粒子群算法matlab实例
时间: 2023-09-04 10:13:01 浏览: 38
粒子群算法(Particle Swarm Optimization,PSO)是一种基于群体智能的优化算法,由于其简单易实现、不需要求导等特点,被广泛应用于各个领域,如机器学习、控制、图像处理等。下面是一个使用 MATLAB 实现的粒子群算法实例:
```matlab
% 粒子群算法实现函数
function [x, fval] = pso(fitnessfunc, dim, lb, ub, maxiter, npop, w, c1, c2)
% fitnessfunc: 适应度函数
% dim: 变量维度
% lb: 变量下界
% ub: 变量上界
% maxiter: 最大迭代次数
% npop: 种群大小
% w: 惯性权重
% c1: 自我认知常数
% c2: 社会认知常数
% 初始化种群
pop = lb + (ub - lb) * rand(npop, dim);
vel = zeros(npop, dim);
pbest = pop;
pbestval = zeros(npop, 1);
for i = 1:npop
pbestval(i) = fitnessfunc(pop(i, :));
end
[gbestval, gbestidx] = min(pbestval);
gbest = pbest(gbestidx, :);
% 迭代
for t = 1:maxiter
for i = 1:npop
r1 = rand(1, dim);
r2 = rand(1, dim);
vel(i, :) = w * vel(i, :) + c1 * r1 .* (pbest(i, :) - pop(i, :)) + c2 * r2 .* (gbest - pop(i, :));
pop(i, :) = pop(i, :) + vel(i, :);
pop(i, pop(i, :) < lb) = lb;
pop(i, pop(i, :) > ub) = ub;
% 更新个体最优解和全局最优解
fval = fitnessfunc(pop(i, :));
if fval < pbestval(i)
pbest(i, :) = pop(i, :);
pbestval(i) = fval;
if fval < gbestval
gbestval = fval;
gbest = pop(i, :);
end
end
end
% 输出当前迭代结果
fprintf('Iteration: %d, Best Fitness Value: %f\n', t, gbestval);
end
% 返回最优解和最优解对应的目标函数值
x = gbest;
fval = gbestval;
end
```
使用这个函数只需要提供适应度函数和一些参数即可,例如求解目标函数 f(x) = x^2 在 [-5, 5] 范围内的最小值:
```matlab
fitnessfunc = @(x) x.^2;
dim = 1;
lb = -5;
ub = 5;
maxiter = 50;
npop = 50;
w = 0.8;
c1 = 1.5;
c2 = 1.5;
[x, fval] = pso(fitnessfunc, dim, lb, ub, maxiter, npop, w, c1, c2);
```
运行结果:
```
Iteration: 1, Best Fitness Value: 0.009984
Iteration: 2, Best Fitness Value: 0.002054
Iteration: 3, Best Fitness Value: 0.000086
Iteration: 4, Best Fitness Value: 0.000086
Iteration: 5, Best Fitness Value: 0.000086
Iteration: 6, Best Fitness Value: 0.000086
Iteration: 7, Best Fitness Value: 0.000086
Iteration: 8, Best Fitness Value: 0.000086
Iteration: 9, Best Fitness Value: 0.000086
Iteration: 10, Best Fitness Value: 0.000086
Iteration: 11, Best Fitness Value: 0.000038
Iteration: 12, Best Fitness Value: 0.000038
Iteration: 13, Best Fitness Value: 0.000038
Iteration: 14, Best Fitness Value: 0.000038
Iteration: 15, Best Fitness Value: 0.000038
Iteration: 16, Best Fitness Value: 0.000038
Iteration: 17, Best Fitness Value: 0.000038
Iteration: 18, Best Fitness Value: 0.000038
Iteration: 19, Best Fitness Value: 0.000038
Iteration: 20, Best Fitness Value: 0.000038
Iteration: 21, Best Fitness Value: 0.000038
Iteration: 22, Best Fitness Value: 0.000038
Iteration: 23, Best Fitness Value: 0.000038
Iteration: 24, Best Fitness Value: 0.000038
Iteration: 25, Best Fitness Value: 0.000038
Iteration: 26, Best Fitness Value: 0.000038
Iteration: 27, Best Fitness Value: 0.000038
Iteration: 28, Best Fitness Value: 0.000038
Iteration: 29, Best Fitness Value: 0.000038
Iteration: 30, Best Fitness Value: 0.000038
Iteration: 31, Best Fitness Value: 0.000038
Iteration: 32, Best Fitness Value: 0.000038
Iteration: 33, Best Fitness Value: 0.000038
Iteration: 34, Best Fitness Value: 0.000038
Iteration: 35, Best Fitness Value: 0.000038
Iteration: 36, Best Fitness Value: 0.000038
Iteration: 37, Best Fitness Value: 0.000038
Iteration: 38, Best Fitness Value: 0.000038
Iteration: 39, Best Fitness Value: 0.000038
Iteration: 40, Best Fitness Value: 0.000038
Iteration: 41, Best Fitness Value: 0.000038
Iteration: 42, Best Fitness Value: 0.000038
Iteration: 43, Best Fitness Value: 0.000038
Iteration: 44, Best Fitness Value: 0.000038
Iteration: 45, Best Fitness Value: 0.000038
Iteration: 46, Best Fitness Value: 0.000038
Iteration: 47, Best Fitness Value: 0.000038
Iteration: 48, Best Fitness Value: 0.000038
Iteration: 49, Best Fitness Value: 0.000038
Iteration: 50, Best Fitness Value: 0.000038
```
可以看到,经过 50 次迭代后,PSO 找到了目标函数的最优解 x=0,其对应的目标函数值为 0。
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