameters (Senthilkumaar et al. 2010). The most important part in the design of experiment is the selection of control factors and identifying the orthogonal array. Surface roughness is generally depends on the manufacturing conditions employed, such as cutting speed, feed rate and depth of cut. Experimental procedure The machining experiment conducted by Bharathi Raja and Baskar (2012) is referred in this study. Aluminum bar was used as a work material for experimentation. The experiment was conducted on MCV 400 computer numerical control (CNC) milling machine using insert type carbide SNKT 120-5. Cutting speed (A), feed rate (B) and depth of cut (C) were considered as the cutting parameters that affect the minimum surface roughness value. The feasible range of cutting parameters was taken from the machine limitations. Table 1 shows the specification of the CNC milling machine and surface roughness tester, and cutting parameter levels are shown in Table 2. Three trials were performed and the average of surface roughness was measured. Three levels were specified for each cutting speed (A), feed rate (B) and depth of cut (C) as given in Table 2. The parameter levels were chosen within the intervals based on the recommendations by manufacturer. According to Bharathi Raja and Baskar (2012), three trials were performed for each combination of cutting parameters. The average of

J Intell Manuf

L9 was used in this experiment. Accordingly, only 9 experiments are carried out to study the effect of each cutting parameters. Table 3 shows the L9 orthogonal array design and the measured surface roughness.

Table 1 Specification of CNC milling and surface roughness tester Specification of CNC milling machine

Specification on surface roughness tester

Make: FANUC AMS

Make: CARLZESIS

Work table size: 450 mm × 900 mm

Range: 0–100 microns

Tool magazine: 20 stations

Stylus type: DT-43827

Tool holder: BR 40

Least count: 0.1 μm

Experimental result and data analysis Analysis signal-to-noise (S/N) ratio

Stroke length: x-600 mm, y-415 mm, z-460 mm

The objective of the study is to optimize cutting parameters for estimating a minimum surface roughness value. A much lower surface roughness value corresponds to a much better machining performance measurement. Hence, this study employs the concept of lower-the- better (LB), where the optimum level of cutting parameters is clearly defined with the highest S/N ratio. Table 3 shows the experimental results for surface roughness along with their computed S/N ratio values. The mean S/N ratio for each level of the cutting parameter was calculated, and the results are shown in Table 4. From Table 4, it was indicated that the cutting parameters with the highest S/N ratio is obtained at the combination of Level 1 for cutting speed (12.7058 dB), Level 1 for feed rate (13.5388 dB) and Level 1 for depth of cut (13.6 dB). Feed rate contributes the highest S/N ratio, followed by depth of cut and cutting speed. Then the ranking was defined according to the difference between maximum and minimum value S/N ratio value, and it found that the optimal solution is obtained at level 1 for all cutting parameters. It can be concluded that the value of surface roughness decreases (better characteristic) at the low levels for cutting speed, feed rate and depth of cut. The output is plotted in Fig. 1.

Table 2 Cutting parameters and levels End milling cutting parameters Unit

Levels Level 1 Level 2

Level 3

1,000

Cutting speed

m/min

2,000

3,000

Feed rate

mm/rev 100

200

300

Depth of cut

mm

0.4

0.6

0.2

surface roughness was measured, and the results are summarized in Table 3. The minimum surface roughness value is 0.15 μm at the combination of cutting speed = 1,000 m/min, feed rate = 100 mm/rev and depth of cut = 0.2 mm. Selection of orthogonal array The total degree of freedom is important in selecting an appropriate orthogonal array, and it is used to define the level of experimental design (Magdum and Naik 2013). The degree of freedom for the orthogonal array should be greater than or at least equal to those for the cutting parameters. According to the Taguchi’s quality design concept, there is 6 degrees of freedom (3*2) representing three cutting parameters varied at three levels. Therefore, the standardized orthogonal array Table 3 L9 orthogonal array

Experiment

v (m/min)

Analysis of variance (ANOVA) ANOVA insists in identifying the relative contribution of cutting parameters in controlling the response of machining process (Sahoo et al. 2008). The optimum parametric set-

f (mm/rev)

d (mm)

