FACTA UNIVERSITATIS  
Series: Mechanical Engineering Vol. 18, N

o
 2, 2020, pp. 281 - 300 

https://doi.org/10.22190/FUME200218028K 

© 2020 by University of Niš, Serbia | Creative Commons License: CC BY-NC-ND 

Original scientific paper 

TEACHING-LEARNING-BASED PARAMETRIC OPTIMIZATION 

OF AN ELECTRICAL DISCHARGE MACHINING PROCESS 

 

Vidyapati Kumar
1
, Sunny Diyaley

2
, Shankar Chakraborty

3
 

1
Central Institute of Mining and Fuel Research, Dhanbad, Jharkhand, India 

2
Department of Mechanical Engineering, Sikkim Manipal Institute of Technology,  

Sikkim Manipal University, Majitar, Sikkim, India 
3
Department of Production Engineering, Jadavpur University, Kolkata, West Bengal, India 

Abstract. Due to several unique features, electrical discharge machining (EDM) has 

proved itself as one of the efficient non-traditional machining processes for generating 

intricate shape geometries on various advanced engineering materials in order to fulfill 

the requirement of the present day manufacturing industries. In this paper, the 

machining capability of an EDM process is studied during standard hole making 

operation on pearlitic SG iron 450/12 grade material, while considering gap voltage, 

peak current, cycle time and tool rotation as input parameters. On the other hand, 

material removal rate, surface roughness, tool wear rate, overcut and circularity error 

are treated as responses. Based on single- and multi-objective optimization models, this 

process is optimized using the teaching-learning-based optimization (TLBO) algorithm, 

and its performance is contrasted against firefly algorithm, differential evolution 

algorithm and cuckoo search algorithm. It is revealed that the TLBO algorithm 

supersedes the others with respect to accuracy and consistency of the derived optimal 

solutions, and computational efforts. 

Key Words: EDM Process, TLBO Algorithm, Metaheuristics, Optimization 

1. INTRODUCTION 

Electrical discharge machining (EDM) has already been accepted as an efficient 

thermo-electrical material removal process in tool and die making, aerospace and 

automotive industries, and also in finishing of surgical components due to its ability to 

maintain close tolerances and attain higher dimensional accuracy [1, 2]. In this process, a 

series of successive discharges between the tool (electrode) and the workpiece is responsible 

                                                           
Received February 18, 2020 / Accepted June 08, 2020 

Corresponding author: Shankar Chakraborty 

Department of Production Engineering, Jadavpur University, Kolkata, West Bengal, India 

E-mail: s_chakraborty00@yahoo.co.in 



282 V. KUMAR, S. DIYALEY, S. CHAKRABORTY 

for removing material in the presence of a dielectric medium (kerosene or de-ionized 

water). During electrical discharge, a discharge channel is developed having a temperature 

around 12000°C causing melting and evaporation of material from the workpiece surface. 

The electrode is advanced towards the workpiece until the inter-electrode gap is small 

enough for the higher impressed voltage to ionize the dielectric [3]. In EDM process, a 

perfect replication of the tool shape is generated on the workpiece surface. This process is 

especially suitable for generating complex shape profiles on electrically conductive materials 

with low machinability [4]. 

As there is no direct contact between the tool and the workpiece, this process is free 

from any mechanical stress generation, chatter/burr formation and vibration problem. Its 

machining performance is also uninfluenced by the hardness of the work material 

because the material removal takes place by melting due to high intensity localized heat 

generation. Since no cutting force is generated, extremely deep narrow holes with high 

aspect ratio can be machined using this process with minimum tool wear. It can even 

generate intricate cavities in a single operation. But EDM process also suffers from several 

drawbacks, like generation of recast layer and heat-affected zone (HAZ), low material 

removal rate (MRR), high machining time and related cost, low flexibility, capability of 

machining only electrically conductive materials, etc.  

It has been observed that the machining performance of an EDM process with respect to 

MRR, surface roughness (SR), tool wear rate (TWR), HAZ, radial overcut (ROC) etc. is 

significantly affected by different electrical parameters (peak current, pulse-on time, pulse-

off time, gap voltage, polarity, etc.) and non-electrical parameters (electrode material, type 

of the dielectric used, dielectric pressure, rotation of the electrode, etc.). Thus, in order to 

fulfill the requirements of better response values, it is always preferred to operate an EDM 

set-up while maintaining the settings of its different input parameters as their optimal levels. 

It would also lead to a higher production rate with reduced machining time. 

Keeping in mind the requirements of finding out the optimal parametric mixes for EDM 

processes, this paper deals with the application of teaching-learning-based optimization 

(TLBO) algorithm to study the influences of various input parameters of an EDM process 

on its responses (outputs) while machining pearlitic SG iron 450/12 grade work material. 

