一、算法介绍

算法步骤：

1. 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
2. 找到当前种群下的最优个体 best 和最差个体 worst
3. 遍历所有个体，根据公式(1)更新个体参数
   
   讯享网

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

4. 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
5. 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

讯享网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

讯享网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：

讯享网变量值为： [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：

讯享网 # 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