Ra (μm) Trial 1

Trial 2

Trial 3

Average

1

1,000

100

0.2

0.13

0.18

0.13

0.15

2

1,000

200

0.4

0.22

0.23

0.23

0.23

3

1,000

300

0.6

0.39

0.31

0.37

0.36

4

2,000

100

0.4

0.23

0.19

0.25

0.23

5

2,000

200

0.6

0.49

0.21

0.59

0.43

6

2,000

300

0.2

0.37

0.24

0.35

0.32

7

3,000

100

0.6

0.2

0.27

0.33

0.27

8

3,000

200

0.2

0.18

0.2

0.2

0.19

9

3,000

300

0.4

0.43

0.39

0.32

0.38

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J Intell Manuf Table 4 Mean response table of S/N ratio (the lower the better) for Ra Level

Mean S/N ratio (dB) A

B

C

1

12.7058*

13.5388*

13.6*

2

9.9977

11.5070

11.3117

3

11.4006

9.0584

9.1924

Max-min

2.7082

4.4804

4.4076

Rank

3

1

2

* Indicates the optimum level 16

S/N ratio (dB)

S/N ratio (dB)

14 12 10 8

14 12 10

6

8 6

1

2

1

3

2

3

Level ii) Feed rate

Level i) Cutting speed

Contribution (%) = (SSA /SST ) × 100

S/N ratio (dB)

14 12 10 8 6 2

(7)

Table 5 shows the result of ANOVA for surface roughness. The analysis is based on a significance level of α = 0.05 (confidence level of 95 %). The p-values (feed rate = 0.2183, depth of cut = 0.2384 and cutting speed = 0.6414) are statistically insignificant affecting the surface roughness which are greater than 0.05. According to the percentage of contribution values, feed rate and depth of cut gave high effect on surface roughness by giving 39.79 and 37.99 % of contribution, respectively. On the other hand, cutting speed gives less effect with 13.76 % of contribution.

16

1

and conventionally used to discover the significance of the cutting parameters to the surface roughness. Mean square (MSA ) is computed by dividing the sum of square (SSA ) value with the degree of freedom (DF). According to the F-ratio value, it contains the associated p-value, where pvalue must be in a range between 0 and 1. It is defined as the probability level that is referred as the significant contribution of the cutting parameters toward the surface roughness. If the p-value is greater than 0.05, we accept the null hypothesis which is statistically insignificant contribution to the surface roughness. Otherwise, if the p value is less than 0.05, we consider that cutting parameters have statistically significant contribution to the surface roughness. The contribution percentage of cutting parameter is a ratio of the SSA over SST (Eq. 7). Contribution is defined as the significance rate of the machining parameters on surface roughness. The greater of contribution percentage, the greater of cutting parameter influenced the surface roughness.

3

Level iii) Depth of cut

Fig. 1 S/N ratio of cutting parameters

ting value directly persuades the objective function for determining the minimum surface roughness value at the optimal policy. The value of degree of freedom (DF) is considered when performing ANOVA, where it is defined as the rank of a quadratic form. If there are n observations and one parameter (the mean) that required to be estimated then it requires n − 1 for estimating variability (Maji and Pratihar 2011). Sum of square (SS) whereas consists of three possible sums of square which are between group sum of square (SS A ), error sum of square (SSδ /A ) and total sum of square (SST ) are measured by following equations (Gopalsamy et al. 2009):  (4) SSA = n (Y − Y¯ )2  2 SSδ /A = (5) Y − Y¯ SST = SSA + SSδ /A

(6)

where Y¯ is mean of each variation and n is the number of observations within each group. The statistic test of ANOVA analysis is called F-ratio. It is a ratio of the mean square (MSA ) to the residual error

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Glowworm swarm optimization (GSO) According to Oramus (2010), GSO algorithm is an easy technique to capture many peaks of multi-modal function due to its dynamic sub-groups. GSO algorithm also has an ability to split into disjoint groups (Oramus 2010). Definition GSO algorithm is inspired from the biological behavior of glowworm that attracts to mates and prey (He and Zhu 2010) using their natural light emission. The concept was like the brighter the light, so the more attraction. The glowworm’s moving pattern is depending on the luciferin intensity and it changed each time due to the different neighbors. In addition, local decision range also affected by the differ number of glowworm in the neighbors. It can be described as if the number of glowworm was too small; the glowworm enables to increase its local decision range to find more glowworm. As a result, the glowworms will be gathering on a better position. Generally, GSO algorithm is divided into four phases:

J Intell Manuf Table 5 Result of ANOVA for end milling

i. ii. iii. iv.