For this process, gap voltage, peak current, cycle time and rotation of the tool are considered 

as input parameters, whereas, MRR, SR, TWR, overcut (OC) and circularity error (CE) are 

treated as responses. Both the single- and multi-objective optimization models are developed 

and subsequently solved using the considered algorithm. Its optimization performance is also 

contrasted with that of firefly algorithm (FA), differential evolution (DE) algorithm and 

cuckoo search (CS) algorithm. The TLBO algorithm supersedes the other algorithms with 

respect to accuracy and consistency of the derived optimal solutions, and computational 

effort. The results of two-tailed paired t-tests also confirm its superiority over the others. 

2. REVIEW OF THE LITERATURE 

Mandal et al. [5] first applied artificial neural network (ANN) with back-propagation 

algorithm to model an EDM process and non-dominating sorting genetic algorithm-II 

(NSGA-II) was later adopted to optimize the said process. Using controlled elitist NSGA 

technique, Bharti et al. [6] optimized different input parameters of a die-sinking EDM 

process. The ANN with back-propagation algorithm was also adopted to model the 



 Teaching-Learning-Based Parametric Optimization of an Electrical Discharge Machining Process 283 

considered process. Baraskar et al. [7] employed NSGA-II technique to identify the optimal 

settings of pulse-on time, pulse-off time and discharge current for an EDM process to 

achieve better values of SR and MRR responses. Shivakoti et al. [8] studied the effects of 

salt-mixed de-ionized water as a dielectric on MRR, TWR, ROC and taper during EDM 

operation of D3 die steel. The Taguchi method was later utilized to optimize the considered 

EDM process parameters. Aich and Banerjee [9] applied weight-varying multi-objective 

simulated annealing technique to develop the corresponding Pareto optimal front for 

simultaneous optimization of MRR and SR in an EDM process. Radhika et al. [10] 

considered peak current, pulse-on time and flushing pressure as the input parameters of an 

EDM process. A hybrid optimization technique consisting of ANN and genetic algorithm 

(GA) was later employed to minimize SR and TWR, and maximize MRR. A Pareto-

optimal front was also developed offering a set of non-dominated solutions. Tiwari et al. 

[11] applied GA technique to simultaneously optimize MRR and SR during an EDM 

operation. The corresponding Pareto-optimal solutions were subsequently proposed. 

Mazarbhuiya et al. [12] performed eight experimental runs in an EDM set-up based on 

Taguchi’s design plan, and applied grey relational analysis (GRA) technique to determine 

the optimal settings of discharge current, flushing pressure, pulse-on time and polarity for 

achieving maximum value of MRR and minimum SR value. Mohanty et al. [13] considered 

open circuit voltage, discharge current, pulse-on time, duty factor, flushing pressure and 

type of the tool material as the control parameters of a die-sinking EDM process. Based on 

a multi-objective particle swarm optimization (PSO) algorithm, the optimal values of 

different process responses, like MRR, EWR, SR and ROC were subsequently determined. 

While considering peak current, polarity, pulse-on time, gap voltage and spindle speed as 

the input parameters of an EDM process, Gohil and Puri [14] adopted Taguchi-GRA 

technique to maximize MRR and minimize SR while machining titanium alloys. Satpathy 

et al. [15] combined principal component analysis with technique for order of preference by 

similarity to ideal solution (TOPSIS) for multi-objective optimization of an EDM process, 

while taking into account peak current, pulse-on time, duty cycle and gap voltage as the 

input parameters, and MRR, TWR, ROC and SR as the responses. Applying VIKOR index 

as a multi-objective optimization tool for an EDM process, Mohanty et al. [16] determined 

the optimal settings of current, pulse-on time and voltage for having better values of MRR, 

TWR, SR and ROC. Singh et al. [17] utilized NSGA-II technique to optimize MRR and 

TWR in an EDM process while considering peak current, pulse-on time, pulses-off time 

and gap voltage as the input parameters. Gostimirovic et al. [18] modeled the energy 

efficiency of an EDM process with respect to MRR and SR responses. Evolutionary multi-

objective optimization was later performed to derive a set of optimal solutions for discharge 

energy taking into account discharge current and discharge duration as the input parameters. 

Ramprabhu et al. [19] applied passing vehicle search (PVS) as a multi-objective 

optimization tool for optimizing various input parameters of an EDM process. The 

performance of the adopted technique was also compared with that of other intelligent 

computing models. Based on GRA technique, Tharian et al. [20] performed multi-objective 

optimization of MRR and SR during EDM operation of Al7075 alloy. Huu et al. [21] 

proposed the application of multi-objective optimization based on ratio analysis (MOORA) 

method for having better values of MRR, SR and TWR during EDM operation of SKD61 

die steel with low-frequency vibration. Analytic hierarchy process (AHP) was utilized to 

estimate relative weights of the considered responses. While employing response surface 

methodology (RSM)-based regression models, Niamat et al. [22] endeavored to study the 



284 V. KUMAR, S. DIYALEY, S. CHAKRABORTY 

influences of current, pulse-on time and pulse-off time on MRR, SR and TWR in an EDM 

process. Multi-objective optimization was also performed to achieve sustainability while 

optimizing the conflicting responses. 

