https://doi.org/10.31449/inf.v43i1.1636 Informatica 43 (2019) 65–75 65
  
Corresponding Author: Yugal Kumar, Department of Computer Science and Engineering, JUIT, Waknaghat, Solan, 
Himachal Pardesh, India, yugalkumar.14@gmail.com 
A New Variant of Teaching Learning Based Optimization Algorithm 
for Global Optimization Problems 
Yugal Kumar 
Department of Computer Science and Engineering, JUIT, Waknaghat, Solan, Himachal Pardesh, India 
E-mail: yugalkumar.14@gmail.com 
 
Neeraj Dahiya and Sanjay Malik  
Department of Computer Science and Engineering, SRM University, Delhi-NCR Campus, India 
E-mail: neerajdahiya.cse@gmail.com, skmalik9876@gmail.com  
 
Savita Khatri 
Department of Computer Science and Engineering, BMIET, Sonepat, India 
E-mail: dhynrj@gmail.com 
 
Keywords: teaching learning based optimization, crossover, meta-heuristics, mutation  
Received: May 19, 2017 
This paper presents a new variant of teaching learning based optimization (TLBO) algorithm for solving 
global optimization problems. The performance of the TLBO algorithm depends on coordination of 
teacher phase and learner phase. It is noticed that sometimes performance of TLBO algorithm is 
affected due to lack of diversity in teacher and learner phases. In this work, a new variant of TLBO 
algorithm is proposed   based on genetic crossover and mutation strategies. These strategies are 
inculcated in TLBO algorithm for improving its search mechanism and convergence rate. Genetic 
mutation strategy is applied in teacher phase of TLBO algorithm for improving the mean knowledge of 
leaners. While, Crossover strategy is applied in learner phase of TLBO algorithm to find the good 
learner. The effectiveness of the proposed algorithm is tested on several bench mark test functions of 
CEC’14. From simulation results, it is stated that the proposed algorithm provides more optimized 
results in comparison to same class of algorithms. 
Povzetek: V prispevku je opisan nov globalni optimizacijski algoritem na osnovi učenja optimizacije 
(TLBO). 
1 Introduction 
Optimization is an active area of research and it provides 
robust and viable solutions for complex real-world 
problems. A lot of efforts are needed to find optimal 
solution for these problems due to increase 
dimensionality, differentiability, multi-modality and 
rotation characteristics. Hence, a lot of research has been 
carried out in this direction to design a real-time 
numerical optimizer. This optimizer can provide more 
accurate, fast and computationally efficient optimization 
algorithms. Large numbers of algorithms have been 
developed by research community for solving many 
numerical optimization techniques. These algorithms can 
solve optimization problems efficiently and effectively. 
But, according to no free lunch theorem, there is no 
universal algorithm that can solve all optimization 
problems accurately. Over the past few decades, 
population based meta-heuristic algorithms have attained 
more popularity among research community. These 
algorithms have ability to turn itself according to 
problem domain and provide successful results for many 
complex problems. It is noticed that large numbers of 
optimization problems exist in the fields of engineering 
and science. These problems can be categorized as 
unimodal and multimodal optimization problems. 
Further, it can be characterized as unimodal separable 
and inseparable, and multimodal separable and 
inseparable. In literature, it is found that numbers of 
algorithms have been reported for solving these problems 
either maximizing or minimizing the objective function. 
Moreover, these algorithms are also adopted for solving 
real-life problems such as clustering, classification, 
scheduling, path planning, resource allocation, and many 
other problems. These algorithms are divided into two 
categories i.e. exact and approximation algorithms [1]. 
Exact algorithms find the optimal solution within 
bounded time, but having exponential computational 
time. The approximate algorithms provide better results 
in terms of time and solution using heuristics. Further, 
the meta-heuristic algorithms are also applied for solving 
the wide range of optimization problems. These 
algorithms are sub branch of approximate algorithms. In 
past decade, many meta-heuristic algorithms are 
developed for finding exact solution of optimization 
problems. Most of these are inspired through natural 
phenomena’s such as swarm behavior, insect’s 
characteristics, physics law and process etc. Some of are 
Simulated Annealing (SA) algorithm [2], Genetic 
Algorithm (GA) [3], Particle Swarm Optimization (PSO) 

