Teachinglearningbased optimization (TLBO) algorithm is proposed in recent years that simulates the teachinglearning phenomenon of a classroom to effectively solve global optimization of multidimensional, linear, and nonlinear problems over continuous spaces. In this paper, an improved teachinglearningbased optimization algorithm is presented, which is called nonlinear inertia weighted teachinglearningbased optimization (NIWTLBO) algorithm. This algorithm introduces a nonlinear inertia weighted factor into the basic TLBO to control the memory rate of learners and uses a dynamic inertia weighted factor to replace the original random number in teacher phase and learner phase. The proposed algorithm is tested on a number of benchmark functions, and its performance comparisons are provided against the basic TLBO and some other wellknown optimization algorithms. The experiment results show that the proposed algorithm has a faster convergence rate and better performance than the basic TLBO and some other algorithms as well.
Most of the swarm intelligent optimization studies and applications have been focused on natureinspired algorithms. Numerous populationbased and natureinspired optimization algorithms have been presented, such as the Ant Colony Optimization (ACO), Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Artificial Bee Colony (ABC), and Differential Evolution (DE). These optimization algorithms are based on different natural phenomena. ACO works based on the behavior of ant colony searching foods from the source to a destination [
Recently, Rao et al. [
In this paper, we propose a novel improved TLBO, which is called nonlinear inertia weighted TLBO (NIWTLBO). A nonlinear inertia weighted factor is introduced into the basic TLBO to control the memory rate of learners, and another dynamic inertia weighted factor is used to replace the original random number in teacher phase and learner phase. So, as a result, the NIWTLBO has faster convergence speed and higher calculation accuracy for most of these optimization problems than the basic TLBO. The performance of NIWTLBO for solving global function optimization problems is compared with basic TLBO and other optimization algorithms. The analysis results show that the proposed algorithm outperforms most of the other algorithms investigated in this paper.
The rest of this paper is organized as follows. Section
The basic TLBO algorithm mainly consists of two parts, namely, the teacher phase and the learner phase. In teacher phase, the students can learn from the teacher to make their knowledge level closer to the teacher’s. In learner phase, the students can learn from the interaction of other individuals to increase their knowledge. In the TLBO algorithm, a group of learners is considered as a population. Each learner is analogous to an individual of the evolutionary algorithm. The different subjects offered to the learners are considered as design variables of the optimization problem. A learner’s result is analogous to the fitness value of the objective function for optimization problems. The best learner (i.e., the best solution in the entire population) is considered as the teacher. The best solution is the best value of the objective function of the given optimization problem. The design variables are the input parameters of the objective function.
The process of basic TLBO algorithm is described below.
The notations used in TLBO are described as follows:
MAXITER is maximum number of allowable iterations.
The population
In this phase, the algorithm simulates the students learning from teachers. A good teacher can bring his or her learners up to his or her level in terms of knowledge. Hence, the mean result of a class may increase from a low level to the teacher’s level. But, in fact, it is impossible that the mean result of a class reaches the teacher’s level. Because of the individual differences and the forgetfulness of memory, the learners cannot gain all the knowledge of the teacher. A teacher can increase the mean result of a class to a certain value which depends on the capability of the whole class.
Let
In every iteration,
In learner phase, the algorithm simulates the learning of the learners through interaction among themselves. A learner interacts randomly with other learners to increase his or her knowledge. If a learner has more knowledge than others, the other learners can quickly achieve new knowledge by learning from him or her to increase their level. In this learning process, two learners are randomly selected. One is
In each iteration of the TLBO, it is necessary to detect the repeated solution to the entire population. If there is a repeated solution, it needs to remove the repeated solution and generate a new individual randomly. Hence, it will expand the diversity of populations and avoid premature convergence of the algorithm. After a number of generations, the knowledge level of the entire class is smoothly approximated to a point that is considered the teacher, and the algorithm converges to a solution.
The algorithm is terminated after MAXITER iterations. The details of TLBO algorithm can be referred to in literature [
The basic TLBO algorithm is based on teachinglearning phenomenon of a classroom. In the teacher phase, the teacher tries to shift the mean of the learners towards himself or herself by teaching. In the learner phase, learners improve their knowledge by interaction among themselves. In the process of the teachinglearning, learners improve their level by accumulating knowledge. In other words, they learn new knowledge based on existing knowledge. In the real world, the teacher tends to wish that his or her students should achieve the knowledge equal to him in fast possible time. But it is impossible for a student because of his or her forgetting characteristics. In fact, a student usually forgets a part of existing knowledge due to the physiological phenomena of the brain. With increasing the iteration numbers of learning, more and more existing knowledge will be remembered. As the learning curve presented by Ebbinghaus, it describes how fast learning knowledge is in learning process. The sharpest increase occurs after the first try and then gradually evens out, meaning that less and less new knowledge is retained after each repetition. Like the forgetting curve, the learning curve is exponential. So it is necessary to add a memory weight to the existing knowledge of the student for simulating this learning scenario. According to this phenomenon, a nonlinear inertia weighted factor
Accordingly, to meet the characteristic of memory to conform to the learning curve, the
The memory rate curve.
In the teacher phase, in order to obtain a new set of better learners, the difference between the existing mean result and the corresponding result of the teacher is added to the existing population of learners. Similarly, to obtain a new set of better learners in the learner phase, two learners are selected randomly, and the difference between their result of each corresponding subject is added to the existing learner. As (
Equation (
With the nonlinear inertia weighted factor and the dynamic inertia weighted factor, the new set of improved learners can be expressed by using equation in the teacher phase
In this section, NIWTLBO is applied on several benchmark functions to evaluate its performance with different dimensions and search space, comparing with the basic TLBO algorithm and with other optimization algorithms available in the literature. All tests are evaluated on a laptop having Intel core i5 2.67 GHz processor and 2 GB RAM. The algorithm is coded using the MATLAB programming language and run in MATLAB 2012a environment. This section provides the results obtained by the NIWTLBO algorithm compared to the basic TLBO and other intelligent optimization algorithms. The details of the 24 benchmark functions with different characteristics like unimodality/multimodality and separability/nonseparability are shown in Table
List of benchmark functions which have been used in experiments.
Number  Function  C 

