樽海鞘算法解决约束优化问题

1. 约束优化问题

\[Minimize \qquad f(Y) = (y_3+2)y_2y_1^2 \\ s.t.\begin{cases} g_1(Y) = 1 - \frac{y_2^3y_3}{71785y_1^4} \leq 0 \\ g_2(Y) = \frac{4y_2^2 - y_1y_2}{12566(y_2y_1^3 - y_1^4)} + \frac{1}{5108y_1^2} - 1 \leq 0 \\ g_3(Y) = 1 - \frac{140.45y_1}{y_2^2y_3} \leq 0 \\ g_4(Y) = 1 - \frac{y_1 + y_2}{1.5} - 1 \leq 0 \\ \end{cases} \]

\[0.05 \leq y_1 \leq 2; \qquad 0.25 \leq y_2 \leq 1.3; \qquad 2 \leq y_3 \leq 15 \]

2. 樽海鞘算法解决约束优化问题

function [fitness_set, best_Solves] = SSA()
    %% 问题参数设置
    ub = [2, 1.3, 15];     % 上界
    lb = [0.05, 0.25, 2];  % 下界
    
    Max_iter = 300;      % 最大迭代次数
    n = 50;              % 种群数目
    dim = 3;             % 维数
    
    Convergence_curve = zeros(1,Max_iter); % 算法每一次迭代的最好值
    
    run_times = 30;            % 运行次数
    fitness_set = zeros(run_times,1);
    best_Solves = zeros(run_times,dim);
    for run = 1:run_times
        %% 初始化
        FoodPosition = zeros(1,dim); % 食物位置
        FoodFitness  = inf;          % 食物适应度值

        %% 初始化种群
        SalpPositions = zeros(n,dim);
        SalpFitness = zeros(n,1);

        for i=1:n
            for j=1:dim
                SalpPositions(i,j) = z(i,j)*(ub(j) - lb(j)) + lb(j); % 初始化个体
            end
            SalpFitness(i) = fobj(SalpPositions(i,:));

            if SalpFitness(i)<FoodFitness
                FoodPosition = SalpPositions(i,:);
                FoodFitness = SalpFitness(i);
            end
        end

        %% 开始仿真
        l = 0;  % 迭代次数
        while (l<=Max_iter)
            c1 = 2*exp(-(4*l/Max_iter)^2);
            for i=1:n
                SalpPositions = SalpPositions';
                if i<=n/2
                    for j=1:dim
                        c2 = rand;
                        c3 = rand;
                        if c3<0.5
                            SalpPositions(j,i) = FoodPosition(j)+c1*((ub(j)-lb(j))*c2+lb(j));
                        else
                            SalpPositions(j,i) = FoodPosition(j)-c1*((ub(j)-lb(j))*c2+lb(j));
                        end
                    end
                elseif i>n/2 && i<n+1
                    point1 = SalpPositions(:,i-1);
                    point2 = SalpPositions(:,i);
                    SalpPositions(:,i)=(point2+point1)/2;      % SSA算法追随者更新公式
                end
                SalpPositions = SalpPositions';
            end
           %% 边界处理<-修改了
            for i=1:n
                Tp = SalpPositions(i,:)>ub;
                Tm = SalpPositions(i,:)<lb;
                SalpPositions(i,:) = (SalpPositions(i,:).*(~(Tp+Tm))) + ub.*Tp + lb.*Tm;

                SalpFitness(i) = fobj(SalpPositions(i,:));

               %% 精英保留机制
                if SalpFitness(i)<FoodFitness
                    FoodPosition = SalpPositions(i,:);
                    FoodFitness = SalpFitness(i);
                end
            end

            l = l + 1;  % 更新迭代次数
            Convergence_curve(l) = FoodFitness;
            
        end
        best_Solves(run,:) = FoodPosition;
        fitness_set(run) = FoodFitness;  % 算法每次运行的结果
    end
end



%% 拉伸弹簧
function out = fobj(X) 
    y1 = X(:,1);
    y2 = X(:,2);
    y3 = X(:,3);
    % 目标函数
    fx = (y3+2).*y2.*y1.^2;
    
    % 不等式约束
    g(:,1) = 1-(y2.^3.*y3)./(71785.*y1.^4);
    g(:,2) = (4.*y2^2-y1.*y2)./(12566.*(y2.*y1.^3-y1.^4))+(1./(5108.*y1.^2)) -1;
    g(:,3) = 1-(140.45.*y1./(y2.^2.*y3));
    g(:,4) = (y1+y2)./1.5-1;
    
    % 惩罚项定义
    pp=10^9;
    penalty =[];
    for i=1:size(g,1)
        for j=1:size(g,2)
            if g(i,j)>0
                penalty(i,j) = pp.*g(i,j);
            else 
                penalty(i,j) = 0;
            end
        end
    end
    out = fx + sum(penalty,2);
end