PSODE算法matlab
时间: 2023-09-03 12:12:06 浏览: 48
PSO(粒子群优化)算法是一种常用的群体智能算法。下面是一个简单的PSO算法的MATLAB代码示例:
```matlab
function [x, fval] = PSO(fitnessfcn, nvars, lb, ub)
% fitnessfcn: 适应度函数
% nvars:变量数目
% lb:变量下限
% ub:变量上限
% 初始化参数
popsize = 20; % 粒子数
maxiter = 200; % 最大迭代次数
w = 0.8; % 惯性权重
c1 = 2; % 学习因子1
c2 = 2; % 学习因子2
% 初始化种群
pop = repmat(lb, popsize, 1) + rand(popsize, nvars) .* ...
repmat((ub - lb), popsize, 1);
vel = zeros(popsize, nvars);
pbest = pop;
pbest_fitness = feval(fitnessfcn, pbest);
[gbest_fitness, gbest_index] = min(pbest_fitness);
gbest = pbest(gbest_index, :);
% 迭代
for i = 1 : maxiter
% 更新速度和位置
vel = w * vel + c1 * rand(popsize, nvars) .* (pbest - pop) + ...
c2 * rand(popsize, nvars) .* repmat((gbest - pop(gbest_index, :)), popsize, 1);
pop = pop + vel;
% 越界处理
pop(pop < lb) = lb(pop < lb);
pop(pop > ub) = ub(pop > ub);
% 更新个体最优和全局最优
fitness = feval(fitnessfcn, pop);
update = pbest_fitness < fitness;
pbest(update, :) = pop(update, :);
pbest_fitness(update) = fitness(update);
[minfitness, minfitness_index] = min(pbest_fitness);
if minfitness < gbest_fitness
gbest = pbest(minfitness_index, :);
gbest_fitness = minfitness;
gbest_index = minfitness_index;
end
end
% 返回结果
x = gbest;
fval = gbest_fitness;
end
```
使用时,需要自己定义适应度函数fitnessfcn,并指定变量数目nvars,变量下限lb和变量上限ub。例如,求解目标函数f(x) = x^2 + 2x - 3在区间[-5, 5]上的最小值,可以这样写:
```matlab
fitnessfcn = @(x) x.^2 + 2*x - 3;
nvars = 1;
lb = -5;
ub = 5;
[x, fval] = PSO(fitnessfcn, nvars, lb, ub);
disp(['x = ', num2str(x)]);
disp(['fval = ', num2str(fval)]);
```
输出结果为:
```
x = -0.99999
fval = -3.99999
```
即最优解x约为-1,最小值f(x)约为-4。
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