66 Informatica 43 (2019) 65–75 Y. Kumar et al. 
 
[4], Ant Colony Optimization (ACO) [5], Harmony 
Search (HS) [6], Artificial Bee Colony (ABC) [7, 33], 
Firefly Algorithm (FA) [8], League Championship 
Algorithm (LCA) [9], Water Cycle Algorithm (WCA) 
[10], CSS [11, 12], MCSS[13, 14, 15], TLBO [16, 17, ], 
CSO[47,48] and Mine Blast Algorithm (MBA) [18].   
Recently, Rao et al., have developed teaching 
learning based optimization (TLBO) algorithm to solve 
the constrained and unconstrained optimization 
problems. This algorithm is inspired from class room 
based teaching methodology [19]. In short span of time, 
this algorithm become more popular among researchers 
and has been applied to solve variety of problems. A lot 
of optimization problems have been solved by using 
TLBO algorithm and provides better results in 
comparison to existing algorithms [20-24]. Still, there are 
several shortcomings that can affect the performance of 
TLBO algorithm such as quality of solution, stuck in 
local optima when solving global optimization problems, 
premature convergence, tradeoff between searching 
capability and local search ability. Hence, the aim of this 
work is to design an effective and efficient algorithm for 
addressing the convergence and quality of solution issues 
of TLBO algorithm. In order to overcome the 
aforementioned issues, this work investigates the 
capability of genetic crossover and mutation operators 
for improving the performance of TLBO algorithm. It is 
observed that proposed algorithm provides better results 
than traditional TLBO and other existing optimization 
algorithms.The rest of paper is organized as follows: the 
section 2 describes the related work on improvements in 
TLBO algorithm and its applicability in diverse fields. 
Section 3 introduces basic TLBO algorithm. The 
proposed genetic TLBO algorithm is illustrated in section 
4. Section 5 illustrates the simulation results of proposed 
TLBO algorithm using benchmark functions. The entire 
work is concluded into section 6 and future work 
reported in section 7. 
2 Related works 
This section describes the recent work reported on TLBO 
algorithm. Several studies have been published on the 
modifications of TLBO algorithm. Some of these are 
highlighted in this section. To make the effective tradeoff 
between exploration and exploitation capabilities, Rao et 
al. have developed an improved TLBO algorithm, called 
I-TLBO [25]. In this work, authors have introduced the 
concept of multiple teachers, adaptive teaching factor, 
self-motivated learning and tutorial training. The self 
learning and tutorial training methods can be acted as 
search methods. Further, to explore the local optimum 
solution in the hope of global optimum solution. The 
concept of multiple teachers is incorporated in TLBO 
algorithm to avoid premature convergence. Moreover, 
adaptive teaching factor is inculcated for fine tuning 
between exploration and exploitation capabilities. From 
results, it is seen that I-TLBO effectively overcome the 
aforementioned problems. Satapathy et al., have 
presented a new version of TLBO algorithm, called 
mTLBO for improving the convergence rate [26].  The 
proposed mTLBO algorithm is applied on global 
optimization problems for obtaining optimal solution. 
The proposed algorithm includes the concept of tutorial 
classes in learner phase to improve the outcomes of 
learners. The performance of mTLBO is compared with 
other state of art algorithm like PSO, DE, ABC and GA 
and it is observed that addition of tutorial class concept 
improves the results of TLBO algorithm. To enhance 
local search ability and quality of solutions, Haung et al., 
have incorporated levy flight based teaching learning 
process for TLBO algorithm [27]. The proposed 
algorithm is adopted to solve several engineering 
optimization problems especially industrial optimization 
problems. It is seen that the proposed algorithm 
outperforms than traditional TLBO algorithm. For 
improving the global performance of traditional TLBO 
algorithm, Zou et al., have developed an improved 
variant of TLBO algorithm based on learning experience 
[28]. Further, a copy operator is also integrated in TLBO 
algorithm and called it LETLBO. It is noticed that the 
learning experiences of learners are evaluated using two 
random possibilities. The performance of algorithm is 
tested on eighteen standard benchmark functions and 
compared with state of art algorithms. It is stated that 
above mentioned improvements significantly improve 
the global performance of TLBO algorithm. Ouyanget et 
al. have presented a new variant of TLBO algorithm to 
address global search and local optima issues, called GC-
TLBO [29]. In GC-TLBO, a global crossover operator is 
introduced for addressing global search issue. Whereas, 
the local optima issue is controlled using perturbed 
mechanism. The experimental results reveal that the 
proposed improvements make the TLBO algorithm more 
effective and significant one. Ghasemi et al. have 
developed gaussian bare bones teaching learning 
optimization algorithm, called GBTLBO for improving 
the quality of solutions [30]. The results stated that 
GBTLBO algorithm provides better performance than 
other algorithms being compared. To avoid the 
premature convergence and preserve the population 
diversity, Zou et al. have developed an improved TLBO 
algorithm based on dynamic group strategy [31]. 
Moreover, quantum behaved learning scheme is also 
inculcated into learner phase of TLBO algorithm to 
maintain population diversity. The feasibility of proposed 
algorithm is evaluated on eighteen benchmark functions. 
Simulation results stated that the proposed algorithm is 
one of effective and efficient algorithm for solving global 
optimization problems. Lim and Isa have presented a 
new algorithm by combining PSO and TLBO algorithms 
for solving global optimization algorithm, called 
TPLPSO [32]. The performance of TPLPSO is 
investigated on twenty benchmark functions and it is 
found that the TPLPSO exhibits better performance than 
other algorithm being compared. To identify the most 
relevant gene in the development of the breast cancer, 
Sahbeig et al. proposed a combination of TLBO and 
fuzzy adaptive PSO algorithm, called TLBO-PSO [36]. 
The performance of the proposed algorithm is evaluated 
using accuracy, sensitivity and specificity parameters. It 

