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Implementation of Teaching Learning Based Optimization

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  • Last Updated : 10 Dec, 2021
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The previous article Teaching Learning Based Optimization (TLBO) talked about the inspiration of teaching learning-based optimization, it’s mathematical modeling and algorithms. In this article we will implement Teaching learning-based optimization (TLBO) for two fitness functions 1) Rastrigin function    2) Sphere function.  The algorithm will run for a predefined number of maximum iterations and will try to find the minimum value of these fitness functions.

Fitness function

1) Rastrigin function

Rastrigin function is a non-convex function and is often used as a performance test problem for optimization algorithms.

function equation: 

f(x_1 \cdots x_n) = 10n + \sum_{i=1}^n (x_i^2 -10cos(2\pi x_i))

\text{minimum at }f(0, \cdots, 0) = 0

Fig1: Rastrigin function for 2 variables

For an optimization algorithm, rastrigin function is a very challenging one. Its complex behavior causes optimization algorithms to often be stuck at local minima. Having a lot of cosine oscillations on the plane introduces the complex behavior to this function.

2) Sphere function

Sphere function is a standard function for evaluating the performance of an optimization algorithm.

function equation:

f(x_1 \cdots x_n) = \sum_{i=1}^n x_i^2

\text{minimum at }f(0, \cdots, 0) = 0

Fig 2: Sphere function for 2 variables

Choice of hyper-parameters

Parameters of problem:

  • Number of dimensions (d) = 3
  • Lower bound (minx) = -10.0
  • Upper bound (maxx) = 10.0

Hyperparameters of the algorithm:  

  • Number of particles (N) = 50
  • Maximum number of iterations (max_iter) = 100

Inputs

  • Fitness function
  • Problem parameters ( mentioned above)
  • Population size (N) and Maximum number of iterations  (max_iter)
  • Algorithm Specific hyperparameters (None in teaching-learning based optimization)

Pseudocode

The pseudocode of the teaching-learning-based optimization is already described in the previous article. Data structures to store students as well as a data structure to store data specific to the individual students were also discussed.

Implementation

Python3




# python implementation of Teaching learning based optimization (TLBO)
# minimizing rastrigin and sphere function
 
import random
import math    # cos() for Rastrigin
import copy    # array-copying convenience
import sys     # max float
 
 
#-------fitness functions---------
 
# rastrigin function
def fitness_rastrigin(position):
  fitness_value = 0.0
  for i in range(len(position)):
    xi = position[i]
    fitness_value += (xi * xi) - (10 * math.cos(2 * math.pi * xi)) + 10
  return fitness_value
 
#sphere function
def fitness_sphere(position):
    fitness_value = 0.0
    for i in range(len(position)):
        xi = position[i]
        fitness_value += (xi*xi);
    return fitness_value;
#-------------------------
 
#Student class
class Student:
  def __init__(self, fitness, dim, minx, maxx, seed):
    self.rnd = random.Random(seed)
 
    # a list of size dim
    # with 0.0 as value of all the elements
    self.position = [0.0 for i in range(dim)]
 
    # loop dim times and randomly select value of decision var
    # value should be in between minx and maxx
    for i in range(dim):
      self.position[i] = ((maxx - minx) *
        self.rnd.random() + minx)
 
    # compute the fitness of student
    self.fitness = fitness(self.position)
 
 
# Teaching learning based optimization
def tlbo(fitness, max_iter, n, dim, minx, maxx):
  rnd = random.Random(0)
 
  # create n random students
  classroom = [Student(fitness, dim, minx, maxx, i) for i in range(n)]
 
  # compute the value of best_position and best_fitness in the classroom
  Xbest = [0.0 for i in range(dim)]
  Fbest = sys.float_info.max       
 
  for i in range(n): # check each Student
    if classroom[i].fitness < Fbest:
      Fbest = classroom[i].fitness
      Xbest = copy.copy(classroom[i].position)
 
  # main loop of tlbo
  Iter = 0
  while Iter < max_iter:
     
    # after every 10 iterations
    # print iteration number and best fitness value so far
    if Iter % 10 == 0 and Iter > 1:
      print("Iter = " + str(Iter) + " best fitness = %.3f" % Fbest)
 
    # for each student of classroom
    for i in range(n):
 
      ### Teaching phase of ith student
 
      # compute the mean of all the students in the class
      Xmean = [0.0 for i in range(dim)]
      for k in range(n):
          for j in range(dim):
              Xmean[j]+= classroom[k].position[j]
       
      for j in range(dim):
          Xmean[j]/= n;
       
      # initialize new solution
      Xnew = [0.0 for i in range(dim)]
 
      # teaching factor (TF)
      # either 1 or 2 ( randomly chosen)
      TF = random.randint(1, 3)
 
      # best student of the class is teacher
      Xteacher = Xbest
 
      # compute new solution
      for j in range(dim):
          Xnew[j] = classroom[i].position[j] + rnd.random()*(Xteacher[j] - TF*Xmean[j])
       
      # if Xnew < minx OR Xnew > maxx
      # then clip it
      for j in range(dim):
          Xnew[j] = max(Xnew[j], minx)
          Xnew[j] = min(Xnew[j], maxx)
       
      # compute fitness of new solution
      fnew = fitness(Xnew)
 
      # if new solution is better than old
      # replace old with new solution
      if(fnew < classroom[i].fitness):
          classroom[i].position = Xnew
          classroom[i].fitness = fnew
        