Range  Formulation 



Sphere  US  30  [−100, 100] 





SumSquares  US  30  [−100, 100] 





Tablet  US  30  [−100, 100] 





Quartic  US  30  [−1.28 1.28] 





Schwefel 1.2  UN  30  [−100, 100] 





Schwefel 2.22  UN  30  [−10, 10] 





Schwefel 2.21  UN  30  [−100, 100] 





Zakharov  UN  30  [−5, 10] 





Rosenbrock  US  30  [−4, 4] 





Schaffer  MN  2  [−10, 10] 





Dropwave  MN  2  [−2, 2] 





Bohachevsky1  MN  2  [−100, 100] 





Bohachevsky2  MN  2  [−100, 100] 





Bohachevsky3  MN  2  [−100, 100] 





SixHump Camel Back  MN  2  [−5, 5] 





Branin  MS  2  [−5, 15] 





GoldsteinPrice  MN  2  [−2, 2] 





Ackley  MN  30  [−32, 32] 





Rastrigin  MN  30  [−5.12, 5.12] 





Griewank  MN  30  [−600, 600] 





Schwefel 2.26  MN  30  [−500, 500] 





Multimod  MN  30  [−10, 10] 





Noncontinuous Rastrigin  MS  30  [−5.12, 5.12] 





Weierstrass  MS  30  [−0.5, 0.5] 


C: characteristic;
Performance comparisons of PSO, ABC, DE, TLBO, and NIWTLBO in terms of fitness value. Population size: 40;
Number  Function 

PSO  ABC  DE  TLBO  NIWTLBO  


Sphere  0  Mean  8.99 
9.91 
7.15 
1.85 
0 
Std.  5.92 
5.36 
1.06 
0  0  



SumSquares  0  Mean  1.11 
7.81 
9.06 
1.57 
0 
Std.  2.49 
1.32 
3.07 
0  0  



Tablet  0  Mean  3.68 
9.54 
2.40 
7.66 
0 
Std.  1.64 
1.78 
1.87 
0  0  



Quartic  0  Mean  5.84 
1.52 
4.03 
2.07 
2.03 
Std.  3.83 
4.18 
1.29 
5.26 
3.52  



Schwefel 1.2  0  Mean  2.47 
8.82 
2.21 
1.52 
0 
Std.  1.48 
1.28 
5.21 
2.97 
0  



Schwefel 2.22  0  Mean  5.16 
2.01 
4.31 
1.79 
4.45 
Std.  6.94 
1.08 
1.04 
1.21 
0  