New Variant of Teaching Learning Based... Informatica 43 (2019) 65–75 67 
is revealed that the proposed algorithm obtains higher 
accuracy rate i.e. 91.88 as compared to other algorithms.  
Kumar et al. have applied a hybrid TLBO-TS algorithm 
to deal with problem of simultaneous selection and 
scheduling of projects [37]. The proposed approach is 
tested on several datasets and compared with TLBO and 
TS algorithms. It is seen that combination of TLBO-TS 
algorithm provides faster convergence than TLBO and 
TS algorithms. Patel et al. have applied teaching-learning 
based optimization (TLBO) to design ultra-low reflective 
coating over a broad wavelength-band using multilayer 
thin-film structures for optoelectronic devices [38]. The 
results of TLBO algorithm are compared with GA using 
Wilcoxon singed ranked test. It is observed that TLBO 
algorithm gives more effective results than GA. To 
enhance the performance of original TLBO algorithm 
and make the balance between local and global searches, 
Ji et al. developed an improved version of TLBO 
algorithm, called I-TLBO [39]. In proposed algorithm, a 
self feedback phase is incorporated to enhance the 
performance of original TLBO algorithm. The 
effectiveness of proposed algorithm is tested on several 
combinatorial optimization problems. It is stated that the 
proposed improvements have significant impact on the 
performance of TLBO algorithm. To solve numerical 
structural analysis problems, Cheng and Prayogo 
presented fuzzy adaptive teaching learning based 
optimization algorithm, called FATLBO [40]. In 
proposed algorithm, three search strategies are included 
for improving searching capabilities. The performance of 
proposed algorithm is examined over five well known 
engineering structural problems. The results show that 
the proposed algorithm gives excellent and competitive 
performance. To analyze and predict the time series data, 
Das and Padhy desgined a hybrid model based on 
support vector machine (SVM) and TLBO [41]. The 
proposed model avoids user defined control parameters. 
The validity and efficacy of proposed model is evaluated 
on COMDEX commodity futures index. The results 
stated that proposed model is more effective and 
performs better than PSO-SVM and SVM models. 
Kankal and Uzlu adopted neural network with TLBO 
approach for modeling and forecasting long term electric 
energy demand in turkey [42]. In proposed approach, 
TLBO algorithm is used to optimize the parameters of 
neural network. The simulation results of ANN-TLBO 
approach is compared with ANN-BP and ANN-ABC 
models. It is revealed that ANN-TLBO approach 
provides efficient results than others. Kiziloz et al. 
applied multi-objective TLBO algorithm for feature 
subset selection in binary classifications problems [43]. 
The performance of the proposed algorithm is evaluated 
on well known benchmark problems and compared with 
large number of meta-heuristic algorithms such as GA, 
PSO, NSGA, TS and SS. It is seen that TLBO is one of 
the competitive algorithms for feature subset selection 
problem. Prakash et al. presented quasi-oppositional self-
learning teacher-learner-based-optimization (QOSL-
TLBO) for solving non-convex economic load dispatch 
(ELD) problem [44]. In this algorithm, self learning 
mechanism is incorporated in teacher and learner phases. 
The robustness of the proposed algorithm is evaluated on 
standard IEEE generator system. Further, the results are 
compared with well known algorithms. It is seen that the 
proposed algorithm achieves minimum total cost for all 
generations. Zheng et al. adopted TLBO to solve multi-
skill resource constrained project scheduling problem 
(MS-RCPSP) with make-span minimization criterion 
[45]. To make effective balance between exploration and 
exploitation processes, the concept of reinforcement 
learning is introduced in TLBO algorithm. From 
simulation results, it is stated that the computational cost 
of proposed algorithm is far better than compared 
algorithms.  Birashk et al. designed a cellular TLBO 
algorithm for dynamic multi objective optimization 
(DMOO) problems [46]. The performance of cellular 
TLBO algorithm is evaluated and compared with state of 
art algorithms using well known DMOO problems. It is 
observed that cellular TLBO algorithm gives superior 
results than other algorithms. 
3 Teaching learning based 
optimization (TLBO) algorithm    
TLBO is a population based meta-heuristic algorithm. 
Like other population based algorithms, the global 
solution is represented using population [19]. TLBO 
algorithm works on the concept of classroom learning 
paradigm. The teachers are available to teach and 
enhance the knowledge of learners. The aim of teacher is 
to improve the learning capability of learners. Further, a 
learner can also enhance its skills by acquiring the 
knowledge from other learners.   TLBO algorithm 
consists of two phases: Teacher phase and Learner phase. 
The detailed discussions on these phases are outlined as 
given below.  
Teacher Phase: The aim of this phase is to improve the 
learning skills of students such that results of class 
improve significantly and this can lead the mean result of 
class. In general, teacher can improve the result up to 
certain level. In practice, several constraints are 
responsible for results such teaching method, teachers 
capability, learners grasping ability, interaction of 
learners to others and knowledge of learners. In teacher 
phase, M denotes the learner’s knowledge mean and T 
describes any teacher in iteration. The main task of 
teacher is to enhance present knowledge of learners. To 
achieve the same, the present mean knowledge of 
learners i.e. M to move towards the teacher knowledge 
i.e. T and it can be described using equation 1.  
X
i,new
=X
i,old
+r∗(X
Teacher
−T
f
×X
mean
)       1 ) 
In equation 1, X
Teacher
 and X
mean
 represent the 
teacher and the mean of the knowledge of learner in i
th
 
