matlab基于遗传算法的高斯烟雨气体扩散模型代码

遗传算法（Genetic Algorithm，简称GA）是一种基于生物进化过程的搜索优化算法，主要用于优化问题的求解。高斯烟雨气体扩散模型是大气环境学中的一个经典问题，通过该模型可以模拟气体在大气中的扩散和传播过程。下面是基于遗传算法的高斯烟雨气体扩散模型的Matlab代码：

% GA algorithm for Gaussian plume model

% problem definition
fobj = @(x) gaussian_plume_model(x(1), x(2), x(3), x(4), x(5), x(6), x(7), x(8), x(9));
nvar = 9; % number of variables
lb = [0.01 1 10 0.01 1 10 0 0 0]; % lower bound of variables
ub = [10 100 1000 10 100 1000 360 360 360]; % upper bound of variables

% GA parameters
pop_size = 100; % population size
max_gen = 100; % maximum number of generations
pc = 0.8; % crossover probability
nc = 2*round(pc*pop_size/2); % number of offsprings (even)
pm = 0.1; % mutation probability
nm = round(pm*pop_size*nvar); % number of mutations
elitism = true; % elitism flag
min_fit = 0; % minimum fitness value for termination

% initialization
pop = repmat(lb, pop_size, 1) + repmat(ub-lb, pop_size, 1).*rand(pop_size, nvar);
fit = zeros(pop_size, 1);

% GA main loop
for gen = 1:max_gen
    % evaluation
    for i = 1:pop_size
        fit(i) = fobj(pop(i, :));
    end
    
    % termination
    if min(fit) <= min_fit
        break;
    end
    
    % elitism
    if elitism
        [best_fit, best_idx] = min(fit);
        best_sol = pop(best_idx, :);
    end
    
    % selection
    fit_scaled = fit - min(fit);
    fit_scaled = fit_scaled/sum(fit_scaled);
    idx = randsample(1:pop_size, pop_size, true, fit_scaled);
    parents = pop(idx, :);
    
    % crossover
    offsprings = zeros(nc, nvar);
    for k = 1:2:nc
        i1 = k;
        i2 = k + 1;
        if rand() < pc
            [offsprings(i1, :), offsprings(i2, :)] = crossover(parents(i1, :), parents(i2, :));
        else
            offsprings(i1, :) = parents(i1, :);
            offsprings(i2, :) = parents(i2, :);
        end
    end
    
    % mutation
    idx = randsample(1:pop_size, nm);
    offsprings(idx, :) = mutation(offsprings(idx, :), lb, ub);
    
    % new population
    pop = [best_sol; offsprings];
end

% display result
disp(['Best solution: ' num2str(best_sol)]);
disp(['Best fitness: ' num2str(best_fit)]);

% crossover operator
function [c1, c2] = crossover(p1, p2)
    nvar = length(p1);
    pos = randi(nvar-1) + 1;
    c1 = [p1(1:pos) p2(pos+1:end)];
    c2 = [p2(1:pos) p1(pos+1:end)];
end

% mutation operator
function offsprings = mutation(offsprings, lb, ub)
    nvar = size(offsprings, 2);
    for i = 1:nvar
        if rand() < 0.5
            offsprings(:, i) = offsprings(:, i) + (ub(i) - offsprings(:, i)).*rand(size(offsprings, 1), 1);
        else
            offsprings(:, i) = offsprings(:, i) - (offsprings(:, i) - lb(i)).*rand(size(offsprings, 1), 1);
        end
    end
end

% Gaussian plume model
function fval = gaussian_plume_model(x0, y0, z0, u, H, sigY, sigZ, theta, phi)
    % constants
    k = 0.4; % von Karman constant
    g = 9.81; % gravitational acceleration
    T = 288; % temperature
    rho0 = 1.225; % air density at sea level
    p0 = 101325; % atmospheric pressure at sea level
    R = 287; % gas constant
    alpha = 1.4; % heat capacity ratio
    beta = 1/T; % temperature coefficient
    
    % wind speed and direction
    uY = u*cosd(theta)*cosd(phi);
    uZ = u*sind(theta);
    uX = u*cosd(theta)*sind(phi);
    
    % atmospheric stability parameter
    L = -H/k;
    
    % effective wind speed and direction
    if L > 0 % unstable
        uE = u;
        thetaE = theta;
        phiE = phi;
    elseif L < 0 % stable
        uStar = k*u/(log(z0/z0));
        uE = uStar/log(z0/z0);
        thetaE = atan2d(uY, uE);
        phiE = atan2d(uX, uE);
    else % neutral
        uE = u;
        thetaE = theta;
        phiE = phi;
    end
    
    % plume model
    f = @(x, y, z) (1/(2*pi*sigY*sigZ))*exp(-(y-y0)^2/(2*sigY^2)-(z-z0)^2/(2*sigZ^2));
    integrand = @(x, y, z) f(x, y, z)*uE;
    Q = integral3(integrand, -Inf, Inf, -Inf, Inf, 0, H);
    C = Q/(2*pi*uE*sigY*sigZ);
    rho = rho0*(1-beta*z0)^alpha;
    p = p0*(1-beta*z0)^(alpha/(alpha-1));
    sigma = sqrt(C/(rho*uE));
    fval = 1 - normcdf((x0-uX*z0/uZ)/sigma);
end

需要注意的是，以上代码中的`gaussian_plume_model`函数是高斯烟雨气体扩散模型的实现，需要根据具体问题进行修改。另外，遗传算法的参数也需要根据实际情况进行调整，以获得最佳的优化结果。