用matlab求标准遗传算法求函数y=21.5+x1sin(4πx1)+ x2sin(20πx2)极值,plot函数怎么写
时间: 2024-06-05 08:06:14 浏览: 120
以下是一个使用标准遗传算法求解函数y=21.5 x1sin(4πx1) x2sin(20πx2)极值的MATLAB代码:
%% 初始化参数
pop_size = 100; % 种群大小
chrom_len = 40; % 染色体长度
pc = 0.8; % 交叉概率
pm = 0.01; % 变异概率
max_gen = 100; % 最大迭代次数
%% 初始化种群
pop = rand(pop_size, chrom_len);
%% 迭代
for i = 1:max_gen
% 计算适应度
fitness = evaluate(pop);
% 选择
parents = select(pop, fitness);
% 交叉
offspring = crossover(parents, pc);
% 变异
offspring = mutate(offspring, pm);
% 合并新旧种群
pop = [pop; offspring];
% 精英策略
[~, idx] = sort(evaluate(pop), 'descend');
pop = pop(idx(1:pop_size), :);
end
%% 绘制结果
x1 = linspace(-3, 3, 100);
x2 = linspace(-2, 2, 100);
[X1, X2] = meshgrid(x1, x2);
Y = 21.5 .* X1 .* sin(4 .* pi .* X1) + X2 .* sin(20 .* pi .* X2);
figure;
surf(X1, X2, Y);
hold on;
plot3(pop(:, 1), pop(:, 2), evaluate(pop), 'ro', 'MarkerSize', 10, 'MarkerFaceColor', 'r');
xlabel('x_1');
ylabel('x_2');
zlabel('y');
title('Standard Genetic Algorithm');
%% 辅助函数
function fitness = evaluate(pop)
x1 = decode(pop(:, 1:20), -3, 3);
x2 = decode(pop(:, 21:40), -2, 2);
fitness = 21.5 .* x1 .* sin(4 .* pi .* x1) + x2 .* sin(20 .* pi .* x2);
end
function parents = select(pop, fitness)
[~, idx] = sort(fitness, 'descend');
parents = pop(idx(1:round(size(pop, 1) * 0.5)), :);
end
function offspring = crossover(parents, pc)
offspring = parents;
for i = 1:2:size(parents, 1)
if rand < pc
idx = randi(size(parents, 2) - 1);
offspring(i, idx+1:end) = parents(i+1, idx+1:end);
offspring(i+1, idx+1:end) = parents(i, idx+1:end);
end
end
end
function offspring = mutate(offspring, pm)
for i = 1:size(offspring, 1)
for j = 1:size(offspring, 2)
if rand < pm
offspring(i, j) = 1 - offspring(i, j);
end
end
end
end
function x = decode(chrom, lb, ub)
x = lb + (ub - lb) .* bi2de(chrom, 'left-msb') ./ (2^size(chrom, 2) - 1);
end
其中,evaluate函数用于计算适应度,select函数用于选择操作,crossover函数用于交叉操作,mutate函数用于变异操作,decode函数用于将二进制编码转换为实数。在绘制结果时,采用了surf函数绘制函数曲面,plot3函数绘制种群分布。
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