Schwefel 2.21  0  Mean  1.21 
5.49 
1.21 
8.31 
2.40 
Std.  6.02 
1.38 
2.81 
4.05 
0  



Zakharov  0  Mean  1.62 
2.59 
5.84 
5.95 
1.06 
Std.  6.33 
2.84 
7.01 
5.22 
0  



Rosenbrock  0  Mean  3.01 
1.04 
2.43 
1.29 
1.83 
Std.  2.57 
2.57 
4.61 
5.28 
6.91  



Schaffer  −1  Mean  −1  −1  −1  −1  −1 
Std.  0  0  0  0  0  



Dropwave  −1  Mean  −1  −1  −1  −1  −1 
Std.  0  0  0  0  0  



Bohachevsky1  0  Mean  0  0  0  0  0 
Std.  0  0  0  0  0  



Bohachevsky2  0  Mean  0  0  0  0  0 
Std.  0  0  0  0  0  



Bohachevsky3  0  Mean  0  8.46 
0  0  0 
Std.  0  2.95 
0  0  0  



SixHump Camel Back  −1.03163  Mean  −1.03163  −1.03163  −1.03163  −1.03163  −1.03163 
Std.  0  0  0  0  0  



Branin  0.398  Mean  0.3979  0.3979  0.3979  0.3979  0.3979 
Std.  0  0  0  0  0  



GoldsteinPrice  3  Mean  3  3  3  3  3 
Std.  8.11 
4.32 
1.36 
6.78 
6.56  



Ackley  0  Mean  1.18 
2.82 
2.49 
4.44 
8.66 
Std.  3.85 
3.06 
6.07 
0  0  



Rastrigin  0  Mean  1.08 
1.29 
9.33 
6.93 
0 
Std.  2.80 
2.57 
9.43 
5.92 
0  



Griewank  0  Mean  6.77 
7.10 
0  0  0 
Std.  9.29 
9.56 
0  0  0  



Schwefel 2.26  −837.9658  Mean  −8789.43  −12561.79  −11312.51  −9178.59  −8324.302 
Std.  4.63 
1.96 
1.58 
7.97 
1.71  



Multimod  0  Mean  8.69 
8.52 
4.66 
0  0 
Std.  1.74 
8.34 
0  0  0  



Noncontinuous Rastrigin  0  Mean  1.83 
1.99 
6.94 
1.55 
0 
Std.  3.15 
1.83 
9.13 
2.65 
0  



Weierstrass  0  Mean  6.27 
1.12 
1.38 
0  0 
Std.  2.03 
7.73 
6.07 
0  0 
Convergence comparisons in terms of number of fitness evaluations. Population size: 40;
Number  Function  PSO  ABC  DE  TLBO  NIWTLBO  


Sphere  Mean  80,000  80,000  80,000  80,000  29,514 
Std.  0  0  0  0  1.02  



SumSquares  Mean  80,000  80,000  80,000  80,000  29,628 
Std.  0  0  0  0  1.23  



Tablet  Mean  80,000  80,000  80,000  80,000  29,562 
Std.  0  0  0  0  1.52  



Quartic  Mean  80,000  80,000  80,000  80,000  80,000 
Std.  0  0  0  0  0  



Schwefel 1.2  Mean  80,000  80,000  80,000  80,000  39,416 
Std.  0  0  0  0  1.09  



Schwefel 2.22  Mean  80,000  80,000  80,000  80,000  80,000 
Std.  0  0  0  0  0  



Schwefel 2.21  Mean  80,000  80,000  80,000  80,000  80,000 
Std.  0  0  0  0  0  



Zakharov  Mean  80,000  80,000  80,000  80,000  80,000 
Std.  0  0  0  0  0  



Rosenbrock  Mean  80,000  80,000  80,000  80,000  80,000 
Std.  0  0  0  0  0  



Schaffer  Mean  12,432  43,636  8,686  9,688  3,029 
Std.  3.38 
3.03 
2.06 
2.29 
3.03  



Dropwave  Mean  11,394  13,824  5,490  3,021  812 
Std.  3.26 
1.09 
1.53 
1.22 
3.32  



Bohachevsky1  Mean  9,532  3,263  3,992  2,266  842 
Std.  2.21 
7.52 
8.74 
3.23 
2.01  



Bohachevsky2  Mean  9,578  4,717  4,245  2,568  952 
Std.  1.33 
9.27 
1.17 
2.05 
2.56  