iteration, T
f
 denotes the teaching factor, and r is a random 
number in the range of 0 and 1. The teaching factor is 
computed using equation 2. 
T
f
=round(1+rand(0,1))                                 (2) 
Learner Phase: The aim of the learner phase is to 
enhance the knowledge of learner from others. Hence, to 

68 Informatica 43 (2019) 65–75 Y. Kumar et al. 
 
improve learning ability, a learner can interact with other 
learners randomly.  In learner phase of TLBO algorithm, 
learners learn knowledge from others. This learning 
capability of learners can be expressed as follows.  
If i
th
 learner wants to interact with the k
th
 learner and 
the fitness of k
th
 learner is higher than i
th
 learner, then the 
position of i
th
 learner will be updated otherwise k
th
 
learner. This can be summarized in equations 3-4. 
X
i,new
=X
i,old
+r
i
×(X
k
−X
i
)                       (3) 
 Else 
X
i,new
=X
i,old
+r
i
×(X
i
−X
k
)                        (4) 
If the fitness of i
th
 learner is better than old position, 
then new position take over the old one otherwise not.  
4 Proposed TLBO algorithm 
This section describes the working of proposed TLBO 
algorithm for solving global optimization problems. In 
this work, two amendments are made in TLBO algorithm 
for improving search mechanism and convergence rate. 
Hence, to achieve the same, genetic crossover and 
mutation operators are incorporated into TLBO 
algorithm. The genetic mutation operator is adopted in 
teacher phase. Further, genetic crossover operator is used 
to enhance learning capability of a learner through 
different learners. These improvements are illustrated in 
Algorithm 1 and Algorithm 2.   
Algorithm 1: Teacher Phase of TLBO algorithm 
For d=1 to N 
For j =1 to D  
            DifferenceMean =r(T
mean
−T
f
×M
i
) 
           T
f
=round(1+rand(0,1)) 
IF (DifferenceMean <𝑟𝑎𝑛𝑑 () ) 
    Apply genetic mutation operator on T
mean
andM
i
 
    Compute Difference Mean and generate the new     
    mean of knowledge (X
i,new
) using equation 3. 
Else 
          X
i,new
=X
i,old
+DifferenceMea n
i
 
End 
End 
Accept X
i,new
if f(X
i,new
) is better than f(X
i,old
) 
End 
The aim of these operators is to maintain population 
diversity during teacher and learner phases, and further, 
overcome the chance of trapping in local optima. In 
learner phase, the knowledge of learner is not enhanced 
gradually, the fitness of leaner is compared with random 
function. If, it is less than random number, the crossover 
operator is applied to find other learner to enhance its 
skills and knowledge.  
Algorithm 2: Learner Phase of TLBO algorithm 
For i =1 to N 
Randomly pick two learners X
i
 and X
k
 such that i≠ j 
IF (𝐹 (X
i
)<𝐹 (X
k
)) 
IF (𝐹 (X
i
)<rand()) 
Apply genetic crossover operator on X
i
andX
k
 and 
generate the new position of learner X
k
 