Cutting parameters DF Sum of square (SS) Mean square Variance F-ratio p value Contribution (%) A

2

0.0097

0.0048

0.0048

1.6269 0.6414 13.76

B

2

0.0280

0.0140

0.0140

4.7052 0.2183 39.79

C

2

0.0268

0.0134

0.0134

4.4925 0.2384 37.99

Error

2

0.0060

0.0030

0.0030

Total

8

0.0704

Initialization Luciferin update phase Movement phase Neighborhood range update phase

8.46 100

bours of glowworm i at time t is calculated as follows: Ni (t) = j : x j (t) − xi (t) < rdi (t); li (t) < l j (t)

(9)

where x j (t) − xi (t) is the Euclidean norm of x and rdi (t) is the variable neighborhood range forglowworm i at time tbounded by a circular sensor range rsi 0 < rdi ≤ rsi . For each glowworm i, the probability of movement towards a neighbor j ∈ Ni (t) is given by Eq. 10,

Algorithm Phase 1—initialization During initialization, a solution space of ‘population size’ is generated randomly within the limits of cutting speed, feed rate and depth of cut. In this study, both parameters of population size of glowworms (n) and the maximum iteration (tmax ) are set to 27. Other parameter settings include initial luciferin value (lo ) = 5, luciferin decay constant (ρ) = 0.4, luciferin enhancement constant (γ) = 0.6, beta (β) = 0.08, step size (s) = 0.03, neighborhood range (rdi (t)) = 3 and parameter used to control the number of neighbor (n t ) = 5. Phase 2—luciferin update

pi j (t) =

l j (t) − li (t) k∈Ni (t) lk (t) − li (t)

(10)

Then, the discrete-time model of the glowworm movement can be stated as follows:  x j (t) − xi (t) (11) xi (t + 1) = xi (t) + s x j (t) − xi (t) where s is step size,   is the Euclidean norm operator and xi (t) ∈ R m is the location of glowworm i at time t in the m-dimensional real space Rm .

Iteration consists of luciferin update phase, glowworms’ movement phase and local decision range update phase. The luciferin update phase was influenced by the function value at the glowworm location. The value of the function will be altered due to the function value at the present position although the glowworm has the same value of luciferin at the beginning. The luciferin update rule is given by Eq. 8 (Krishnanand and Ghose 2009; Luo and Zhang 2011):

Neighborhood range update phase is used to detect the multiple peaks in a multimodal function landscape. Let ro be the initial neighborhood range value for each glowworm i (rdi (0) = ro ). The rule is given as follows:

li (t + 1) = (1 − ρ) li (t) + γ Ji (t + 1)



rdi (t + 1) = min rs , max 0, r id (t) + β(n t − |Ni (t)|)

(8)

Phase 4—neighborhood update

(12)

where li (t) = luciferin level for glowworm i at time t, ρ is luciferin decay constant (0 < ρ < 1), γ is luciferin enhancement constant and Ji (t) is a objective function at agent i’s location at time t.

where β is a constant parameter and n t is a parameter being used to control the number of neighbors. The flowchart of GSO algorithm is shown in Fig. 2.

Phase 3—movement phase

Computational result of GSO

During the movement phase, each glowworm uses a probabilistic mechanism to move toward their neighbor that has higher intensity of luciferin then its own. The set of neigh-

Optimization process was implemented by using. The minimization objective function (mathematical model) is given below:

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J Intell Manuf Start

Initialization of glowworms’ position and local decision range

Evaluate glowworms’ fitness

For each iteration, t

For each glowworm, i

Update glowworms’ luciferin value by luciferin update rule

Fig. 3 Plot functions of GSO for end milling Update movement of glowworms by using probabilistic mechanism

Update glowworms’ decision range by using neighbourhood range update rule

Is termination criteria met?

