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_testclear;%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}.bestGeneend;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。