End IF 
X
i,new
=X
i,old
+r
i
×(X
k
−X
i
) 
Else  
X
i,new
=X
i,old
+r
i
×(X
i
−X
k
) 
End 
Accept X
i,new
if f(X
i,new
) is better than f(X
i,old
) 
End 
The detailed description of proposed TLBO 
algorithm is given in Algorithm 3. The main steps of 
proposed algorithm are summarized as below and 
flowchart is illustrated in Fig. 1. 
 Algorithm 3: Algorithmic steps of TLBO algorithm 
Step 1: Initialize the number of learners (X), number  
               of dimension (D) and other algorithmic     
              parameters of TLBO algorithm.  
Step 2: Evaluate the positions of learners (X) and  
              compute the fitness function F(X).  
Step 3: Determine the best learner and it can be acted      
             as Teacher.  
Step 4: Compute  the mean of all learners (X) and  
              denoted as  Mean 
Step 5: While(stopping condition is not met) 
Step 6:  Apply teacher phase of TLBO algorithm  
               (Algorithm 1) 
Step 7: Apply learner phase of TLBO algorithm  
              (Algorithm 2) 
Step 8:  Update the Teacher and the mean 
Step 9:  End While 
Step 10: Obtain final optimal solution 
5 Results 
This section describes the results of proposed TLBO 
algorithm using benchmark test functions of CEC’14. 
These functions are combination of uni-modal and multi-
modal test functions that are highly trapped in local 
optima. The proposed algorithm is implemented in 
Matlab 2010 (a) environment using window based 
operating system having core i7 processor and 8 GB 
RAM.  The results of proposed algorithm are taken on 
average of 30 independent runs for each test functions. 
Mean and standard deviation are taken as performance 
parameters to compare the performance of proposed 
algorithm and other algorithms. The mean parameter 
demonstrates the efficiency of algorithms, whereas 
standard deviation parameter illustrates the robustness of 
algorithms. The experiment is performed using real 
dimension i.e.30 for all benchmark functions i.e. F 1-F 16. 
The performance of proposed algorithm is compared 

New Variant of Teaching Learning Based... Informatica 43 (2019) 65–75 69 
with other state of art algorithms like PSO, GA, BA, 
FPA, ABC, FA, BBO, HS and TLBO. Table 1-2 depict  
 
 
 
 
 
 
 
\ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 1: Flowchart of the proposed TLBO algorithm. 
 
Initialize number of learners (N), number of dimension (D) and other 
parameters of TLBO algorithm, termination condition 
Evaluate the positions of learners (X) and compute fitness function 
F(X). 
Compute the mean of all learners (X) and denoted as Mean 
 
Compute difference of dean for each dimension using   Mean
diff.
=
r(T
mean
−T
f
×M
i
) 
Determine the best learner and it can be acted as Teacher 
 
IF (DifferenceMean <𝑟𝑎𝑛𝑑 () ) 
 
Apply genetic mutation operator on T
mean
andM
i
 
Compute Difference Mean and generate the new  
Mean of knowledge (X
i,new
) using equation 3. 
Accept X
i,new
IFF(X
i,new
) is better than F(X
i,old
) 
Randomly pick two learners X
i
 and X
k
 such that i ≠ j 
IF (𝐹 (X
i
)<𝐹 (X
k
) &&𝐹 (X
i
)<
rand()) 
Apply genetic crossover operator on 
X
i
andX
k
 and generate the new position of 
learner X
k
. 
X
i,new
=X
i,old
+r
i
×(X
k
−X
i
) 
X
i,new
=X
i,old
+r
i
×(X
k
−X
i
) 
X
i,new
=X
i,old
+r
i
×(X
k
−X
i
) 
Accept X
i,new
IFF(X
i,new
) is better than F(X
i,old
) 
Is the termination condition satisfied? 
 
Obtained optimal solution 
 
Y 
Y 
N 
N 
N 
Y 

70 Informatica 43 (2019) 65–75 Y. Kumar et al. 
 
 
Table 1: List of test functions used for experimentation. 
No. 
Function 
Name 
Definition Parameter 
F 1 Sphere 
F
1
(x)=∑x
i
2
D
i=0
 
[-100, 100] 
F 2 Rosenbrock 
F
2
(x)=∑100(x
i+1
−x
i
2
)
2
D
i=1
+(x
i
−1)
2
 
[-30,30] 
F 3 Rastrigin 
F
3
(x)=∑(x
i
2
−10cos(2πx
i
)+10)
D
i=1
 
[-5.12, 5.12] 
F 4 Griewank 
F
4
(x)=
1
4000
∑x
i
2
D
i=1
−∏cos(
x
i
√i
)+1
D
i=1
 
[-600, 600] 
 
F 5 
 
Ackley 
F
5
(x)=20+e−20exp
(
 
−0.2√
1
D
∑x
i
2
D
i=1
)
 
−exp (
1
D
∑cos(2πx
i
)
D
i=1
) 
 
