【智能优化算法】基于融合Sin混沌和分段权值的阿基米德优化算法(SAOA) 求解单目标优化问题附matlab代码-CFANZ编程社区

1 简介

针对阿基米德优化算法（Archimedes Optimization Algorithm，AOA）存在全局搜索能力弱、收敛精度低，易陷入局部最优等问题，提出融合Sin混沌和分段权值的阿基米德优化算法（SAOA）。首先，采用无限折叠迭代的Sin混沌反向学习策略初始化种群，提高初始阶段解的质量，为全局搜索多样性奠定基础；其次，引入算数交叉算子，将当前个体向与全局最优个体进行交叉，引导种群向最优解区域寻优，提高全局搜索能力；同时，引入分段权值策略，平衡算法的全局勘探与局部开发能力，降低算法陷入局部最优的概率；最后，通过对8个测试函数和部分CEC2014函数进行仿真实验及Wilcoxon秩和检验来评估改进算法的寻优性能，实验结果表明改进算法在搜索精度、收敛速度和稳定性等方面均有较大提升。另外，引入优化机械设计案例进行测试分析，进一步验证SAOA在工程优化问题上的可行性和适用性。

2 部分代码

function [Xbest, Scorebest,Convergence_curve] = AOA(Materials_no,Max_iter,fobj, dim,lb,ub,C3,C4)
% Initialization
C1=2;C2=6;
u=.9;l=.1;   %paramters in Eq. (12)
X=lb+rand(Materials_no,dim)*(ub-lb);%initial positions Eq. (4)
den=rand(Materials_no,dim); % Eq. (5)
vol=rand(Materials_no,dim);
acc=lb+rand(Materials_no,dim)*(ub-lb);% Eq. (6)
for i=1:Materials_no
    Y(i)=fobj(X(i,:));
end
[Scorebest, Score_index] = min(Y);
Xbest = X(Score_index,:);
den_best=den(Score_index,:);
vol_best=vol(Score_index,:);
acc_best=acc(Score_index,:);
acc_norm=acc;
for t = 1:Max_iter
    TF=exp(((t-Max_iter)/(Max_iter)));   % Eq. (8)
    if TF>1
        TF=1;
    end
    d=exp((Max_iter-t)/Max_iter)-(t/Max_iter); % Eq. (9)
    acc=acc_norm;
    r=rand();
    for i=1:Materials_no
        den(i,:)=den(i,:)+r*(den_best-den(i,:));   % Eq. (7)
        vol(i,:)=vol(i,:)+r*(vol_best-vol(i,:));
        if TF<.45%collision
            mr=randi(Materials_no);
            acc_temp(i,:)=(den(mr,:)+(vol(mr,:).*acc(mr,:)))./(rand*den(i,:).*vol(i,:));   % Eq. (10)
        else
            acc_temp(i,:)=(den_best+(vol_best.*acc_best))./(rand*den(i,:).*vol(i,:));   % Eq. (11)
        end
    end
    acc_norm=((u*(acc_temp-min(acc_temp(:))))./(max(acc_temp(:))-min(acc_temp(:))))+l;   % Eq. (12)
    for i=1:Materials_no
        if TF<.4
            for j=1:size(X,2)
                mrand=randi(Materials_no);
                Xnew(i,j)=X(i,j)+C1*rand*acc_norm(i,j).*(X(mrand,j)-X(i,j))*d;  % Eq. (13)
            end
        else
            for j=1:size(X,2)
                p=2*rand-C4;  % Eq. (15)
                T=C3*TF;
                if T>1
                    T=1;
                end
                if p<.5
                    Xnew(i,j)=Xbest(j)+C2*rand*acc_norm(i,j).*(T*Xbest(j)-X(i,j))*d;  % Eq. (14)
                else
                    Xnew(i,j)=Xbest(j)-C2*rand*acc_norm(i,j).*(T*Xbest(j)-X(i,j))*d;
                end
            end
        end
    end
    Xnew=fun_checkpositions(dim,Xnew,Materials_no,lb,ub);
    for i=1:Materials_no
        v=fobj( Xnew(i,:));
        if v<Y(i)
            X(i,:)=Xnew(i,:);
            Y (i)=v;
        end
    end
    [var_Ybest,var_index] = min(Y);
    Convergence_curve(t)=var_Ybest;
    if var_Ybest<Scorebest
        Scorebest=var_Ybest;
        Score_index=var_index;
        Xbest = X(var_index,:);
        den_best=den(Score_index,:);
        vol_best=vol(Score_index,:);
        acc_best=acc_norm(Score_index,:);
    end
end
end
function vec_pos=fun_checkpositions(dim,vec_pos,var_no_group,lb,ub)
Lb=lb*ones(1,dim);
Ub=ub*ones(1,dim);
for i=1:var_no_group
    isBelow1 = vec_pos(i,:) < Lb;
    isAboveMax = (vec_pos(i,:) > Ub);
    if isBelow1 == true
        vec_pos(i,:) =Lb;
    elseif find(isAboveMax== true)
        vec_pos(i,:) = Ub;
    end
end
end