对立学习差分进化算法matlab
时间: 2023-10-16 17:20:40 浏览: 34
对立学习差分进化算法(Oppositional Learning Differential Evolution,OLDE)是一种用于全局优化问题的进化算法。它是差分进化算法(Differential Evolution,DE)的改进版,通过引入对立学习(Oppositional Learning,OL)机制来提高算法的搜索能力。
OLDE算法的基本步骤包括:
1. 初始化种群:随机生成一定数量的个体作为初始种群。
2. 对立学习:将初始种群中的每个个体复制一份并对其所有变量取相反数,得到对立个体。将对立个体加入到种群中,形成对立种群。
3. 差分进化:使用差分进化算法对对立种群进行进化,得到新的种群。
4. 对立学习更新:对新种群进行对立学习,得到新的对立种群。
5. 重复步骤3-4,直到满足停止条件。
在MATLAB中实现OLDE算法的具体步骤可以参考以下代码:
```matlab
function [best_x, best_fval] = olde(fitness_func, lb, ub, dim, pop_size, max_iter)
% fitness_func: 适应度函数
% lb: 变量下界
% ub: 变量上界
% dim: 变量维数
% pop_size: 种群大小
% max_iter: 迭代次数
% 初始化种群
pop = repmat(lb, pop_size, 1) + repmat((ub-lb), pop_size, 1).*rand(pop_size, dim);
% 对立学习
op_pop = repmat(ub, pop_size, 1) - (pop - repmat(lb, pop_size, 1));
% 计算适应度值
fit_pop = fitness_func(pop);
fit_op_pop = fitness_func(op_pop);
% 更新最优解
[best_fval, best_idx] = min([fit_pop; fit_op_pop]);
if best_idx > pop_size
best_x = op_pop(best_idx-pop_size, :);
else
best_x = pop(best_idx, :);
end
% 迭代
for i = 1:max_iter
% 差分进化
idx = randperm(pop_size);
for j = 1:pop_size
r1 = idx(1);
r2 = idx(2);
r3 = idx(3);
trial_pop(j, :) = pop(r1, :) + rand()*(pop(r2, :) - pop(r3, :));
trial_pop(j, :) = max(trial_pop(j, :), lb);
trial_pop(j, :) = min(trial_pop(j, :), ub);
end
% 对立学习更新
op_trial_pop = repmat(ub, pop_size, 1) - (trial_pop - repmat(lb, pop_size, 1));
fit_trial_pop = fitness_func(trial_pop);
fit_op_trial_pop = fitness_func(op_trial_pop);
for j = 1:pop_size
if fit_trial_pop(j) > fit_pop(j)
pop(j, :) = trial_pop(j, :);
fit_pop(j) = fit_trial_pop(j);
if fit_trial_pop(j) > best_fval
best_fval = fit_trial_pop(j);
best_x = trial_pop(j, :);
end
end
if fit_op_trial_pop(j) > fit_op_pop(j)
op_pop(j, :) = op_trial_pop(j, :);
fit_op_pop(j) = fit_op_trial_pop(j);
if fit_op_trial_pop(j) > best_fval
best_fval = fit_op_trial_pop(j);
best_x = op_trial_pop(j, :);
end
end
end
end
end
```
在使用时,需要定义适应度函数,例如:
```matlab
function fval = rastrigin(x)
% Rastrigin函数
n = size(x, 2);
fval = 10*n + sum(x.^2 - 10*cos(2*pi*x), 2);
end
```
然后可以调用OLDE函数进行优化:
```matlab
lb = -5.12; % 变量下界
ub = 5.12; % 变量上界
dim = 30; % 变量维数
pop_size = 50; % 种群大小
max_iter = 1000; % 迭代次数
[best_x, best_fval] = olde(@rastrigin, lb, ub, dim, pop_size, max_iter);
```
这里以Rastrigin函数为例,求解30维变量的全局最优解。
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