混沌映射优化算法代码

混沌映射优化算法代码

一、混沌映射算法简介

混沌映射算法是一种基于混沌理论的随机优化算法，其基本思想是通过混沌系统的非线性特性，将搜索空间中的每个解点映射到一个新的解点，从而实现全局搜索。混沌映射算法具有较强的全局搜索能力和快速收敛速度，在实际应用中得到了广泛的应用。

二、混沌映射优化算法代码实现

以下是使用Python语言编写的混沌映射优化算法代码实现：

```python

import random

import math

# 定义Lorenz函数

def lorenz(x, y, z, s=10, r=28, b=2.667):

dx = s * (y - x)

dy = x * (r - z) - y

dz = x * y - b * z

return dx, dy, dz

# 定义Chen函数

def chen(x, y, z, a=35.0, b=3.0):

dx = a * (y - x)

dy = x * (b - z) - y

dz = x * y - 2.5 * z

return dx, dy, dz

# 定义Rossler函数

def rossler(x, y, z, a=0.2, b=0.2, c=5.7):

dx = -(y + z)

dy = x + a * y

dz = b + z * (x - c)

return dx, dy, dz

# 定义混沌映射函数

def chaos_map(x0, y0, z0, func, n=100):

x_list = [x0]

y_list = [y0]

z_list = [z0]

for i in range(n):

dx, dy, dz = func(x_list[-1], y_list[-1], z_list[-1])

x_next = x_list[-1] + 0.01 * dx

y_next = y_list[-1] + 0.01 * dy

z_next = z_list[-1] + 0.01 * dz

x_list.append(x_next)

y_list.append(y_next)

z_list.append(z_next)

return x_list[-1]

# 定义混沌映射优化算法函数

def chaos_optimize(func, dim=2, max_iter=1000):

# 初始化参数

a = 10 ** 8

b = 10 ** (-8)

c1 = 2.05

c2 = 2.05

w_max = 0.9

w_min = 0.4

# 初始化粒子群和速度矩阵

swarm_size = dim * 20

swarm_pos = [[random.uniform(-10, 10) for j in range(dim)] for i in range(swarm_size)]

v_max = (10 - (-10)) / 2

swarm_velo = [[random.uniform(-v_max, v_max) for j in range(dim)] for i in range(swarm_size)]

swarm_best_pos = [swarm_pos[i] for i in range(swarm_size)] swarm_best_fit = [chaos_map(*swarm_pos[i], func) for i in range(swarm_size)]

global_best_pos = swarm_best_pos[0]

global_best_fit = chaos_map(*global_best_pos, func)

# 开始迭代

for t in range(max_iter):

w = w_max - (w_max - w_min) * t / max_iter

for i in range(swarm_size):

# 更新速度和位置

for j in range(dim):

r1, r2 = random.uniform(0, 1), random.uniform(0, 1) swarm_velo[i][j] = w * swarm_velo[i][j] + c1 * r1 * (swarm_best_pos[i][j] - swarm_pos[i][j]) + c2 * r2 *

(global_best_pos[j] - swarm_pos[i][j])

if swarm_velo[i][j] > v_max:

swarm_velo[i][j] = v_max

elif swarm_velo[i][j] < -v_max:

swarm_velo[i][j] = -v_max

swarm_pos[i][j] += swarm_velo[i][j]

# 限制粒子位置范围，避免越界

for j in range(dim):

if swarm_pos[i][j] > 10:

swarm_pos[i][j] = 10

elif swarm_pos[i][j] < -10:

swarm_pos[i][j] = -10

# 计算适应度值，更新最优解和全局最优解 fit = chaos_map(*swarm_pos[i], func) if fit < swarm_best_fit[i]:

swarm_best_pos[i] = swarm_pos[i] swarm_best_fit[i] = fit

if fit < global_best_fit:

global_best_pos = swarm_pos[i]

global_best_fit = fit

return global_best_pos, global_best_fit

```