Matlab基于遗传算法的高斯烟雨扩散模型代码

这里提供一个基于遗传算法的高斯烟雨扩散模型的 Matlab 代码，供参考。

% 遗传算法参数
popSize = 100; % 种群大小
maxGen = 100; % 最大迭代次数
pc = 0.8; % 交叉概率
pm = 0.01; % 变异概率

% 模型参数
xRange = [0, 1000]; % x 范围
yRange = [0, 1000]; % y 范围
sigma = 100; % 高斯函数标准差
Q = 10; % 源强度
u = 2; % 风速
v = 0; % 风向
D = 0.1; % 扩散系数
dt = 1; % 时间步长

% 初始化种群
pop = rand(popSize, 2) .* [diff(xRange), diff(yRange)] + [xRange(1), yRange(1)];

% 迭代
for gen = 1:maxGen
    % 计算适应度
    fitness = zeros(popSize, 1);
    for i = 1:popSize
        x = linspace(xRange(1), xRange(2), 100);
        y = linspace(yRange(1), yRange(2), 100);
        [X, Y] = meshgrid(x, y);
        z = Q / (2 * pi * u * sigma) * exp(-((X - pop(i, 1)).^2 + (Y - pop(i, 2)).^2) / (2 * sigma^2)) .* exp(-D*dt*(u*(X - pop(i, 1)) + v*(Y - pop(i, 2)))^2);
        fitness(i) = sum(sum(z));
    end

    % 选择
    [sortedFitness, indices] = sort(fitness, 'descend');
    elite = pop(indices(1:ceil(popSize/10)), :);
    roulette = cumsum(sortedFitness) / sum(sortedFitness);
    parents = zeros(popSize, 2);
    for i = 1:popSize
        r = rand;
        for j = 1:popSize
            if r < roulette(j)
                parents(i, :) = pop(indices(j), :);
                break;
            end
        end
    end

    % 交叉
    offspring = zeros(popSize, 2);
    for i = 1:popSize/2
        if rand < pc
            idx1 = randi(popSize);
            idx2 = randi(popSize);
            alpha = rand;
            offspring(2*i-1, :) = alpha*parents(idx1, :) + (1-alpha)*parents(idx2, :);
            offspring(2*i, :) = alpha*parents(idx2, :) + (1-alpha)*parents(idx1, :);
        else
            offspring(2*i-1, :) = parents(randi(popSize), :);
            offspring(2*i, :) = parents(randi(popSize), :);
        end
    end

    % 变异
    for i = 1:popSize
        if rand < pm
            offspring(i, 1) = offspring(i, 1) + randn * diff(xRange) / 10;
            offspring(i, 2) = offspring(i, 2) + randn * diff(yRange) / 10;
        end
    end

    % 更新种群
    pop = [elite; offspring];
end

% 计算最优解
x = linspace(xRange(1), xRange(2), 100);
y = linspace(yRange(1), yRange(2), 100);
[X, Y] = meshgrid(x, y);
z = zeros(size(X));
for i = 1:popSize
    z = z + Q / (2 * pi * u * sigma) * exp(-((X - pop(i, 1)).^2 + (Y - pop(i, 2)).^2) / (2 * sigma^2)) .* exp(-D*dt*(u*(X - pop(i, 1)) + v*(Y - pop(i, 2)))^2);
end
z = z / popSize;

% 绘图
surf(X, Y, z);
xlabel('x');
ylabel('y');
zlabel('concentration');