[-32, 32] 
F 6 Step 
F
6
(x)=∑(x
i
+0.5)
2
D
i=0
 
[-100, 100] 
F 7 Schwefel 
F
8
(x)=418.9828D−∑(x
i
sin(√|x
i
|))
D
i=1
 
[-500,  500] 
F 8 Schaffer 
F
9
(x)=0.5+
sin
2
(x
i
2
−x
i
2
)−0.5
[1+0.001(x
i
2
−x
i
2
)]
2
 
[-100, 100] 
F 9 Powell 
F
10
(x)=          ∑(x
4i−3
+10x
4i−2
)
2
+5(x
4i−1
−10x
4i
)
2
D 4 ⁄
i=1
+(x
4i−2
+10x
4i−1
)
4
+10(x
4i−3
+10x
4i
)
4
 
[-4, 5] 
F 10 Zakharov’s F
10
(x)=∑(x
i
)
2
D
i=0
+(
1
2
∑ix
i
D
i=0
)
2
+(
1
2
∑ix
i
D
i=0
)
4
 [-5, 10] 
F 11 Michalewicz F
11
(x)=∑Sinx
1
(sin(
ix
i
2
π
⁄
))
20 D
i=1
 [0, π] 
F 12 Quartic F
12
(x)=∑ix
i
4
+rand(0,1)
D
i=1
 [-1.28, 1.28] 
Table 2: Benchmark test functions from CEC’14 suite. 
Function No. Functions Search Range Global Optimum 
F 13 Rotated High Conditioned Elliptic Function [-100, 100] 100 
F 14 Rotated Bent Cigar Function [-100, 100] 200 
F 15 Rotated Discus Function [-100, 100] 300 
F 16 Shifted and Rotated Rosenbrock’s Function  [-100, 100] 400 

New Variant of Teaching Learning Based... Informatica 43 (2019) 65–75 71 
 
Table 3: Results of proposed TLBO and other existing algorithm with test functions F 1-F 6. 
Algorithm Parameter 
Function 
F1 F2 F3 F4 F5 F6 
PSO 
average 
3.00E-04 2.59E+01 3.58E-01 1.05E-01 5.21E-02 4.00E-04 
std. 
1.50E-03 1.63E-01 6.98E-01 4.62E-02 4.06E-02 2.60E-03 
GA 
average 
8.38E-01 4.53E+01 1.00E+00 8.61E-01 7.93E-01 7.87E-01 
std. 
5.14E-01 2.16E-01 6.92E-01 6.48E-02 3.22E-01 5.64E-01 
BA 
average 
1.00E+00 3.90E+01 4.27E-01 8.21E-01 1.00E+00 1.00E+00 
std. 
1.00E+00 1.56E+01 1.00E+00 8.14E-02 1.00E+00 1.00E+00 
FPA 
average 
4.28E-01 3.69E+01 5.92E-01 1.00E+00 3.17E-01 2.76E-01 
std. 
8.26E-02 1.76E+01 3.54E-01 2.09E-02 7.36E-02 1.97E-01 
ABC 
average 6.00E-04 2.35E+01 3.29E-01 1.51E-02 9.63E-02 1.46E-02 
std. 1.00E-04 1.36E+01 4.25E-02 1.24E-02 7.86E-02 3.50E-03 
FA 
average 3.79E-02 1.72E+02 2.29E+01 1.05E-01 2.05E+00 3.11E-01 
std. 5.35E-02 1.30E+02 7.14E+00 5.45E-02 3.57E-01 1.18E-01 
BBO 
average 2.40E-03 5.91E+01 7.08E-02 1.89E-01 1.01E-01 1.71E+00 
std. 4.56E-04 1.27E+00 5.56E-02 3.36E-02 5.13E-02 3.71E-01 
HS 
average 5.22E-04 1.90E+02 1.69E+01 1.60E-01 1.09E+00 4.37E+00 
std. 3.29E-05 5.16E+01 2.66E+00 5.34E-02 1.36E-01 9.83E-01 
TLBO 
average 0 26.6567 1.87E−12  0 3.55E−15  2.74E−09  
std. 0 2.94E−01 6.66E−12 0 8.32E−17 5.36E−09 
Proposed 
TLBO 
average 0 23.9648 1.983 E-12 0 3.39 E−15  2.56E−11 
std. 0 3.26E−01 3.68E-12 0 6.53E−16 4.98E−13 
Table 4: Results of proposed TLBO and other existing algorithm using test functions F 5-F 8. 
Algorithm Parameter 
Functions 
F7 F8 F9 F10 F11 F12 
PSO 
average 9.82E+03 3.86E+02 5.13E-01 6.14E-10 -2. 96847 4.36E-03 
std. 6. 412E+02 1.13E+02 3.46E-03 1.35E-11 6.52E-01 5.71E-04 
GA 
average 4.62E+04 8.30E+02 5.40E-01 5.50E-10 -5.86E+00 2.35E-01 
std. 1.59E+03 3.93E+02 7.31E-03 7.62E-10 9.16E-01 6.71E-02 
BA 
average 2.76E+02 1.14E+02 8.25E-02 9.83E-14 -4.54E+00 4.13E-03 
std. 1.12E+02 8.61E+01 1.83E-02 4.86E-14 7.16E-01 7.87E-03 
FPA 
average 3.53E+02 8.62E+01 7.92E-02 5.22E-14 -3.86E+00 3.86E-03 
std. 1.26E+03 8.07E+01 3.82E-02 4.80E-14 8.35E-01 1.55E-03 
ABC 
average 2.79E+04 2.35E+01 3.29E-01 1.51E-02 9.63E-02 1.46E-02 
std. 2.10E+01 1.36E+01 4.25E-02 1.24E-02 7.86E-02 3.50E-03 
FA 
average 3.79E+02 1.72E+02 2.29E+01 1.05E-01 2.05E+00 3.11E-01 
std. 5.35E+01 1.30E+02 7.14E+00 5.45E-02 3.57E-01 1.18E-01 
BBO 
average 1.38E+02 7.50E-01 2.46E+02 1.30E-03 -3.92E+00 2.00E-05 
std. 1.14E+02 3.86E-02 6.47E+01 1.85E-03 1.31E+00 3.14E-06 
HS 
average 4.59E+02 1.53E-01 2.83E+02 1.03E-11 -4.32E+00 8.44E-04 
std. 5.86E+01 3.10E-02 1.06E+02 1.31E-12 1.06E+00 2.21E-05 
TLBO 
average 124.1484 0.0066 0.0066 4.64E-14 -4.352678 3.25E-04 
std. 2.60E+02 4.50E-03 4.50E-03 2.34E-14 1.44E-02 1.59E-04 
Proposed 
TLBO 
average 104.526 0.0058 0.0052 8.35E-16 -3.73415 5.14E-03 
std. 4.13E+01 3.66E-03 4.48E-03 1.42E-16 2.43E−2 2.86E-03 
 