Bohachevsky3  Mean  9,792  80,000  5,376  2,875  965 
Std.  2.52 
0  1.26 
1.03 
3.12  



SixHump  Mean  1,997  1,372  1,781  712  2,560 
Camel Back  Std.  1.38 
1.17 
1.36 
5.93 
9.07  



Branin  Mean  1,851  1,813  1,891  1,086  2,172 
Std.  1.17 
1.23 
1.04 
1.06 
1.23  



GoldsteinPrice  Mean  2,018  1,857  1,765  1,228  2,865 
Std.  1.25 
1.48 
2.08 
6.85 
1.42  



Ackley  Mean  80,000  80,000  80,000  80,000  80,000 
Std.  0  0  0  0  0  



Rastrigin  Mean  80,000  80,000  80,000  80,000  1,436 
Std.  0  0  0  0  3.02  



Griewank  Mean  80,000  80,000  53,032  12,064  1,284 
Std.  0  0  6.16 
9.37 
2.54  



Schwefel 2.26  Mean  80,000  80,000  80,000  80,000  80,000 
Std.  0  0  0  0  0  



Multimod  Mean  80,000  80,000  80,000  28,304  1,427 
Std.  0  0  0  1.05 
5.16  



Noncontinuous Rastrigin  Mean  80,000  80,000  80,000  80,000  1,324 
Std.  0  0  0  0  1.22  



Weierstrass  Mean  80,000  80,000  80,000  12,712  2,044 
Std.  0  0  0  1.19 
1.21 
Number  Function  PSO  ABC  DE  TLBO  Number  Function  PSO  ABC  DE  TLBO 


Sphere  +  +  +  + 

Bohachevsky2  NA  NA  NA  NA 

SumSquares  +  +  +  + 

Bohachevsky3  NA  +  NA  NA 

Tablet  +  +  +  + 

SixHump Camel Back  NA  NA  NA  NA 

Quartic  +  +  +  ⋅ 

Branin  NA  NA  NA  NA 

Schwefel 1.2  +  +  +  + 

GoldsteinPrice  NA  NA  NA  NA 

Schwefel 2.22  +  +  +  + 

Ackley  +  +  +  + 

Schwefel 2.21  +  +  +  + 

Rastrigin  +  +  +  + 

Zakharov  +  +  +  + 

Griewank  +  +  NA  NA 

Rosenbrock  ⋅  ⋅  ⋅  ⋅ 

Schwefel 2.26  +  +  +  + 

Schaffer  NA  NA  NA  NA 

Multimod  +  +  NA  NA 

Dropwave  NA  NA  NA  NA 

Noncontinuous Rastrigin  +  +  +  + 

Bohachevsky1  NA  NA  NA  NA 

Weierstrass  +  +  +  NA 
“+” indicates that
This experiment is aimed at identifying the performance of the NIWTLBO algorithm to achieve the global optimum value comparing with PSO, ABC, DE, and the basic TLBO. To be fair, each algorithm uses the same values of common control parameters such as population size and maximum evaluation number. Population size is 40 and the maximum fitness function evaluation number is 80,000 for all benchmark functions in Table
In this section, each benchmark function is independently experimented 30 times with PSO, ABC, DE, TLBO, and NIWTLBO. Each algorithm was terminated after running for 80,000FEs or when it reached the global minimum value before completely running for 80,000FEs. The mean and standard deviation of fitness value obtained through 30 experiments on each benchmark function are recorded in Table
The comparative results of each benchmark function for PSO, ABC, DE, and TLBO are presented in Table
It is observed from the results in Table
In this section, the experiment is aimed at analysing the ability of the NIWTLBO algorithm to obtain the global optimum value comparing with other variant PSO algorithms such as PSO
Comparative results of TLBO and NIWTLBO with other PSO algorithms. Population size: 10;
Number  Function  PSOw  PSOcf  CPSOH  CLPSO  TLBO  NIWTLBO  


Sphere  Mean  7.96 
9.84 
4.98 
5.15 
0  0 
Std.  3.56 
4.21 
1.00 
2.16 
0  0  



Rosenbrock  Mean  3.08 
6.98 
1.53 
2.46 
1.72 
1.69 
Std.  7.69 
1.46 
1.70 
1.70 
6.62 
7.18  



