PSO算法算是寻优算法中比较简单的一种，其大概思想是：
现在我们计算：
的极大值，每一个变量的取值范围都是(1，25)。
Python代码为：
# -*- coding: utf-8 -*-"""@Time ： /9/13 10:08@Author ：KI @File ：pso.py@Motto：Hungry And Humble"""import mathimport randomimport numpy as npimport matplotlib.pyplot as pltimport pylab as mplmpl.rcParams['font.sans-serif'] = ['SimHei']class PSO:def __init__(self, dimension, time, size, low, up, v_low, v_high):# 初始化self.dimension = dimension # 变量个数self.time = time # 迭代的代数self.size = size # 种群大小self.bound = [] # 变量的约束范围self.bound.append(low)self.bound.append(up)self.v_low = v_lowself.v_high = v_highself.x = np.zeros((self.size, self.dimension)) # 所有粒子的位置self.v = np.zeros((self.size, self.dimension)) # 所有粒子的速度self.p_best = np.zeros((self.size, self.dimension)) # 每个粒子最优的位置self.g_best = np.zeros((1, self.dimension))[0] # 全局最优的位置# 初始化第0代初始全局最优解temp = -1000000for i in range(self.size):for j in range(self.dimension):self.x[i][j] = random.uniform(self.bound[0][j], self.bound[1][j])self.v[i][j] = random.uniform(self.v_low, self.v_high)self.p_best[i] = self.x[i] # 储存最优的个体fit = self.fitness(self.p_best[i])# 做出修改if fit > temp:self.g_best = self.p_best[i]temp = fitdef fitness(self, x):"""个体适应值计算"""x1 = x[0]x2 = x[1]x3 = x[2]x4 = x[3]x5 = x[4]y = math.floor((x2 * np.exp(x1) + x3 * np.sin(x2) + x4 + x5) * 100) / 100# print(y)return ydef update(self, size):c1 = 2.0 # 学习因子c2 = 2.0w = 0.8 # 自身权重因子for i in range(size):# 更新速度(核心公式)self.v[i] = w * self.v[i] + c1 * random.uniform(0, 1) * (self.p_best[i] - self.x[i]) + c2 * random.uniform(0, 1) * (self.g_best - self.x[i])# 速度限制for j in range(self.dimension):if self.v[i][j] < self.v_low:self.v[i][j] = self.v_lowif self.v[i][j] > self.v_high:self.v[i][j] = self.v_high# 更新位置self.x[i] = self.x[i] + self.v[i]# 位置限制for j in range(self.dimension):if self.x[i][j] < self.bound[0][j]:self.x[i][j] = self.bound[0][j]if self.x[i][j] > self.bound[1][j]:self.x[i][j] = self.bound[1][j]# 更新p_best和g_bestif self.fitness(self.x[i]) > self.fitness(self.p_best[i]):self.p_best[i] = self.x[i]if self.fitness(self.x[i]) > self.fitness(self.g_best):self.g_best = self.x[i]def pso(self):best = []self.final_best = np.array([1, 2, 3, 4, 5])for gen in range(self.time):self.update(self.size)if self.fitness(self.g_best) > self.fitness(self.final_best):self.final_best = self.g_best.copy()print('当前最佳位置：{}'.format(self.final_best))temp = self.fitness(self.final_best)print('当前的最佳适应度：{}'.format(temp))best.append(temp)t = [i for i in range(self.time)]plt.figure()plt.plot(t, best, color='red', marker='.', ms=15)plt.rcParams['axes.unicode_minus'] = Falseplt.margins(0)plt.xlabel(u"迭代次数") # X轴标签plt.ylabel(u"适应度") # Y轴标签plt.title(u"迭代过程") # 标题plt.show()if __name__ == '__main__':time = 50size = 100dimension = 5v_low = -1v_high = 1low = [1, 1, 1, 1, 1]up = [25, 25, 25, 25, 25]pso = PSO(dimension, time, size, low, up, v_low, v_high)pso.pso()
运行结果：
收敛过程：
可以看出，不到10次就收敛了。
matlab代码：
z=@(x)-(x(2)*exp(x(1))+x(3)*sin(x(2))+x(4)*x(5));x0=[1;1;1;1;1];[x,feval]=fmincon(z,x0,[],[],[],[],[1;1;1;1;1],[25;25;25;25;25])
运行结果：
x =25.000025.000013.14001.00021.0002feval =-1.8001e+12
如果想要利用上述代码求极小值，可以有以下两种办法：
将fitness函数中的返回值改为-y，此时如果求出的值为z，那么函数的极小值就为-z。将第34行代码处的temp改为一个很大的值；将第42、83、85以及93行代码处的">“改为”<"。
