教学学习优化的实施

介绍

教学学习优化(TLBO)基于教师和学生之间的关系。在一个特定的班级中，教师通过他/她的辛勤工作向学生传授知识。学生们之间相互交流并提高他们的知识。

让我们通过这篇文章深入了解教学学习优化。

什么是TLBO

让我们考虑一个群体p(特别是一个班级)和班级中的学生数量l。对于优化问题可能存在决策变量(学生获取知识的主题)。学习可以通过以下两种方式进行：

通过教师(教学阶段)
通过学生之间的互动(学习阶段)

我们关注的是学生的结果，即适应度值。

TLBO优化函数

优化算法中涉及两种类型的函数。

球函数 -用于评估性能

数学表达式如下：

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

最小值为f(0,…0) = 0

Rastrigin函数 -非凸函数用作测试函数，数学表达式如下：

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

在Python中实现TLBO算法

示例

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)

输出

教学学习优化的实施

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