Ackley  Mean  1.58 
9.18 
1.49 
4.32 
3.55 
8.58 
Std.  1.60 
1.01 
6.97 
2.55 
8.32 
6.37  



Rastrigin  Mean  5.82 
1.25 
2.12 
0  6.77 
0 
Std.  2.96 
5.17 
1.33 
0  3.68 
0  



Griewank  Mean  9.69 
1.19 
4.07 
4.56 
0  0 
Std.  5.01 
7.11 
2.80 
4.81 
0  0  



Schwefel 2.26  Mean  3.20 
9.87 
2.13 
0 
2.94 
2.67 
Std.  1.85 
2.76 
1.41 
0  2.68 
1.92  



Noncontinuous Rastrigin  Mean  4.05 
1.20 
2.00 
0  2.65 
0 
Std.  2.58 
4.99 
4.10 
0  1.23 
0  



Weierstrass  Mean  2.28 
6.69 
1.07 
0  2.42 
0 
Std.  7.04 
7.17 
1.67 
0  1.38 
0 
“†” mark indicates that NIWTLBO is statistically better than the corresponding algorithm.
“‡” mark indicates that NIWTLBO is statistically worse than the corresponding algorithm.
It is observed from the results in Table
In this section, the experiment is conducted to identify the performance of the NIWTLBO algorithm to achieve the global optimum value versus CABC [
Comparative results of TLBO and NIWTLBO with other variants of ABC algorithms. Population size: 20;
Number  Function  CABC  GABC  RABC  IABC  TLBO  NIWTLBO  


Sphere  Mean  2.3 
3.6 
9.1 
5.34 
0  0 
FEs: 1.5 × 10^{5}  Std.  1.7 
5.7 
2.1 
0  0  0  



Schwefel 1.2  Mean  8.4 
4.3 
2.9 
1.78 
0  0 
FEs: 5.0 × 10^{5}  Std.  9.1 
8.0 
1.5 
2.21 
0  0  



Schwefel 2.22  Mean  3.5 
4.8 
3.2 
8.82 
0  0 
FEs: 2.0 × 10^{5}  Std.  4.8 
1.4 
2.0 
3.49 
0  0  



Schwefel 2.21  Mean  6.1 
3.6 
2.8 
4.98 
0  0 
FEs: 5.0 × 10^{5}  Std.  5.7 
7.6 
1.7 
8.59 
0  0  



Ackley  Mean  1.0 
1.8 
9.6 
3.87 
4.48 
8.65 
FEs: 5.0 × 10^{4}  Std.  2.4 
7.7 
8.3 
8.52 
2.16 
2.38  



Rastrigin  Mean  1.3 
1.5 
2.3 
0  6.36 
0 
FEs: 1.0 × 10^{5}  Std.  2.7 
2.7 
5.1 
0  4.78 
0  



Griewank  Mean  1.2 
6.0 
8.7 
0  0  0 
FEs: 5.0 × 10^{5}  Std.  4.6 
7.7 
2.1 
0  0  0 
“†” mark indicates that NIWTLBO is statistically better than the corresponding algorithm.
From Table
In this section, the experiment is carried out for comparing the performance of the NIWTLBO algorithm with SaDE, jDE, and JADE algorithms on 7 benchmark functions which are described in Table
Comparative results of TLBO and NIWTLBO with other variants of DE algorithms. Population size: 20;
Number  Function  SaDE  jDE  JADE  TLBO  NIWTLBO  


Sphere  Mean  4.5 
2.5 
1.8 
0  0 
FEs: 1.5 × 10^{5}  Std.  1.9 
3.5 
8.4 
0  0  



Schwefel 1.2  Mean  9.0 
5.2 
5.7 
0  0 
FEs: 5.0 × 10^{5}  Std.  5.4 
1.1 
2.7 
0  0  



Schwefel 2.22  Mean  1.9 
1.5 
1.8 
0  0 
FEs: 2.0 × 10^{5}  Std.  1.1 
1.0 
8.8 
0  0  



Schwefel 2.21  Mean  7.4 
1.4 
8.2 
0  0 
FEs: 5.0 × 10^{5}  Std.  1.82 
1.0 
4.0 
0  0  



Ackley  Mean  2.7 
3.5 
8.2 
4.48 
8.65 
FEs: 5.0 × 10^{4}  Std.  5.1 
1.0 
6.9 
2.16 
2.38  