The above-cited review of the existing literature reveals that parametric optimization of 

EDM processes has already caught the attention of the research community, and several 

optimization techniques, like GA, NSGA-II, simulated annealing, PVS, PSO, etc. have been 

applied in this direction. Those adopted algorithms have too many algorithmic parameters, 

which if not properly tuned, may increase the computational effort and result in local 

optimal solutions. Similarly, numerous multi-criteria decision making approaches, such as 

VIKOR, TOPSIS, GRA, AHP, MOORA, etc. have also been utilized to determine the most 

feasible parametric mixes for EDM processes. But, in most of the cases, near optimal or 

sub-optimal solutions have been arrived at. Moreover, there is a scarcity of research works 

dealing with comparative analysis of the optimization performance of the available 

metaheuristic algorithms. In order to overcome such drawbacks, the TLBO algorithm is 

applied in this paper for the first time to find out the best combination of four EDM process 

parameters while machining pearlitic SG iron 450/12 grade work material in order to 

simultaneously optimize the responses under consideration. The TLBO algorithm is a 

population-based optimization technique, requiring no algorithmic specific parameters and 

has already earned a broad acceptance among the researchers in the optimization domain. 

This algorithm is efficient, simple and capable of achieving almost global optimal solutions 

with less computational effort. The comparative analysis results reveal that it is more 

flexible, robust and reliable as compared to other mostly preferred metaheuristic algorithms, 

like FA, DE and CS techniques. Their optimization performance is compared with respect 

to three metrics, i.e. accuracy of the derived solutions, consistency of the solutions and 

convergence speed. These comparison results are also validated using the developed boxplots 

and paired t-test. 

3. TLBO ALGORITHM 

The TLBO algorithm is based on the concept of improving knowledge of the students 

within the classroom by the teacher first, and the knowledge is further upgraded by the 

mutual interaction among the students [23]. This algorithm thus consists of two phases, 

i.e. a) teacher phase and b) student phase. The knowledge acquired by the students from 

the teacher is known as the teacher’s phase. On the other hand, enrichment in knowledge 

through mutual interactions among the students is known as the student’s phase [24].  

Teacher Phase 

In this algorithm, the teacher is supposed to be the best solution in an entire set of 

solutions and the learners acquire knowledge from the teacher. A teacher always attempts 

to improve the grades of all the students in the class by bettering the mean result of the 

entire class. But, from the practical point of view, it is not at all possible to uplift the 

mean result of the class because the learning capability of the class depends on the ability 

of the students to grab knowledge from the concerned teacher. Let Xj,k,i be any value in 

the solution, where j is the design variable (subject taken by the learners) (j = 1,2,...,m); k 

is the population member (i.e. learner) (k = 1,2,...,n) and i is the iteration number (i = 

1,2,...,Genmax) (Genmax is the number of maximum iterations). The teacher phase begins 



 Teaching-Learning-Based Parametric Optimization of an Electrical Discharge Machining Process 285 

with the identification of the teacher (best solution) from the available population, based 

on the objective function value. Ati
th

 iteration, Xk,i represents the best solution having the 

value of f(Xk,i) being minimum among the population. This best solution is denoted as 

Xkbest,i.. The mean result Mj,i of the learners in j
th

 subject is computed. In this algorithm, 

the teacher always attempts to uplift the mean result of the entire class in a particular 

subject. Thus, the difference between the result of the teacher and mean result of the 

learners in each subject is represented as: 

 Difference_Meanj,k,i  = rj,i(Xj,kbest,i – TfMj,i) (1) 

where rj,iis a random number between 0 and 1,Xj,kbest,i  is the result of the best learner in j
th
 

subject, and Tf is the teaching factor which chooses the value of the mean to be modified. 

The value of Tf can be either 1 or 2 and is decided randomly using the following equation: 

 Tf = round [1 + rand (0,1){2-1}] (2) 

Based on the value of Difference_Meanj,k,i, the existing solution is upgraded using the 

following expression: 

 X'j,k,i= Xj,k,i + Difference_Meanj,k,i (3) 

where X'j,k,i  is the updated value of Xj,k,i. The X'j,k,i value is accepted if it has a better 

function value. At the end of this phase, all the accepted function values are retained 

which serve as the inputs to the learner phase. 

Learner Phase 

In this phase, the learners endeavor to boost their knowledge through interactions 

among themselves. A learner learns from other learners if they have more knowledge than 

him/her. For a population size of n, at i
th
 iteration, each learner is randomly compared with 

other learners. For this comparison, two different learners A and B are randomly chosen so 

that X'A,i≠ X'B,i, where X'A,i and X'B,i are the revised values at the end of the teacher phase. 

 X"j,A,i = X'j,A,i+rj,i (X'j,A,i – X'j,B,i), if f (X'A,i)< f (X'B,i) (4) 

 X"j,A,i = X'j,A,i+rj,i (X'j,B,i – X'j,A,i), if f (X'B,i)< f (X'A,i) (5) 

If X"j,A,i   has a better function value, it is accepted. At i
th

 iteration, the learner phase is 

accomplished applying the following loops: 

Fork= 1:n 

Let the present learner be X'A,i 

Randomly select another learner X'B,i, so that X'A,i≠ X'B,i 

Iff (X'A,i) <f  (X'B,i), 

Forj = 1:m; X"j,A,i = X'j,A,i+ rj,i(X'j,A,i–X'j,B,i); End For 

Else; For j = 1:m; X"j,A,i = X'j,A,i+ rj,i(X'j,B,i–X'j,A,i); End For; 

End If 

End For 

At the end of this phase, all the accepted function values are saved so that they 

become the new inputs to the teacher phase in the next generation. The flowchart for 

TLBO algorithm is exhibited in Fig. 1. 



