### 改进粒子群优化
算法简介
改进粒子群优化
算法（Improved Particle Swarm Optimization, IPSO）旨在克服标准粒子群优化
算法中的局限性，如早熟收敛
和局部最优等问题。通过引入新的机制或与其他优化方法相结合，IPSO能够更有效地探索解空间
并提高全局搜索能力。
#### 遗传粒子群优化
算法 (GPSO)
遗传粒子群优化
算法融合了遗传
算法的思想，利用交叉、变异操作增强种群多样性，防止过早陷入局部极值点[^1]。这种混合策略不仅保持了原有PSO快速收敛的优点，还提升了跳出局部最优点的能力。
```python
import numpy as np
from sklearn.datasets import make_regression
def
gpsa(X, y, n_particles=30, max_iter=100):
# 初始化参数
w = 0.7298 # 惯性权重
c1 = 1.4962 # 自我认知加速系数
c2 = 1.4962 # 社会认知加速系数
dim = X.shape[1]
# 初始化位置与速度矩阵
positions = np.random.uniform(-5, 5, size=(n_particles, dim))
velocities = np.zeros_like(positions)
personal_best_positions = positions.copy()
global_best_position = positions[np.argmin([fitness(x, X, y) for x in positions])]
for t in range(max_iter):
r1 = np.random.rand(n_particles, dim)
r2 = np.random.rand(n_particles, dim)
velocities = w * velocities \
+ c1*r1*(personal_best_positions - positions) \
+ c2*r2*(global_best_position.reshape(1,-1)-positions)
positions += velocities
current_fitnesses = [fitness(p, X, y) for p in positions]
better_than_personal = current_fitnesses < [fitness(pb, X, y) for pb in personal_best_positions]
personal_best_positions[better_than_personal] = positions[better_than_personal]
best_idx = np.argmin(current_fitnesses)
if fitness(global_best_position, X, y) > current_fitnesses[best_idx]:
global_best_position = positions[best_idx].copy()
return global_best_position
def fitness(weights, X, y):
predictions = X @ weights.T
error = ((predictions.flatten() - y)**2).mean()
return error
```
此
代码片段展示了一个简单的线性回归模型训练过程，其中`
gpsa()`函数
实现了基于遗传算子调整后的粒子群优化
算法来寻找最佳权重向量。
#### 混沌粒子群优化
算法 (CPSO)
混沌粒子群优化则借助于混沌理论中特有的遍历性
和随机性质改善传统 PSO 易陷于局部最优的问题。具体来说，在更新粒子的速度时加入由 Logistic映射产生的伪随机数序列作为扰动项，从而打破原有的单调变化趋势，促进全局搜索效率提升。
```
matlab
function [gbest_pos, gbest_val] = cpso(fitness_func, lb, ub, num_dim, num_part, iter_max)
% CPSO Chaotic Particle Swarm Optimizer
%
% Inputs:
% fitness_func - Fitness function handle.
% lb - Lower bounds of search space.
% ub - Upper bounds of search space.
% num_dim - Number of dimensions.
% num_part - Population size (#particles).
% iter_max - Maximum number of iterations.
w_min = 0.4; % Minimum inertia weight
w_max = 0.9; % Maximum inertia weight
c1 = 2; % Cognitive acceleration coefficient
c2 = 2; % Social acceleration coefficient
r = rand(); % Initial chaos value from logistic map
mu = 4;
pos = zeros(num_part, num_dim);
vel = zeros(num_part, num_dim);
for i = 1:num_part
pos(i,:) = lb + (ub-lb).*rand(1,num_dim); %#ok<AGROW>
end
pbest_pos = pos;
pbest_fit = arrayfun(@(i) fitness_func(pos(i,:)), 1:num_part);
[~, idx_gbest] = min(pbest_fit(:));
gbest_pos = pos(idx_gbest,:);
gbest_val = pbest_fit(idx_gbest);
for it = 1:iter_max
w = w_max-(it/iter_max)*(w_max-w_min);
for i = 1:num_part
vel(i,:) = ...
w*vel(i,:)...
+c1*rand().*(pbest_pos(i,:)-pos(i,:))...
+c2*rand().*(gbest_pos-pos(i,:));
% Chaos disturbance on velocity update rule
r = mu*r*(1-r);
vel(i,:) = vel(i,:) + r*(ub-lb)*sign(rand()-0.5);
pos(i,:) = pos(i,:) + vel(i,:);
pos(i,:) = max(min(pos(i,:), ub), lb);
fit_i = fitness_func(pos(i,:));
if fit_i < pbest_fit(i)
pbest_pos(i,:) = pos(i,:);
pbest_fit(i) = fit_i;
if fit_i < gbest_val
gbest_pos = pos(i,:);
gbest_val = fit_i;
end
end
end
end
end
```
上述
MATLAB脚本定义了一个名为 `cpso` 的函数用于执行带有混沌扰动的粒子群优化流程，
并返回最终发现的最佳解决方案及其对应的适应度得分。
本文详细介绍了基于GPSA（Generalized Phase-Sift Algorithm）和AIA（Alternating Iterative Algorithm）的相位提取算法原理，并提供了MATLAB代码实现。这两种算法在数字信号处理中用于图像和声音处理，通过稀疏表示降低计算量，提高效率。
订阅专栏 解锁全文
扫一扫
205
被折叠的 条评论
为什么被折叠?
到【灌水乐园】发言
