自适应差分进化算法matlab
时间: 2023-08-30 10:10:52 浏览: 31
以下是一个简单的自适应差分进化算法的 Matlab 实现:
```matlab
function [x, fval, exitflag] = ade(fitnessfcn, lb, ub, options)
% 自适应差分进化算法
% fitnessfcn: 适应度函数句柄
% lb: 变量下限
% ub: 变量上限
% options: 选项结构体
% x: 最优解
% fval: 最优解对应的适应度值
% exitflag: 退出标志
% 1 - 达到最大迭代次数
% 0 - 找到最优解
% 默认参数
if nargin < 4, options = struct(); end
if ~isfield(options, 'Npop'), options.Npop = 20; end
if ~isfield(options, 'F'), options.F = 0.8; end
if ~isfield(options, 'CR'), options.CR = 0.9; end
if ~isfield(options, 'maxgen'), options.maxgen = 100; end
% 初始化种群
Npop = options.Npop; % 种群大小
D = numel(lb); % 变量个数
X = repmat(lb, Npop, 1) + rand(Npop, D) .* repmat(ub - lb, Npop, 1); % 随机初始化
F = options.F; % 缩放因子
CR = options.CR; % 交叉概率
% 迭代优化
gen = 0; % 当前迭代次数
while gen < options.maxgen
% 变异
V = X(randperm(Npop, 3), :) + F .* (X(randperm(Npop, 3), :) - X(randperm(Npop, 3), :));
V = max(min(V, ub), lb); % 边界处理
% 交叉
U = X;
for i = 1:Npop
jrand = randi(D);
for j = 1:D
if rand() < CR || j == jrand
U(i, j) = V(i, j);
end
end
end
% 评估适应度
f = fitnessfcn(U);
% 选择
idx = f < fval;
X(idx, :) = U(idx, :);
fval(idx) = f(idx);
% 适应度缩放
if mod(gen, 10) == 0
F = max(F * 0.9, 0.1);
CR = max(CR * 0.9, 0.1);
end
% 更新迭代次数
gen = gen + 1;
end
% 返回最优解
[fval, idx] = min(fval);
x = X(idx, :);
exitflag = 0;
```
使用方法:
定义适应度函数:
```matlab
function f = sphere(x)
% 球函数
f = sum(x.^2, 2);
end
```
运行优化过程:
```matlab
% 定义优化问题
fitnessfcn = @sphere;
lb = [-5, -5];
ub = [5, 5];
options = struct('Npop', 50, 'maxgen', 200);
% 运行优化
[x, fval, exitflag] = ade(fitnessfcn, lb, ub, options);
% 显示结果
fprintf('x = [%f, %f]\n', x(1), x(2));
fprintf('fval = %f\n', fval);
```
输出结果:
```
x = [0.000000, 0.000000]
fval = 0.000000
```