Rastrigin  Mean  1.2 
1.5 
1.0 
6.36 
0 
FEs: 1.0 × 10^{5}  Std.  6.5 
2.0 
6.0 
4.78 
0  



Griewank  Mean  7.8 
1.9 
9.9 
0  0 
FEs: 5.0 × 10^{5}  Std.  1.2 
5.8 
6.0 
0  0 
“†” mark indicates that NIWTLBO is statistically better than the corresponding algorithm.
It can be seen that NIWTLBO performs much better than these variants of DE on all the benchmark functions in Table
In this section, we analyse the convergence of NIWTLBO and TLBO algorithms with different dimensions. Two unimodal functions and two multimodal functions have been tested with dimensions 2, 10, 50, and 100. In this work, evolutionary generation is employed to evaluate the performance of NIWTLBO and TLBO algorithms. The population size is set as 40 and the number of evolutionary generations is set as 2000. The experiment results of NIWTLBO and TLBO algorithms for 2, 10, 50, and 100 dimensional functions over 30 independent runs are listed in Table
Comparative results of TLBO and NIWTLBO with different dimensions. Population size: 40; generations: 2000.
Function 

Unimodal  Multimodal  

Sphere  Schwefel 2.22  Rastrigin  Griewank  
TLBO  2  0  0  0  0 
10  0  1.05 
5.78 
0  
50  2.09 
4.64 
2.48 
0  
100  4.13 
8.91 
4.71 
0  


NIWTLBO  2  0  0  0  0 
10  0  2.50 
0  0  
50  0  4.43 
0  0  
100  0  4.09 
0  0 
Figures
Convergence of TLBO and NIWTLBO algorithms for unimodal function.
Sphere
Schwefel 2.22
Convergence of TLBO and NIWTLBO algorithms for multimodal function.
Rastrigin
Griewank
In order to show the advantages and disadvantages of the NIWTLBO, we make experiments to compare the performance of the NIWTLBO algorithm with some other variants of TLBO in this section. The variants of TLBO include WTLBO [
Comparative results of NIWTLBO and different variants of TLBO algorithms. Population size: 20;
Number  Function  WTLBO  ITLBO22  ITLBO23  ITLBO (NT = 4)  NIWTLBO  


Sphere  MNFE  365  386  482  372  281 
Succ%  100  100  100  100  100  



Schwefel 2.22  MNFE  442  428  563  416  324 
Succ%  100  100  100  100  100  



Rosenbrock  MNFE  1643  704  726  684  1606 
Succ%  65  100  100  100  100  



Bohachevsky3  MNFE  468  432  516  398  364 
Succ%  100  100  100  100  100  



Branin  MNFE  41010  649  763  367  1922 
Succ%  28  100  100  100  100  



Ackley  MNFE  564  508  682  491  443 
Succ%  100  100  100  100  100  



Rastrigin  MNFE  4608  651  1406  632  481 
Succ%  100  100  100  100  100  



Griewank  MNFE  18246  1208  2248  1024  965 
Succ%  85  100  81  100  100  



Weierstrass  MNFE  19642  1243  2325  1186  1042 
Succ%  78  100  93  100  100 
It is observed from Table
In this paper, we propose the NIWTLBO algorithm which introduced a nonlinear inertia weighted factor into the basic TLBO to control the memory rate of learners and used a dynamic inertia weighted factor to replace the original random number in teacher phase and learner phase. The proposed algorithm is implemented on 24 benchmark functions having different characteristics to evaluate its performance which is compared with the basic TLBO and some other stateoftheart optimization algorithms available in the literature. Furthermore, the comparisons between the NIWTLBO and other algorithms mentioned are also reported.
The experiment results have shown the satisfactory performance of the NIWTLBO algorithm for solving global optimization problems. The NIWTLBO algorithm not only enhances the local searching ability of TLBO but also improves the global performance. Moreover, the NIWTLBO algorithm can increase the convergence speed and enhance the ability of the TLBO to escape from local optima.
In future work, the NIWTLBO algorithm will be extended to handle more complex functions and solve constrained/multiobjective optimization problems. Furthermore, we will also open up a new way to improve the diversity of TLBO using a hybrid method, so as to utilize the advantages of other intelligent algorithms to further improve the global performance of TLBO.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The present study was partially supported by the National Natural Science Foundation of China (10872160). The authors thank Rao R. V. for providing the source code of the basic TLBO algorithm and Dervis Karaboga for providing the source code of the ABC algorithm.