      # update best student
      if(fnew < Fbest):
          Fbest = fnew
          Xbest = Xnew
 
 
 
      ### learning phase of ith student
 
      # randomly choose a solution from classroom
      # chosen solution should not be ith student
      p = random.randint(0, n-1)
      while(p==i):
          p = random.randint(0, n-1)
       
      # partner solution
      Xpartner = classroom[p]
 
      Xnew = [0.0 for i in range(dim)]
      if(classroom[i].fitness < Xpartner.fitness):
          for j in range(dim):
              Xnew[j] = classroom[i].position[j] + rnd.random()*(classroom[i].position[j] - Xpartner.position[j])
      else:
          for j in range(dim):
              Xnew[j] = classroom[i].position[j] - rnd.random()*(classroom[i].position[j] - Xpartner.position[j])
 
      # if Xnew < minx OR Xnew > maxx
      # then clip it
      for j in range(dim):
          Xnew[j] = max(Xnew[j], minx)
          Xnew[j] = min(Xnew[j], maxx)
       
      # compute fitness of new solution
      fnew = fitness(Xnew)
 
      # if new solution is better than old
      # replace old with new solution
      if(fnew < classroom[i].fitness):
          classroom[i].position = Xnew
          classroom[i].fitness = fnew
        
      # update best student
      if(fnew < Fbest):
          Fbest = fnew
          Xbest = Xnew
 
    Iter += 1
  # end-while
 
  # return best student from classroom
  return Xbest
# end pso
 
 
#----------------------------
# Driver code for rastrigin function
 
print("\nBegin  teaching learning based optimization on rastrigin function\n")
dim = 3
fitness = fitness_rastrigin
 
 
print("Goal is to minimize Rastrigin's function in " + str(dim) + " variables")
print("Function has known min = 0.0 at (", end="")
for i in range(dim-1):
  print("0, ", end="")
print("0)")
 
num_particles = 50
max_iter = 100
 
print("Setting num_particles = " + str(num_particles))
print("Setting max_iter    = " + str(max_iter))
print("\nStarting TLBO algorithm\n")
 
 
 
best_position = tlbo(fitness, max_iter, num_particles, dim, -10.0, 10.0)
 
print("\nTLBO completed\n")
print("\nBest Student found:")
print(["%.6f"%best_position[k] for k in range(dim)])
fitness_value = fitness(best_position)
print("fitness of best Student = %.6f" % fitness_value)
 
print("\nEnd TLBO for rastrigin function\n")
 
 
print()
print()
 
 
# Driver code for Sphere function
print("\nBegin teaching learning based optimization on sphere function\n")
dim = 3
fitness = fitness_sphere
 
 
print("Goal is to minimize sphere function in " + str(dim) + " variables")
print("Function has known min = 0.0 at (", end="")
for i in range(dim-1):
  print("0, ", end="")
print("0)")
 
num_particles = 50
max_iter = 100
 
print("Setting num_particles = " + str(num_particles))
print("Setting max_iter    = " + str(max_iter))
print("\nStarting TLBO algorithm\n")
 
 
 
best_position = tlbo(fitness, max_iter, num_particles, dim, -10.0, 10.0)
 
print("\nTLBO completed\n")
print("\nBest Student found:")
print(["%.6f"%best_position[k] for k in range(dim)])
fitness_value = fitness(best_position)
print("fitness of best Student = %.6f" % fitness_value)
 
print("\nEnd TLBO for sphere function\n")

Output

Begin  teaching learning based optimization on rastrigin function

Goal is to minimize Rastrigin's function in 3 variables
Function has known min = 0.0 at (0, 0, 0)
Setting num_particles = 50
Setting max_iter    = 100

Starting TLBO algorithm

Iter = 10 best fitness = 3.662
Iter = 20 best fitness = 0.389
Iter = 30 best fitness = 0.389
Iter = 40 best fitness = 0.389
Iter = 50 best fitness = 0.200
Iter = 60 best fitness = 0.132
Iter = 70 best fitness = 0.051
Iter = 80 best fitness = 0.003
Iter = 90 best fitness = 0.001

TLBO completed


Best Student found:
['0.000593', '-0.000040', '-0.000461']
fitness of best Student = 0.000112

End TLBO for rastrigin function




Begin teaching learning based optimization on sphere function

Goal is to minimize sphere function in 3 variables
Function has known min = 0.0 at (0, 0, 0)
Setting num_particles = 50
Setting max_iter    = 100

Starting TLBO algorithm

Iter = 10 best fitness = 0.009
Iter = 20 best fitness = 0.000
Iter = 30 best fitness = 0.000
Iter = 40 best fitness = 0.000
Iter = 50 best fitness = 0.000
Iter = 60 best fitness = 0.000
Iter = 70 best fitness = 0.000
Iter = 80 best fitness = 0.000
Iter = 90 best fitness = 0.000

TLBO completed


Best Student found:
['0.000000', '-0.000000', '-0.000000']
fitness of best Student = 0.000000

End TLBO for sphere function

References

Research paper: R. V. Rao, V. J. Savsani & J. Balic (2012) Teaching–learning-based optimization algorithm for unconstrained and constrained real-parameter optimization problems, Engineering Optimization, 44:12, 1447-1462, DOI: 10.1080/0305215X.2011.652103

Inspiration of the implementation: https://www.mathworks.com/matlabcentral/fileexchange/65628-teaching-learning-based-optimization#:~:text=Teaching%20Learning%20Based%20Optimization%20is,teacher%20and%20the%20student%20phase.


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