Implementation of Teaching Learning Based Optimization

Introduction

Teaching Learning Based Optimization (TLBO) is based on the relationship between a teacher and the learners in a class. In a particular class, a teacher imparts knowledge to the students through his/her hard work. The students or learners then interact with each other among themselves and improve their knowledge.

Let us explore more about Teacher Learning Based Optimization through this article.

What is TLBO?

Let us consider a population p (particularly a class) and the number of learners l in the class. There may be decisive variables (subjects from which learners gain knowledge) for the optimization problem. Two modes of learning can happen−

• Through the teacher (Teaching phase)

• Through the interaction of the learners among themselves (Learning phase)

We are concerned about the result for the learner which will be the fitness value.

TLBO optimization functions

There are two types of functions involved in the optimization algorithm. They are

• The Sphere function − For evaluating the performance

It is written mathematically as,

$$\mathrm{f(x_{1,}x_{2},.........x_{n})=\sum ^{n}_{i=0} \:\:x^{2}_{i}}$$

min at f(0,..0) = 0

• The Rastrigin function − Non-convex function used as a test function It is given mathematically as,

$$\mathrm{f(x_{1,}x_{2},.........x_{n})=10+}\mathrm{\sum_{i=1}^{n} (x^{2}_{i}-10\cos\:\:\cos(2\prod x_{i})}$$

Implementation of TLBO Algorithm in Python

Example

import numpy as np
from pyMetaheuristic.algorithm import teaching_learning_based_optimization
from pyMetaheuristic.utils import graphs

def eas_opt(varval = [0, 0]):
   x_1, x_2 = varval
   fval = -np.cos(x_1) * np.cos(x_2) * np.exp(-(x_1 - np.pi) ** 2 - (x_2 - np.pi) ** 2)
   return fval
plt_params = {
   'min_values': (-6, -6),
   'max_values': (6, 6),
   'step': (0.2, 0.2),
   'solution': [],
   'proj_view': '3D',
   'view': 'notebook'
}
graphs.plot_single_function(target_function = eas_opt, **plt_params)

params = {
   'population_size': 15,
   'min_values': (-5, -5),
   'max_values': (5, 5),
   'generations': 500,
   'verbose': True
}
tlbo = teaching_learning_based_optimization(target_function = eas_opt, **params)

vars = tlbo[:-1]
min = tlbo[ -1]
print('Variables: ', np.around(vars, 5) , ' Minimum Value Found: ', round(min, 5) )

plt_params = {
   'min_values': (-6, -6),
   'max_values': (6, 6),
   'step': (0.2, 0.2),
   'solution': [vars],
   'proj_view': '3D',
   'view': 'notebook'
}
graphs.plot_single_function(target_function = eas_opt, **plt_params)

Output

Generation = 0 f(x) = -0.5748727344288006
Generation = 1 f(x) = -0.7555913129284719
Generation = 2 f(x) = -0.9219320357862593
Generation = 3 f(x) = -0.9644524112155972
Generation = 4 f(x) = -0.9809361915349301
Generation = 5 f(x) = -0.991863434885587
Generation = 6 f(x) = -0.9984949247685845
Generation = 7 f(x) = -0.9991563851570532
Generation = 8 f(x) = -0.9997584334443873
Generation = 9 f(x) = -0.9997584334443873
Generation = 10 f(x) = -0.9998450580252695
Generation = 11 f(x) = -0.9998982502404465
Generation = 12 f(x) = -0.999961847330126
Generation = 13 f(x) = -0.9999810734164969
Generation = 14 f(x) = -0.9999930426674921
Generation = 15 f(x) = -0.9999995055655798
Generation = 16 f(x) = -0.9999999410594664
Generation = 17 f(x) = -0.9999999410594664
Generation = 18 f(x) = -0.9999999877205884
Generation = 19 f(x) = -0.9999999877205884
Generation = 20 f(x) = -0.9999999931826284
-------------------------------------------------------------
-------------------------------------------------------
Generation = 500 f(x) = -0.9999999991966855
Variables: [3.14161 3.14158] Minimum Value Found: -1.0

Advantages of Teaching Learning-Based Optimization

• TLBO algorithm does not require any parameter for its working except two parameters which are the size of the population and iteration count.

• It is more accurate and it does not need derivative,

• Follows the complete path to generate the solution

Disadvantages of Teaching Learning-Based Optimization

• It is a time-consuming method

• A huge amount of space is required for the Optimization algorithm to run

Conclusion

Teaching Learning Based Optimization is a population-based algorithm that heavily relies on the learning relationship between teacher and learners and also among learners themselves.