286 V. KUMAR, S. DIYALEY, S. CHAKRABORTY 

 

Fig. 1 Flowchart of TLBO algorithm 

4. EXPERIMENTAL DETAILS 

This paper deals with the EDM operation for generation of standard holes on pearlitic 

SG iron 450/12 grade material while considering gap voltage, peak current, cycle time and 

rotation of the tool (electrode) as the input parameters. This work material for EDM 

operation is chosen due to its several favorable properties, like good wear and corrosion 

resistance, better castability and machinability, reasonable strength, low cost, suitability for 

hydraulic applications as compared to steel, malleable and grey iron castings, capability to 

generate intricate shapes due to better fluidity as compared to steel castings, requirement of 

less heat treatment resulting in better dimensional stability compared to malleable castings 

etc. It has found wide ranging applications in manufacturing of water pump bodies, pump 

housings, pump covers, pump hub for cooling system of diesel engines, manifolds for inlet 



 Teaching-Learning-Based Parametric Optimization of an Electrical Discharge Machining Process 287 

and exhaust valves, castings for engine mounting arms, engine supports, fly wheels, engine 

couplings, drive coupling assembles, anti-vibration mountings, etc., pulleys for crankshaft 

assembly, castings for reduction gear boxes, bearing covers and end covers, castings for 

machine tool components, etc. The chemical composition and mechanical properties of SG 

iron 450/12 grade material are respectively provided in Tables 1 and 2.    

Table 1 Chemical composition of pearlitic ductile iron 

Element C Si Mn P S Cr Mo Cu Mg Ti Zn Fe Others 

% 3.365 2.393 0.238 0.072 <0.150 0.007 <0.010 0.37 0.085 0.032 0.027 90.75 2.661 

Table 2 Mechanical properties of pearlitic SG iron (450/12 grade) 

Mechanical property Value 

Tensile strength  450 MPa 

Yield strength  310 MPa 

Elongation  12% 

Hardness  197 BHN 

Density  6.95 gm/cm³ 

Relative wear resistance Excellent 

Table 3 EDM process parameters with their operating levels  

Process parameter Symbol Unit 
Level 

-2 -1 0 1 2 

Gap voltage x1 V 40 45 50 55 60 

Peak current x2 A 20 30 40 50 60 

Cycle time x3 μs 80 160   240   320   400   

Tool rotation x4 rpm   5 15 25 35 45 

While performing EDM operation on pearlitic SG iron 450/12 grade material, each of 

the considered EDM process parameters has been varied at five different operating levels, 

as shown in Table 3. According to the central composite design plan, for four factors with 

five levels, 30 experiments have been conducted in an Agietron 250 C EDM set-up. It has 

the following specifications, e.g. working area: [X 700 Y 500 Z 500] mm, maximum 

workpiece dimension: [L 1000 W 700 H 320] mm, maximum workpiece weight: 1200 

kg, maximum electrode weight: 400 kg, work tank volume: 360 l, dielectric unit capacity: 

1200 l and accuracy: 0.001 mm. The photograph of the EDM set-up is shown in Fig. 2. 

During the machining operation, Castrol SE 180 EDM fluid is used as the dielectric 

because of its various advantageous properties, like low odor, higher stability with 

extended fluid life, low viscosity, high flash point, increased reliability and safe use. The 

specimen size has been taken as 15 × 40 mm. 



