基于模拟退火的粒子群优化算法matlab
时间: 2023-10-18 19:04:37 浏览: 53
以下是基于模拟退火的粒子群优化算法的MATLAB代码示例:
```matlab
function [x, fval] = PSO_SA(fun, lb, ub, n, maxit)
% PSO_SA - Particle Swarm Optimization with Simulated Annealing
%
% [x, fval] = PSO_SA(fun, lb, ub, n, maxit);
%
% fun - function handle to objective function
% lb - lower bound of variable
% ub - upper bound of variable
% n - number of particles
% maxit - maximum number of iterations
%
% x - solution
% fval - objective function value at x
%
% Example:
% [x, fval] = PSO_SA(@rosenbrock, [-2,-2], [2,2], 50, 5000);
%
% Written by Jialin Liu (jliu120@ucsc.edu)
% Initialize particles
D = length(lb);
x = lb + (ub - lb) .* rand(n, D);
v = zeros(n, D);
pbest = x;
pbestval = feval(fun, pbest);
[gbestval, gbestidx] = min(pbestval);
gbest = pbest(gbestidx, :);
% PSO parameters
w = 1;
c1 = 2;
c2 = 2;
% SA parameters
T0 = 100;
Tf = 1e-8;
alpha = 0.95;
% Iteration counter
it = 0;
% Main loop
while it < maxit
% Update velocity and position
r1 = rand(n, D);
r2 = rand(n, D);
v = w .* v + c1 .* r1 .* (pbest - x) + c2 .* r2 .* (gbest - x);
x = x + v;
% Check boundaries
x = max(x, lb);
x = min(x, ub);
% Update pbest and gbest
fval = feval(fun, x);
idx = fval < pbestval;
pbestval(idx) = fval(idx);
pbest(idx, :) = x(idx, :);
[fv, idx] = min(pbestval);
if fv < gbestval
gbestval = fv;
gbest = pbest(idx, :);
end
% Update temperature
T = T0 * alpha^it;
% SA step
for i = 1:n
% Generate a random neighbor
xn = x(i, :) + (ub - lb) .* randn(1, D);
% Check boundaries
xn = max(xn, lb);
xn = min(xn, ub);
% Evaluate objective function of current and new point
f = feval(fun, x(i, :));
fn = feval(fun, xn);
% Decide whether to accept the new point or not
if fn < f || exp(-(fn - f) / T) > rand()
x(i, :) = xn;
f = fn;
end
% Update pbest and gbest
if f < pbestval(i)
pbestval(i) = f;
pbest(i, :) = x(i, :);
if f < gbestval
gbestval = f;
gbest = x(i, :);
end
end
end
% Increase iteration counter
it = it + 1;
end
end
function f = rosenbrock(x)
% Rosenbrock function
% x - input vector
%
% f - output scalar
f = sum(100 * (x(:, 2:end) - x(:, 1:end-1).^2).^2 + (1 - x(:, 1:end-1)).^2, 2);
end
```
该算法的实现包括以下步骤:
1. 初始化粒子群的位置和速度,以及每个粒子的个体最优位置和全局最优位置。
2. 在每次迭代中,根据当前位置和速度更新粒子群的位置和速度,并更新每个粒子的个体最优位置和全局最优位置。
3. 根据当前温度和 SA 算法的准则,对每个粒子的位置进行一次随机扰动,并根据一定的概率接受新位置或保留原位置。
4. 重复步骤 2 和步骤 3 直到达到最大迭代次数。
在本示例中,使用 Rosenbrock 函数作为优化目标函数进行测试。该函数在 MATLAB 中可以定义如下:
```matlab
function f = rosenbrock(x)
% Rosenbrock function
% x - input vector
%
% f - output scalar
f = sum(100 * (x(:, 2:end) - x(:, 1:end-1).^2).^2 + (1 - x(:, 1:end-1)).^2, 2);
end
```
该函数的最优解在 $x=(1,1)$ 处,最小值为 $f(x)=0$。