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

遗传算法求解带有基数约束的均值方差模型的Matlab代码如下：

function [x, fval] = GA_mean_var_with_cardinality(nvars, Aeq, beq, lb, ub, maxiter, popsize, pcrossover, pmutation)
% GA_mean_var_with_cardinality: Solve the mean-variance model with cardinality constraint using genetic algorithm.
%
% Input:
%       nvars: number of decision variables (integer)
%       Aeq, beq: equality constraint matrices (matrices)
%       lb, ub: lower and upper bounds of decision variables (vectors)
%       maxiter: maximum number of iterations (integer)
%       popsize: population size (integer)
%       pcrossover: crossover probability (scalar)
%       pmutation: mutation probability (scalar)
%
% Output:
%       x: optimal solution (vector)
%       fval: optimal objective value (scalar)
%
% Example:
%       nvars = 10;
%       Aeq = ones(1, nvars);
%       beq = 5;
%       lb = zeros(1, nvars);
%       ub = ones(1, nvars);
%       maxiter = 100;
%       popsize = 50;
%       pcrossover = 0.8;
%       pmutation = 0.1;
%       [x, fval] = GA_mean_var_with_cardinality(nvars, Aeq, beq, lb, ub, maxiter, popsize, pcrossover, pmutation);
%       disp(x);
%       disp(fval);

% Calculate the objective function
fitnessfcn = @(x) mean_var_with_cardinality(x);

% Set the options for the genetic algorithm
options = gaoptimset('PopulationType', 'doubleVector', ...
    'PopulationSize', popsize, ...
    'Generations', maxiter, ...
    'CrossoverFraction', pcrossover, ...
    'MutationFcn', {@mutationuniform, pmutation}, ...
    'SelectionFcn', {@selectionroulette}, ...
    'Display', 'off');

% Solve the problem using the genetic algorithm
[x, fval] = ga(fitnessfcn, nvars, [], [], Aeq, beq, lb, ub, [], options);

end

function [fval] = mean_var_with_cardinality(x)
% mean_var_with_cardinality: Calculate the objective value of the mean-variance model with cardinality constraint.
%
% Input:
%       x: decision variables (vector)
%
% Output:
%       fval: objective value (scalar)

% Define the parameters of the problem
mu = [0.1 0.2 0.15 0.07 0.11 0.09 0.12 0.16 0.14 0.18];
sigma = [0.3 0.25 0.2 0.15 0.1 0.12 0.13 0.17 0.22 0.3];
c = 0.25;
n = length(mu);

% Calculate the objective value
fval = -(x * mu') + c * (x * sigma')^2;
if sum(x) ~= 5
    fval = fval + 1e5;
end

end

其中，`nvars` 表示决策变量的数量，`Aeq` 和 `beq` 分别表示等式约束的系数矩阵和常数向量，`lb` 和 `ub` 分别表示决策变量的下界和上界，`maxiter` 表示最大迭代次数，`popsize` 表示种群大小，`pcrossover` 表示交叉概率，`pmutation` 表示变异概率。

函数 `mean_var_with_cardinality` 计算均值方差模型的目标函数值，并考虑基数约束。

调用 `GA_mean_var_with_cardinality` 函数即可求解该问题。