利用遗传算法求解带有基数约束的均值方差模型的matlab源码,并输出适应度变化曲线和最优解
时间: 2024-06-09 13:08:47 浏览: 17
很抱歉,我目前不具备编写该算法的能力。但是,以下是一个基于遗传算法求解带有基数约束的均值方差模型的MATLAB代码示例,供您参考:
``` matlab
clc;
clear;
close all;
%% 参数设置
% 基因的长度,即决策变量的个数
n = 100;
% 种群大小
pop_size = 50;
% 最大迭代次数
max_iter = 100;
% 交叉概率
p_c = 0.8;
% 变异概率
p_m = 0.1;
% 目标函数权重
w1 = 0.6; % 均值的权重
w2 = 0.4; % 方差的权重
% 均值和方差的目标值
mu = 0.5;
sigma = 0.1;
% 基数约束条件
k_min = 30;
k_max = 70;
%% 遗传算法主程序
% 生成初始种群
pop = rand(pop_size, n);
% 计算初始种群的适应度
fitness = get_fitness(pop, w1, w2, mu, sigma, k_min, k_max);
% 记录每次迭代的最优解和适应度
best_fitness = zeros(max_iter, 1);
best_individual = zeros(max_iter, n);
for iter = 1:max_iter
% 选择
parents = roulette_wheel_selection(pop, fitness);
% 交叉
offspring = crossover(parents, p_c);
% 变异
offspring = mutation(offspring, p_m);
% 计算适应度
offspring_fitness = get_fitness(offspring, w1, w2, mu, sigma, k_min, k_max);
% 合并种群
pop = [pop; offspring];
fitness = [fitness; offspring_fitness];
% 筛选新种群
[pop, fitness] = selection(pop, fitness, pop_size);
% 记录最优解和适应度
[best_fitness(iter), idx] = min(fitness);
best_individual(iter, :) = pop(idx, :);
% 输出信息
fprintf('迭代次数:%d, 最优解:%f, 平均适应度:%f\n', iter, best_fitness(iter), mean(fitness));
end
%% 结果分析
% 绘制适应度变化曲线
figure;
plot(best_fitness);
xlabel('迭代次数');
ylabel('适应度');
title('适应度变化曲线');
% 输出最优解
fprintf('最优解:');
disp(best_individual(end, :));
% 计算最优解的均值和方差
x = best_individual(end, :);
x_sum = sum(x);
x_mean = x_sum / n;
x_var = sum((x - x_mean).^2) / n;
fprintf('最优解的均值:%f,方差:%f', x_mean, x_var);
%% 函数定义
% 计算适应度
function fitness = get_fitness(pop, w1, w2, mu, sigma, k_min, k_max)
% 计算均值和方差
x_sum = sum(pop, 2);
x_mean = x_sum / size(pop, 2);
x_var = sum((pop - x_mean).^2, 2) / size(pop, 2);
% 计算基数
k = sum(pop, 2);
% 判断基数是否符合约束条件
mask = (k >= k_min) & (k <= k_max);
% 计算适应度
fitness = zeros(size(pop, 1), 1);
fitness(mask) = w1 * abs(x_mean(mask) - mu) + w2 * abs(x_var(mask) - sigma);
fitness(~mask) = inf;
end
% 轮盘赌选择
function parents = roulette_wheel_selection(pop, fitness)
% 计算适应度比例
fitness_sum = sum(fitness);
fitness_ratio = fitness / fitness_sum;
% 选择父代
[~, idx] = histc(rand(pop_size, 1), [0; cumsum(fitness_ratio)]);
parents = pop(idx, :);
end
% 交叉
function offspring = crossover(parents, p_c)
offspring = zeros(size(parents));
for i = 1:2:pop_size
% 随机选择两个父代
p1 = parents(i, :);
p2 = parents(i+1, :);
% 随机选择交叉点
if rand() < p_c
k = randi(n-1);
offspring(i, :) = [p1(1:k) p2(k+1:end)];
offspring(i+1, :) = [p2(1:k) p1(k+1:end)];
else
offspring(i, :) = p1;
offspring(i+1, :) = p2;
end
end
end
% 变异
function offspring = mutation(offspring, p_m)
for i = 1:pop_size
if rand() < p_m
% 随机选择一个基因进行变异
k = randi(n);
offspring(i, k) = 1 - offspring(i, k);
end
end
end
% 筛选
function [pop, fitness] = selection(pop, fitness, pop_size)
[~, idx] = sort(fitness);
pop = pop(idx(1:pop_size), :);
fitness = fitness(idx(1:pop_size));
end
```
需要注意的是,该代码仅供参考,具体实现可能需要根据实际问题进行调整。