Matlab遗传算法性能测试

遗传算法，结合生物学遗传规则用于问题最优解求解，具有广泛的用途。

然而，由于其属于不确定性算法，故在搜索性能和最优解的稳定性上仍有待改善。

利用Matlab的遗传算法，编写代码如下：

function [ output_args ] = ga_test
clear;

%解：X = [0, 0, ...]
%nVar = 30
%dims: [-30, 30]
    function fitness = sphere(vals)
        prod = vals .* vals;
        fitness = sum(prod, 2);
    end

%f(x) = 1/4000 * sum^n_1(x_i)^2 - prod^n_1 * cos(x_i/sqrt(i)) + 1
%f* = 0, x* = [0, 0, ...];
%nVar = 30
%dims: [-600, 600]
    function fitness = griewank(vals)
        [h w] = size(vals);
        p1 = vals.^2;
        p1 = 1/4000 .* sum(p1, 2);

        t = sqrt([1:w]);
        p2 = vals ./ repmat(t, h, 1);
        p2 = cos(p2);
        p2 = prod(p2, 2);
        fitness = p1 - p2 + 1;
    end

%解: X* = [1, 1, 1, ...]
%nVar: 30
    function fitness = RosenBroek(vals)
        [k n] = size(vals);
        vals1 = vals(:, 1:n-1);
        vals2 = vals(:, 2:n);
        tmp = vals2 - vals1 .* vals1;
        tmp = 100 * tmp .* tmp;
        tmp1 = (vals1 - 1).^2;
        fitness = sum(tmp, 2) + sum(tmp1, 2);
    end

%许多局部最小值，最优解：X = [0, 0], 固定2个变量
%nVar = 2
    function fitness = Rastrigin (X)
        v = X.^2 - 10 .* cos(2 * pi .* X) + 10;
        fitness = sum(v, 2);
    end

%参数
popSize = 50; 				% 群规模
Run = 4;                    % 测试轮次
option = gaoptimset('PopulationSize', popSize); %, 'UseParallel', true);

Ans = {};
for r = 1:Run  %轮次
    Func = r;     % 测试适应度函数
    switch Func
        case 1
            Func = @sphere
            Xmin = -100;
            Xmax = 100;
            nVar = 30;
        case 2
            Func = @griewank
            Xmin = -600;
            Xmax = 600;
            nVar = 30;
        case 3
            nVar = 30;
            Func = @RosenBroek
            Xmin = -100;
            Xmax = 100;
        case 4
            nVar = 2;
            Func = @Rastrigin
            Xmin = -5.12;
            Xmax = 5.12;
    end;
    tic;
    [Ans{r}.bestGene, Ans{r}.bestFit] = ga(Func, nVar, [], [], [], [], repmat(Xmin, nVar, 1), repmat(Xmax, nVar, 1), [], option);
    costt = toc
    Ans{r}.costtime = costt;
end %可运行30轮，查看结果
for r = 1:Run
    fprintf('fit=%f, costtime=%f(s) \n', Ans{r}.bestFit, Ans{r}.costtime);
    %Ans{r}.bestGene
end;
end

运行结果：

Func =

@ga_test/sphere

Optimization terminated: average change in the fitness value less than options.TolFun.

costt =

4.2468

Func =

@ga_test/griewank

Optimization terminated: average change in the fitness value less than options.TolFun.

costt =

4.2952

Func =

@ga_test/RosenBroek

Optimization terminated: maximum number of generations exceeded.

costt =

14.4236

Func =

@ga_test/Rastrigin

Optimization terminated: average change in the fitness value less than options.TolFun.

costt =

0.2880

fit=0.000100, costtime=4.246814(s)

fit=0.000150, costtime=4.295222(s)

fit=1.511176, costtime=14.423554(s)

fit=0.000000, costtime=0.288025(s)

从运行时间来看，算法的性能不好。

故类似遗传算法、微分进化等方法，仍有待提出新的机制和算法以解决此类问题。

Matlab遗传算法性能测试