288 V. KUMAR, S. DIYALEY, S. CHAKRABORTY 

Table 4 Details of experimental results  

Exp. No. 
Gap  

voltage 

Peak  

current 

Cycle  

time 
Rotation MRR SR TWR OC CE 

1 50 20 240 25 6.00 8.572 0.589 0.8084 0.2914 

2 40 40 240 25 16.60 8.581 0.671 0.8495 0.2982 

3 50 40 240 45 13.07 8.092 0.623 0.8473 0.1495 

4 50 60 240 25 21.07 8.532 0.698 0.8606 0.3055 

5 50 40 240 25 11.98 8.712 0.612 0.8333 0.3012 

6 50 40 240   5 9.28 9.612 0.599 0.8295 0.3197 

7 60 40 240 25 15.98 8.902 0.663 0.8493 0.2998 

8 50 40 400 25 23.26 8.742 0.726 0.9266 0.3032 

9 50 40 80 25 4.10 8.622 0.531 0.7623 0.2989 

10 50 40 240 25 15.21 8.531 0.659 0.8492 0.3011 

11 45 30 320 35 7.41 8.235 0.590 0.8077 0.1932 

12 55 30 320 15 6.10 9.092 0.586 0.8095 0.3176 

13 50 40 240 25 13.07 8.626 0.627 0.8446 0.3014 

14 45 30 160 15 2.25 9.207 0.522 0.7233 0.3143 

15 55 50 320 15 18.14 9.367 0.677 0.8543 0.3179 

16 45 30 160 35 2.16 8.265 0.518 0.7154 0.1795 

17 45 50 320 15 19.29 9.247 0.696 0.8559 0.3174 

18 45 50 160 35 4.98 8.635 0.545 0.7827 0.1934 

19 50 40 240 25 9.95 8.732 0.597 0.8297 0.3019 

20 55 30 160 35 3.59 8.475 0.529 0.7345 0.2236 

21 55 30 160 15 1.97 9.212 0.511 0.7154 0.3161 

22 55 50 160 35 6.25 8.685 0.593 0.8246 0.2579 

23 55 30 320 35 22.13 8.345 0.719 0.9118 0.2003 

24 50 40 240 25 12.84 8.826 0.618 0.8393 0.3015 

25 45 50 320 35 19.78 8.436 0.692 0.8604 0.2693 

26 45 50 160 15 4.96 9.232 0.548 0.7725 0.3156 

27 55 50 320 35 21.24 8.176 0.702 0.8988 0.2009 

28 50 40 240 25 11.06 8.696 0.605 0.8306 0.3018 

29 55 50 160 15 5.65 9.172 0.552 0.7935 0.3164 

30 45 30 320 15 5.80 9.497 0.567 0.8077 0.3183 

It is worthwhile to mention here that all the 30 experiment runs have been performed in 

random order so that the machining error can be minimized. Five most important responses 

(outputs) of the EDM process are considered here, i.e. MRR (in mm
3
/min), SR (in μm), 

EWR (in mm
3
/min), OC (in mm) and CE (in mm). For measurement of MRR and EWR, an 

electronic weighing balance (A&D GR-202 type) has been employed. On the other hand, 

SR has been measured using HommelWerke Turbo Wave V7.20 roughness tester, and 

ZEISS O-INSPECT 442 CMM machine (with GEOMET universal CMM software) has 

been used for measuring both OC and CE. Table 4 displays the experimental design plan 

along with the measured values of the considered responses. In Fig. 3, the photographs of 

the copper electrode utilized during EDM operation and the machined component are 

provided. Among these responses, MRR is the sole larger-the-better quality characteristic, 

and the remaining three are of smaller-the-better type. 

 



 Teaching-Learning-Based Parametric Optimization of an Electrical Discharge Machining Process 289 

 

Fig. 2 EDM set-up 

 

 

Fig. 3 Round copper tool and machined component (5 mm depth and 20 mm dia.) 

5. OPTIMIZATION OF THE EDM PROCESS 

Now, based on the experimental data of Table 4 and using Minitab software (R17), 

the following RSM-based equations are developed for the five responses, considering the 

main, second order and interaction effects between the considered EDM process 

parameters. Higher values of the corresponding coefficient of determination (R
2
) justify 

that these RSM-based equations are the best fit models depicting the relationships 

between the process parameters and responses. 

 1 2 3 4 1 22
1 4 2 3 3 4

( ) –5.0 0.235 0.727 – 0.05 – 1.436 – 0.0 ...

(

174

0.0241 0.00196 0.00149 81.5 )7

Y MRR x x x x x x

x x x x x x R

  

  
 (6) 

 2
1 2 3 4

( ) 9.57433 0.00305 0.00207 – 0.000105 – 0.0407 85.47( )Y SR x x x x R     (7) 

 
1 2 3 4

2 2 2 2

1 2 3 4
2

1 2 2 4 3 4

0.54 – 0.0134 0.0073 0.000319 0.00329 ...

0.000201 – 0.000008 – 0.000001 – 0.00009 – ...

0.00013

( )

(0.000011 0.00001 84.59)

Y TWR x x x x

x x x x

x x x x x x R

    

  

 (8) 

 

2

1 2 3 4 1
2 2 2

2 3 4 1 2 1 4
2

2 3 2 4 3 4

( ) 0.147 0.0101 0.01212 0.01184 – 0.00912 – 0.000133 – ...

0.000071 – 0.0000001 – 0.000061 – 0.000022 0.000238 – ...

0.000012 – 0.000014  0.000008 84.59( )

Y OC x x x x x

x x x x x x x

x x x x x x R

   



 

 (9) 



290 V. KUMAR, S. DIYALEY, S. CHAKRABORTY 

 
1 2 3 4 

2 2 2

1 2 4 1 2 1 4
2

2 3 2 4

( ) –0.162 0.016 0.00459 0.000158 – 0.00091 – ...

0.000142 – 0.000037 – 0.000196 – 0.000069 0.000056 ...