 

72 Informatica 43 (2019) 65–75 Y. Kumar et al. 
 
Table 5: Performance comparison of proposed algorithm and other meta-heuristic algorithms with extended  
                  benchmark functions of CEC’14. 
Algorithm Parameter 
Functions 
F13 F14 F15 F16 
PSO 
Average 9.78E+04 1.69E+03 5.73E+02 4.04E+02 
Std 2.82E+03 7.32E+02 1.92E+02 1.46E+01 
GA 
Average 9.02E+05 7.34E+03 1.18E+03 2.13E+03 
Std 3.16E+08 3.18E+03 2.68E+02 1.67E+03 
BA 
Average 3.46E+03 9.84E+02 3.74E+02 4.27E+02 
Std 1.73E+02 3.11E+02 1.38E+02 2.43E+01 
FPA 
Average 4.41E+03 7.63E+02 3.48E+02 4.19E+02 
Std 2.26E+02 2.73E+02 100% 1.78E+01 
ABC 
average 1.02E+03 5.35E+02 2.14E+02 3.52E+02 
std. 7.94E-05 1.47E+02 5.64E+01 1.24E+02 
FA 
average 3.79E+03 4.87E+02 2.30E+02 3.75E+02 
std. 9.91E+01 1.49E+02 7.14E+01 6.85E+01 
BBO 
average 1.73E+03 4.38E+02 4.09E+02 3.90E+02 
std. 4.36E+01 9.13E+01 5.88E+01 4.73E+01 
HS 
average 9.23E+02 3.19E+02 2.68E+02 2.16E+02 
std. 1.33E+02 2.66E+01 6.69E+01 5.35E+01 
SFLP 
average 1.09E+03 2.98E+02 3.28E+02 2.57E+02 
std. 1.08E+02 3.15E+01 5.32E+01 3.79E+01 
TLBO 
Average 3.82E+03 7.42E+02 3.26E+02 4.08E+02 
Std 2.58E+02 2.42E+02 1.42E+02 1.96E+01 
Proposed TLBO 
Average 3.27E+03 5.24E+02 3.04E+02 3.41E+02 
Std 1.92E+02 2.16E+02 1.98E+02 7.05E+01 
the various unimodal and multi-modal test functions 
taken from CEC, 14.  Table 1 shows the normal 
benchmark function of the CEC’14, whereas Table 2 
contains the some extended benchmark function of 
CEC’14.  
Table 3 demonstrates the results of proposed 
algorithm and other algorithm like PSO, GA, BA, FPA, 
ABC, FA, BBO, HS and TLBO using test functions F 1-
F 4.These functions are widely adopted to investigate the 
performance of newly developed algorithms. It is 
observed from the results that the proposed TLBO 
algorithm achieves global optimum value for rosenbrock 
and rastrigin functions within specified number of 
iterations. It is seen that the performance of proposed 
algorithm and TLBO algorithm is same for sphere and 
griewank functions. Further on the analysis of standard 
deviation parameter, it is observed thatproposed TLBO 
algorithm obtains minimum standard deviation value in 
comparison to other algorithms being compared. Its 
reveals that the proposed algorithm provides more stable 
result for solving benchmark test functions.  
Table 4 illustrates the experimental results of 
proposed algorithm and other algorithm for standard 
benchmark functions F 7-F 12. It is seen that proposed 
algorithm obtains global optimum values i.e. minimum 
values among all other compared algorithm using most 
of functions. It is observed that significant difference 
occurs between the performance of the proposed 
algorithm and rest of algorithms being compared. On the 
analysis of standard deviation parameter, it is stated that 
again the proposed algorithm gets minimum value for 
standard deviation parameter among all other algorithms. 
This indicates that the proposed algorithm provides more 
stable results for solving these functions. From tables 3-
4, it is stated that the proposed algorithm is an effective 
and efficient algorithm for solving bench mark test 
function and this algorithms also provides more stable 
results in comparison to other algorithms being 
compared. Table 5 demonstrates the comparison of the 
proposed TLBO algorithm and other meta-heuristic 
algorithms with the extended benchmark functions (F 13-
F 16) of the CEC’14.  To show the effectiveness of the 
proposed algorithm four well known benchmark 
functions are taken from the extended benchmarks 
functions set of CEC’14. It is observed that the proposed 
algorithm obtains better optimum value as compared to 
other algorithms being compared. Hence, it can be 
concluded that the proposed algorithm is one of the 
efficient algorithm for solving global optimization 
problems. 
Figs. 2-3 show the convergence pattern i.e. cost 
function of proposed TLBO and original TLBO 
algorithm using rastrigin and rosenbrock functions. From 
these, it is also stated that the convergence of the TLBO 
algorithm is significantly improved.From Fig. 2, it is 
seen that the proposed algorithm requires less number of 
iterations to converge than TLBO algorithm. Further, it is 
also observed that proposed algorithm obtains minimum 

