一、算法介绍
算法步骤:
- 首先初始化种群个体数量,确定每个个体长度以及终止判据
- 找到当前种群下的最优个体 best 和最差个体 worst
- 遍历所有个体,根据公式(1)更新个体参数
其中,i,j,k分别代表迭代代数,个体的某变量,种群中某个体。该公式是Jaya算法的核心
- 判断更新后的个体是否优于更新前的个体,若是,则更新个体,否则保留原个体到下一代
- 判断当前最优个体是否满足终止判据,若是则结束程序,否则遍历步骤2-4
二、 案例实现(一)
2.1 目标函数
第一步:导入模块
import numpy as np
# Jaya
from pyMetaheuristic.algorithm import victory
from pyMetaheuristic.utils import graphs
第二步:目标函数设置
def easom(variables_values = [0, 0]):
x1, x2 = variables_values
func_value = -np.cos(x1) * np.cos(x2) * np.exp(-(x1 - np.pi) ** 2 - (x2 - np.pi) ** 2)
return func_value
plot_parameters = {
'min_values': (-5, -5),
'max_values': (5, 5),
'step': (0.1, 0.1),
'solution': [],
'proj_view': '3D',
'view': 'notebook'
}
graphs.plot_single_function(target_function = easom, **plot_parameters)
如下:
2.2 算法实现
第三步:设置算法参数
# jaya - Parameters
parameters = {
# 该参数50左右
'size': 50,
'min_values': (-5, -5),
'max_values': (5, 5),
# 迭代次数
'iterations': 500,
'verbose': True
}
第四步:执行算法
jy = victory(target_function = easom, **parameters)
第五步:获取算法最优解
variables = jy[:-1]
minimum = jy[ -1]
print('变量值为: ', np.around(variables, 4) , ' 最小值为: ', round(minimum, 4) )
如下:
变量值为: [3.1258 3.1804] 最小值为: -0.9974
第六步:可视化最优值
三、案例(二)
我们换一个目标函数,以五维球形函数的最优化计算为例子.
def easom(variables_values):
x = variables_values
func_value = y=sum(x**2 for x in variables_values)
return func_value
后续参数类似。。不再重复演示。
四、额外补充
4.1 封装代码
如果你希望改进该算法模块,可以研究修改以下代码:
# Required Libraries
import numpy as np
import random
import os
############################################################################
# Function
def target_function():
return
############################################################################
# Function: Initialize Variables
def initial_position(size = 5, min_values = [-5,-5], max_values = [5,5], target_function = target_function):
position = np.zeros((size, len(min_values)+1))
for i in range(0, size):
for j in range(0, len(min_values)):
position[i,j] = random.uniform(min_values[j], max_values[j])
position[i,-1] = target_function(position[i,0:position.shape[1]-1])
return position
# Function: Updtade Position by Fitness
def update_bw_positions(position, best_position, worst_position):
for i in range(0, position.shape[0]):
if (position[i,-1] < best_position[-1]):
best_position = np.copy(position[i, :])
if (position[i,-1] > worst_position[-1]):
worst_position = np.copy(position[i, :])
return best_position, worst_position
# Function: Search
def update_position(position, best_position, worst_position, min_values = [-5,-5], max_values = [5,5], target_function = target_function):
candidate = np.copy(position[0, :])
for i in range(0, position.shape[0]):
for j in range(0, len(min_values)):
a = int.from_bytes(os.urandom(8), byteorder = "big") / ((1 << 64) - 1)
b = int.from_bytes(os.urandom(8), byteorder = "big") / ((1 << 64) - 1)
candidate[j] = np.clip(position[i, j] + a * (best_position[j] - abs(position[i, j])) - b * ( worst_position[j] - abs(position[i, j])), min_values[j], max_values[j] )
candidate[-1] = target_function(candidate[:-1])
if (candidate[-1] < position[i,-1]):
position[i,:] = np.copy(candidate)
return position
############################################################################
# Jaya Function
def victory(size = 5, min_values = [-5,-5], max_values = [5,5], iterations = 50, target_function = target_function, verbose = True):
count = 0
position = initial_position(size, min_values, max_values, target_function)
best_position = np.copy(position[0, :])
best_position[-1] = float('+inf')
worst_position = np.copy(position[0, :])
worst_position[-1] = 0
while (count <= iterations):
if (verbose == True):
print('Iteration = ', count, ' f(x) = ', best_position[-1])
position = update_position(position, best_position, worst_position, min_values, max_values, target_function)
best_position, worst_position = update_bw_positions(position, best_position, worst_position)
count = count + 1
return best_position
4.2 算法论文
http://www.growingscience.com/ijiec/Vol7/IJIEC_2015_32.pdf