0.000002 0.000077 90.5( )6

Y CE x x x x

x x x x x x x

x x x x R

    

 

 

 (10) 

Table 5 Results of single-objective optimization  

Response Method Mean SD 
Optimal 

value 

Parameter 

Gap 

voltage 

Peak 

current 

Cycle  

time 

Tool 

rotation 

MRR 

FA 40.629 1.169 40.824 60 55.172 387.421 45 

DE 38.952 0.576 39.022 55.03 58.75 393.49 39.363 

CS 41.316 1.201 41.508 56.457 57.999 392.36 44.76 

TLBO 44.629 0.246 44.660 60 60 400 45 

SR 

FA 7.938 0.001 7.904 43.482 32.00 361.18 45 

DE 8.009 0.001 7.987 58.05 27.39 194.14 44.23 

CS 8.01 0.017 7.883 40 27.85 372.16 45 

TLBO 7.874 0.0009 7.864 40 20 400 45 

TWR 

 

FA 0.481 0.004 0.480 50.5481 42.169 110.778 45 

DE 0.435 0.01 0.434 45.975 26.991 93.612 45 

CS 0.437 0.009 0.436 46.963 30.184 88.668 45 

TLBO 0.403 0.00069 0.402 40.024 20.001 80 45 

OC 

FA 0.689 0.005 0.688 45.813 23.817 173.132 43.464 

DE 0.626 0.008 0.625 43.351 26.565 117.224 44.966 

CS 0.605 0.006 0.604 43.014 28.959 86.787 45 

TLBO 0.515 0.002 0.514 40.024 20.215 80 45 

CE 

FA 0.078 0.002 0.077 45.77 26.02 116.07 45 

DE 0.058 0.004 0.057 45.86 20.05 94.71 44.68 

CS 0.060 0.004 0.059 43.66 25.411 81.892 45 

TLBO 0.021 0.001 0.020 40 20 80 45 

It has already been mentioned that this paper focuses on the applications of four 
popular metaheuristic algorithms in the form of FA, DE, CS and TLBO techniques for 
both single- and multi-objective optimization of the considered EDM process. While 
solving this parametric optimization problem using the considered algorithms, the 
corresponding values of different algorithmic parameters are set as follows: 

FA: Number of iterations = 500, number of fireflies = 300, light absorption coefficient = 
1, initial randomness = 0.9, randomness factor = 0.91 and randomness reduction = 0.75. 

DE algorithm:  Number of iterations = 500, population size = 300, lower bound of scaling 
factor = 0.2, upper bound of scaling factor = 0.8 and crossover probability = 0.9. 

CS algorithm: Number of iterations = 500, population size (nests) = 300 and discovering 
rate of alien eggs = 0.25. 

TLBO algorithm:  Number of iterations = 500 and population size = 300. 

For single objective optimization, the developed equations are solved using the 
considered metaheuristics within the given sets of constraints as 40 ≤ x1≤ 60, 20 ≤ x2≤ 60, 
80 ≤ x3≤ 400 and 5 ≤ x4≤ 45. The results of this single objective optimization are provided 
in Table 5. It can be clearly unveiled from the table that among the four metaheuristics, the 
TLBO algorithm has the superiority over the others with respect to better values of the 
responses with higher accuracy and lower standard deviation (SD). The results of single 
objective optimization derive the optimal settings of the four EDM process parameters to be 



 Teaching-Learning-Based Parametric Optimization of an Electrical Discharge Machining Process 291 

maintained for maximization/minimization of the considered responses. The boxplots of 
Fig. 4 prove that the optimal solutions derived using the TLBO algorithm are more consistent 
having the lowest variability as compared to others. On the other hand, the convergence 
diagrams, as exhibited in Fig. 5, also demonstrate that TLBO algorithm requires less 
computational effort with respect to both computation speed and time. It can be interestingly 
noticed that the TLBO algorithm provides the optimal solutions for all the five EDM 
responses almost within 5-10 iterations. 

 
(a) 

 
(b) 

 
(c) 

 
(d) 

(e)  

Fig. 4 Boxplots for the considered metaheuristic algorithms 



292 V. KUMAR, S. DIYALEY, S. CHAKRABORTY 

 
(a) 

 
(b) 

 
(c) 

 
(d) 

 
(e) 

Fig. 5 Convergence diagrams for the metaheuristic algorithms 

Table 6 t-test results with respect to the TLBO algorithm 

Response FA DE CS 

MRR 74.817 204.362 60.383 

SR -272.183 -1423.66 -28.1014 

TWR -205.229 -57.451 -63.872 

OC -627.432 -351.727 -436.548 

CE -409.364 -183.558 -191.048 



 Teaching-Learning-Based Parametric Optimization of an Electrical Discharge Machining Process 293 

Finally, in order to validate the uniqueness of the TLBO algorithm over the remaining 

three optimization techniques, two-tailed paired t-tests are performed with the null 

hypothesis and alternative hypothesis as H0(µA= µB) and Hα(µA≠ µB) respectively (where α 

is the level of significance, and µA and µB are respectively the mean response values 

obtained using two algorithms being pair-wise compared). The results of the paired t-tests 

are provided in Table 6. In this table, as the absolute values of t-statistic for all the 

responses for the pair-wise comparisons between TLBO and other algorithms are greater 

than the corresponding tabulated t-value, the null hypotheses can be rejected. It thus 

demonstrates the uniqueness of the optimization performance of the TLBO algorithm 

against the other techniques while providing the best single objective optimization solutions. 