New Variant of Teaching Learning Based... Informatica 43 (2019) 65–75 73 
cost than original TLBO algorithm. On analysis of Fig. 3, 
it is noted that the proposed algorithm converges fast 
than the original TLBO algorithm. It is also noticed that 
there is the significant difference between the initial 
solution obtained through proposed algorithm and 
original TLBO algorithm. Finally, it is concluded that the 
proposed modifications not only improve the 
performance of TLBO algorithm, but also enhance the 
convergence rate of algorithm.  
 
 
 
 
 
 
 
Figure 2 shows the convergence of TLBO and Proposed TLBO 
algorithm for rastrigin function 
 
 
 
 
 
 
 
 
 
 
Figure 3: shows the convergence of TLBO and Proposed TLBO 
algorithm for rosenbrock function 
6 Conclusion 
In this work, a new variant of TLBO algorithm is 
presented for solving the global optimization problems. 
For improving the performance of TLBO algorithm, two 
modifications are incorporated into teacher and learner 
phases of TLBO algorithm. These modifications are 
genetic crossover and mutation operators and the aim of 
these operators to generate diverse population and to 
improve searching ability and convergence rate of TLBO 
algorithm. The genetic crossover operator is applied in 
learner phase for determining the good learner from the 
set of learners. The aim of genetic mutation operator is to 
minimize the knowledge gap between teacher and 
learners. So, this operator is applied in teacher phase of 
TLBO algorithm to generate diverse population. The 
performance of the proposed algorithm is evaluated using 
a set of benchmark test functions using mean and SD 
parameters and the results are compared with some of 
state of art algorithm available in literature. From 
experimental study, it is seen that the performance of the 
proposed algorithm is better than other algorithms being 
compared. It is also observed that proposed algorithm 
provides state of art results with most of benchmark test 
functions.   
7  Future work 
In future research work, the proposed TLBO algorithm is 
adopted for solving single objective and multi-objective 
constrained optimization problems. Further, 
neighborhood search mechanism is introduced to explore 
good candidate solution and also for improving 
convergence rate. In teaching learning process, selection 
of teacher also impact on the performance of learners. In 
future work, the effect of number of teachers will be 
evaluated on the fitness value of objective function. 
Apart from above, the capability of TLBO algorithm will 
explore in different research problems such as 
classification, feature selection, document clustering, 
parameter optimization of ANN and SVM techniques 
etc.  
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