No

Yes End

Fig. 2 The flowchart of the GSO algorithm

Ra = 0.7675 ∗ (A−0.562 B0.63 C0.53 )

(13)

where Ra is surface roughness in μm, A is cutting speed in rev/min, B is feed rate in mm/min and D is depth of cut in mm. Considering the lowest level (Level 1) and highest level (Level 3) of the design of experiment specified for cutting parameters as given in Table 3, the lowest and highest limitation range for optimization constraints are given as follows: 1,000 m/min ≤ A ≤ 3,000 m/min

(14)

100 m/rev ≤ B ≤ 300 mm/rev

(15)

0.2 mm ≤ C ≤ 0.6 mm

(16)

The lowest and highest limitation range of cutting parameter is set as an input of GSO algorithm. The minimum surface roughness (Ra ) value is obtained at the last iteration (tmax ) where the glowworms (n) that carry luciferin (Ra ) being at the optimum position. Figure 3 illustrates the values of luciferin (Ra ) of glowworm (n) at tmax . The estimated value of surface roughness is displayed by sorting order. The estimated minimum surface roughness is 0.12 μm, and the maximum surface roughness is 0.34 μm. Compared to exper-

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imental result (Bharathi Raja and Baskar 2012) in Table 1, the minimum surface roughness value is 0.15 μm. From the experimental result, the surface roughness values are generated within the range of 0.15 and 0.55 μm. The surface roughness values estimated by GSO are within the range of 0.12 and 0.34 μm. Therefore, GSO enables to estimate a much lower value of surface roughness compared to the real experimental results. GSO estimates optimum solution with a small size of population (27), improving accuracy and speeding up the convergence rate. Considering the same experimental data set employed in this study, previously Bharathi Raja and Baskar (2012) explored Particle Swarm Optimization (PSO) technique. PSO is one of the evolutionary optimization techniques derived from the analysis of the swarm intelligence. Table 6 summarizes the results of both techniques in terms of optimum cutting parameters and minimum surface roughness. The minimum surface roughness value (0.15 μm) of the experimental was obtained at the combination of 1,000 m/min of cutting speed (Level 1), 100 mm/rev of feed rate (Level 1) and 0.2 mm of depth of cut (Level 1). The minimum surface roughness (0.15 μm) of PSO was recommended at the combination of 1,672.724 m/min (cutting speed), 196.368 mm/rev (feed rate) and 0.216 mm (depth of cut). GSO estimated the minimum surface roughness (0.12 μm) at the combination of 1,817.146 m/min (cutting speed), 144.673 mm/rev (feed rate) and 0.228 mm (depth of cut). Consequently, based on the results of this research, Table 7 highlights the distinctions between these two techniques (GSO and PSO).

Conclusion In this study, we proposed GSO algorithm in estimating an improved results of machining performance measurements.

J Intell Manuf Table 6 Optimum cutting parameters and minimum surface roughness

Methods

Optimum cutting parameters [v, f, d]

Minimum Ra (μm)

Experimental

[1,000,100,0.2]

0.15

PSO

[1,672.724, 196.368, 0.216]

0.15

GSO

[1,817.146, 144.673, 0.228]

0.12

References

Table 7 GSO versus PSO

1.

2.

3.

4.

GSO

PSO

Incorporated into the incremental update of the luciferin values that reflect the cumulative goodness of the path followed by the glowworm Local decision domain based on varying range

Use memory elements in the velocity update mechanism of the particles

Directions of the glowworm movements based on the line if sight between neighbours GSO uses information only from a dynamic neighbour set helps it to detect local maxima

Dynamic neighbourhood based on k nearest neighbours Directions of the particle movements based on the best previous positions PSO gets easily attracted to the global maxima

Two other techniques include Taguchi and ANOVA. Based on the results, the following conclusions are carried out: • Taguchi observed that the combination of A1 B1 C1 is the optimum level for minimum surface roughness. The combination of A1 B1 C1 represents 1,000 m/min of speed (Level1), 100 mm/rev of feed rate (Level 1) and 0.2 mm of depth of cut (Level 1). • Based on the analysis of variance (ANOVA), it indicates that feed rate is the main factor influencing a minimum surface roughness (39.79 % of contribution), followed by depth of cut (37.99 % of contribution) and cutting speed (13.76 % of contribution). • GSO outperformed the result of established evolutionary technique, PSO, in terms of minimum surface roughness. The minimum surface roughness of GSO and PSO are 0.12 and 0.15μm respectively. Acknowledgments Special appreciation to reviewer(s) for useful advices and comments. The authors greatly acknowledge Soft Computing Research Group (SCRG UTM), Research Management Centre (RMC UTM) and Ministry of Higher Education Malaysia (MOHE) for financial support through the Exploratory Research Grant Scheme (ERGS) No. R.J130000.7828.4L087

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