Based on the optimal solutions provided by the TLBO algorithm, effects of the EDM 

process parameters under consideration on the responses are investigated using the 

developed response graphs of Figs. 6-10. Fig. 6 exhibits how the obtained MRR changes 

with varying values of the process parameters. It can be interestingly noticed that with the 

increasing values of all the EDM process parameters, the MRR values also increase. Higher 

values of gap voltage, peak current and cycle time cause the available discharge energy to 

increase, resulting in more melting and vaporization of material from the workpiece. The 

impulsive force in the spark gap also increases, which is responsible for higher MRR [25].  

 
(a) 

 
(b) 

 
(c) 

 
(d) 

Fig. 6 Effects of EDM process parameters on MRR 



294 V. KUMAR, S. DIYALEY, S. CHAKRABORTY 

In this EDM process, the tool (electrode) rotates normal to the workpiece surface and a 

centrifugal force is thus generated causing more debris removal from the machining zone. 

Tool rotation in the EDM process also results in formation of a thin recast layer, and the 

debris get easily cleared from the melt pool while exposing the workpiece to increased 

spark intensity. Thus, less material remains in the melt cavity to be re-deposited over the 

workpiece surface [26]. Tool rotation eases the flushing problem as encountered during 

the EDM operation. 

The influences of the EDM process parameters on the SR are exhibited in Fig. 7. With 

increasing values of gap voltage and peak current, the SR of the machined components 

slightly increases. It almost remains unaffected due to the changes in cycle time and it 

shows a decreasing trend pattern with increasing values of tool rotation. The increments 

in gap voltage, peak current and cycle time are responsible for stronger discharge energy, 

creating higher temperature and formation of larger craters on the machined surface, 

resulting in poor surface quality [27]. It is also noticed that the tool rotation helps in a 

quick removal of the debris from the machining zone and as a result, with a higher tool 

rotation, the machined surface becomes smoother. With the tool rotation, it is expected 

that there would be 9-10% decrease in the average SR value. 

 
(a) 

 
(b) 

 
(c) 

 
(d) 

Fig. 7 Effects of the EDM process parameters on the SR 



 Teaching-Learning-Based Parametric Optimization of an Electrical Discharge Machining Process 295 

As revealed from Fig. 8, higher values of gap voltage, peak current and cycle time 

cause increments in the TWR values. At those higher parametric settings, there are micro 

tool wears due to availability of higher spark energy density at the machining zone. 

Generally, lower settings of these three EDM process parameters tend to enhance the 

possibility of carbon deposition on the tool surface, which finally helps in lowering the 

value of the TWR. On the contrary, with increment in tool rotational speed, there is also a 

possibility of throwing away the carbon particles from the tool surface, which causes an 

increment in the TWR. But, at higher tool rotation, better flushing occurs and there is a 

better disposition of dielectric fluid in the machining zone, leading to smaller TWR [28].  

 
(a) 

 
(b) 

 
(c) 

 
(d) 

Fig. 8 Effects of the EDM process parameters on the TWR 

During the EDM operation, OC occurs due to side erosion and removal of debris. It 

shows increasing trend patterns with increased values of gap voltage, peak current and cycle 

time, as exhibited in Fig. 9. At higher settings of these three EDM process parameters, 

availability of higher gap voltage and gap width allows breakdown of dielectric at a wide 

gap due to higher electric field [29, 30]. At higher gap voltage and peak current, spark 

energy density would be more with faster machining rate, which is also responsible for 

higher OC. But, with increasing tool rotational speed, OC gradually increases. Increased 

centrifugal force, resulting from a higher tool rotation, removes more debris from the 

machining zone. The removed debris is placed between the side wall of the electrode and 



296 V. KUMAR, S. DIYALEY, S. CHAKRABORTY 

workpiece, causing generation of a spark between them. It leads to higher OC. At a higher 

tool rotational speed, there would be more turbulence taking place at the machining zone 

which would perhaps be responsible for removal of the debris, leading to gradual decrement 

in OC.  

The CE in the machined components occurs due to non-uniform undercut and overcut 

which can be effectively controlled by proper settings of different EDM process parameters. 

As noticed in Fig. 10, with increasing values of gap voltage, peak current and cycle time, 

CE shows an increasing trend pattern. It is also affected by tool rotation. At a higher gap 

voltage, peak current and cycle time, there are occurrences of secondary spark discharges 

caused by poor flushing, which are responsible for inferior CE. Increase in CE is also 

occurred due to high tool wear and sporadic machining at higher voltage [31]. A higher tool 

rotational speed may create turbulence of the dielectric fluid at the machining zone, which 

would be responsible for removal of debris from the external periphery of the machined 

hole. Thus, there may be a high chance of obtaining lower CE at higher tool rotation.    
 

