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我在 MATLAB 中编写了一个脚本来生成遗传算法。问题是我不知道为什么算法会快速收敛。事实上，它在第一次迭代中收敛。我不知道我的主脚本或我写的“Crossover”和“Mutation”函数哪里错了。我使用过“单点交叉”和“二进制突变”。以下代码如下：

function [y1,y2] = SinglePointCv(p1,p2)

    nVar = numel(p1);

    CutPoint = randi([1,nVar-1]);

    y1 = [p1(1:CutPoint),p2(CutPoint+1:end)];   % Vector of First Children
    y2 = [p2(1:CutPoint),p1(CutPoint+1:end)];   % Vector of Second Children

end


function Child = Binary_Mutation(Parent)

    nVar = numel(Parent);               % Number of Variables

    Index = randi([1,nVar]);

    Child = Parent;
    Child(Index) = 1-Parent(Index);     % Binary Mutation

end

主要脚本如下：

% { My Simple Binary GA } 

%% Initialization

nPop = 46;
nVar = 4; 

pc = 0.6;   % X_Rate
pm = 0.2;   % Mut_Rate

nc = 2*round(pc*nPop);              % Selected Population for CrossOver
nm = 2*round(pm*nPop);              % Selected Population for Mutation

CostFunction = @(x) 1-sum(x.^2);
f = CostFunction;
popSize = [nPop,nVar];
pop = randi([0,1],popSize);         % Each Row is a Chromosome with nVar Variables
Costs = f(pop');

% Sort Costs
[Costs,SortIndex] = sort(Costs);
pop = pop(SortIndex,:);

MaxIter = 100;                      % Maximum Iteration
BestCosts = zeros(1,MaxIter);

%% Main Loop

for i=1:MaxIter

    OffSprings = cell(nc/2,2);
    OffSprings_Costs = zeros(nc/2,2);

    %% CrossOver
    for k=1:nc/2

        Index_For_Parents = randsample(nPop,2);   

        % Indices for Both Parents
        I1 = Index_For_Parents(1); 
        I2 = Index_For_Parents(2); 

        % Selected Parents for Xover
        Parent1 = pop(I1,:);
        Parent2 = pop(I2,:);

        % Children Vectors
        [OffSprings{k,1},OffSprings{k,2}] =  SinglePointCv(Parent1,Parent2);
        OffSprings_Costs(k,1) = f(OffSprings{k,1});
        OffSprings_Costs(k,2) = f(OffSprings{k,2});

    end

    OffSprings = reshape(OffSprings,[],1);
    OffSprings_Costs = reshape(OffSprings_Costs,[],1);

    Off = zeros(size(OffSprings,1),nVar);

    for Mat = 1:size(OffSprings,1)
        Off(Mat,:) = OffSprings{Mat}; 

    end

    OffSprings = Off;

    Mutants = zeros(nm,nVar);
    Mutants_Costs = zeros(nm,1);

    %% Mutation
    for j = 1:nm

        Parent_Index = randi([1,nPop]);  % Mutation Parent Index
        Parent = pop(Parent_Index,:);    % Selected Parent For Mutation
        Mutants(j,:) = Binary_Mutation(Parent);
        Mutants_Costs(j) = f(Mutants(j,:));
    end

    %% Merge, Sort, Truncate

    % Merge
    pop=[pop
         OffSprings
         Mutants];

    pop_Costs = [Costs'
                 OffSprings_Costs
                 Mutants_Costs];        % The vEctor Of Costs vALues


     % Sort
     [SortedCosts,SortOrder] = sort(pop_Costs);
     pop = pop(SortOrder,:);

     % Truncate
     pop = pop(1:nPop,:);
     BestSolution = pop(1,:);   % First Row is the Best ANswer
     BestCosts(i) = SortedCosts(1);

end

plot(BestCosts,'k','LineWidth',2)
grid on
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