 

 
(a) 

 
(b) 

 
(c) 

 
(d) 

Fig. 9 Effects of the EDM process parameters on the OC 



 Teaching-Learning-Based Parametric Optimization of an Electrical Discharge Machining Process 297 

 
(a) 

 
(b) 

 
(c)  

(d) 

Fig. 10 Effects of the EDM process parameters on the CE 

It can be noticed from the results of single objective optimization of the considered 

EDM process that separate parametric settings are obtained for different responses based 

on the applications of four metaheuristic algorithms. But, in a real time machining 

environment, it is never possible for an operator to set the EDM process parameters at 

different operating levels in a single EDM set-up. It is thus always advised to derive a 

unique combination of the process parameters so as to simultaneously optimize all the 

five responses. For this purpose, the following multi-objective optimization model is 

developed which is subsequently solved using the considered metaheuristics. 

 min

5

min

4

min

3

min

2

max

1

(CE)

)CE(

(OC)

)OC(

(EWR)

)EWR(

(SR)

)SR(

(MRR)

)MRR(
Minimize

YwYwYwYwYw
Z 

 

(11)

 

where w1, w2, w3, w4 and w5 are the weights allotted to MRR, SR, EWR, OC and CE 

respectively, (MRR)max is the maximum value of MRR, (SR)min, (EWR)min, (OC)min and 

(CE)min are the minimum values of SR, EWR, OC and CE, respectively. These values are 

obtained from the results of single objective optimization of the responses. In this paper, 

equal weights are assigned to all the responses under consideration. The solutions of this 

multi-objective optimization problem are provided in Table 7. It can be clearly unveiled from 

this table that the TLBO algorithm again excels over the remaining three metaheuristics with 



298 V. KUMAR, S. DIYALEY, S. CHAKRABORTY 

respect to accuracy and consistency of the derived optimal solutions. Thus, for obtaining 

the most desired performance of the EDM process while generating standard holes on 

pearlitic SG iron 450/12 grade work material, it is always recommended to set the input 

parameters as gap voltage = 41 V, peak current = 58.58 A, cycle time = 285 μs and tool 

rotation = 45 rpm. Thus, based on the optimal solutions derived using TLBO algorithm, it 

can be concluded that lower gap voltage, higher peak current, moderate cycle time and 

higher tool rotational speed would concurrently optimize all the responses of the 

considered EDM process. 

Table 8 exhibits the percentage improvements in the response values based on the 

multi-objective optimization results of the TLBO algorithm against FA, DE and CS 

techniques. It can be observed from this table that for the considered EDM process, the 

values of MRR, SR, TWR, OC and CE are significantly improved employing the TLBO 

algorithm as compared to other metaheuristic algorithms.  

Table 7 Results of multi-objective optimization 

Method Response Mean SD 
Optimal 

value 
Z 

Parameter 

Gap 

voltage  

Peak 

current 

Cycle  

time  

Tool 

rotation  

FA MRR 

SR 

TWR 

OC 

CE 

2.229 0.107 23.2 

7.96 

0.436 

0.8 

0.182 

2.225 43.258 56.25 290 45 

DE MRR 

SR 

TWR 

OC 

CE 

2.309 0.152 21.953 

7.961 

0.428 

0.788 

0.181 

2.303 42.3 57.25 278.35 45 

CS MRR 

SR 

TWR 

OC 

CE 

2.293 0.192 22.808 

7.959 

0.434 

0.779 

0.179 

2.284 41.23 58.23 283.56 45 

TLBO MRR 

SR 

TWR 

OC 

CE 

2.223 0.09 24.012 

7.959 

0.409 

0.708 

0.178 

2.218 41 58.58 285 45 

Table 8 Percentage improvements in responses using the TLBO algorithm 

Response FA DE CS 

MRR 3.5 9.37 5.27 

SR 0.75 0.75 0 

TWR 6.19 4.43 5.76 

OC 11.5 10.15 9.11 

CE 2.19 1.65 0.55 

 



 Teaching-Learning-Based Parametric Optimization of an Electrical Discharge Machining Process 299 

6. CONCLUSIONS 

The paper studies the capability of an EDM process in generating standard holes on 

pearlitic SG iron 450/12 grade material, which has found wide ranging applications in 

manufacturing of diverse mechanical components. The optimal settings of gap voltage, 

peak current, cycle time and tool rotation for the considered machining application are 

determined using the TLBO algorithm. It is observed that lower gap voltage, higher peak 

current, moderate cycle time and higher tool rotational speed would simultaneously 

optimize material removal rate, surface roughness, tool wear rate, radial overcut and 

circularity error of this EDM process. The effects of all these EDM process parameters on 

the responses are also investigated. The optimization performance of the TLBO algorithm is 

compared with three other metaheuristics, and it is concluded that the TLBO algorithm 

excels over the others with respect to higher accuracy of the optimal solutions with low 

variability and less computational effort. The results of the paired t-tests and developed 

boxplots also confirm this observation. This algorithm provides almost global optimal 

solutions for both single- and multi-objective optimization problems as it is least affected 

due the settings of its different tuning parameters. The applicability of this algorithm for 

optimization of other conventional and non-conventional machining processes can also be 

explored. The effects of changing weights allotted to different responses on the optimization 

performance of TLBO algorithm can be examined as the future scope of this paper. 

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