一、簡介

GOA是一種用於全域性優化的新型元啟發式演算法
提出的蝗蟲優化演算法（GOA）在數學上模擬並模擬了蝗蟲群的行為，以解決優化問題。
提出了一種稱為蚱蜢優化演算法（GOA）的優化演算法，並將其應用於結構優化中具有挑戰性的問題。該演算法通過數學建模和模擬自然界中蝗蟲群的行為來解決優化問題。首先將GOA演算法應用於包括CEC2005在內的一組測試問題上，對其效能進行了定性和定量的測試和驗證。並以52杆桁架、三杆桁架及懸臂樑為例，探討其適用性。

1 GOA數學模型



2 GOA迭代模型


3 GOA演算法的基本流程


4 GOA缺點

二、原始碼

%_________________________________________________________________________%
%  Grasshopper Optimization Algorithm (GOA) source codes demo V1.0        %
%                                                                         %
%  Developed in MATLAB R2016a                                             %


% The Grasshopper Optimization Algorithm
function [TargetFitness,TargetPosition,Convergence_curve,Trajectories,fitness_history, position_history]=GOA(N, Max_iter, lb,ub, dim, fobj)

disp('GOA is now estimating the global optimum for your problem....')

flag=0;
if size(ub,1)==1
    ub=ones(dim,1)*ub;
    lb=ones(dim,1)*lb;
end

if (rem(dim,2)~=0) % this algorithm should be run with a even number of variables. This line is to handle odd number of variables
    dim = dim+1;
    ub = [ub; 100];
    lb = [lb; -100];
    flag=1;
end

%Initialize the population of grasshoppers
GrassHopperPositions=initialization(N,dim,ub,lb);
GrassHopperFitness = zeros(1,N);

fitness_history=zeros(N,Max_iter);
position_history=zeros(N,Max_iter,dim);
Convergence_curve=zeros(1,Max_iter);
Trajectories=zeros(N,Max_iter);

cMax=1;
cMin=0.00004;
%Calculate the fitness of initial grasshoppers

for i=1:size(GrassHopperPositions,1)
    if flag == 1
        GrassHopperFitness(1,i)=fobj(GrassHopperPositions(i,1:end-1));
    else
        GrassHopperFitness(1,i)=fobj(GrassHopperPositions(i,:));
    end
    fitness_history(i,1)=GrassHopperFitness(1,i);
    position_history(i,1,:)=GrassHopperPositions(i,:);
    Trajectories(:,1)=GrassHopperPositions(:,1);
end

[sorted_fitness,sorted_indexes]=sort(GrassHopperFitness);

% Find the best grasshopper (target) in the first population 
for newindex=1:N
    Sorted_grasshopper(newindex,:)=GrassHopperPositions(sorted_indexes(newindex),:);
end

TargetPosition=Sorted_grasshopper(1,:);
TargetFitness=sorted_fitness(1);

% Main loop
l=2; % Start from the second iteration since the first iteration was dedicated to calculating the fitness of antlions
while l<Max_iter+1
    
    c=cMax-l*((cMax-cMin)/Max_iter); % Eq. (2.8) in the paper
    
    for i=1:size(GrassHopperPositions,1)
        temp= GrassHopperPositions';
        for k=1:2:dim
            S_i=zeros(2,1);
            for j=1:N
                if i~=j
                    Dist=distance(temp(k:k+1,j), temp(k:k+1,i)); % Calculate the distance between two grasshoppers
                    
                    r_ij_vec=(temp(k:k+1,j)-temp(k:k+1,i))/(Dist+eps); % xj-xi/dij in Eq. (2.7)
                    xj_xi=2+rem(Dist,2); % |xjd - xid| in Eq. (2.7) 
                    
                    s_ij=((ub(k:k+1) - lb(k:k+1))*c/2)*S_func(xj_xi).*r_ij_vec; % The first part inside the big bracket in Eq. (2.7)
                    S_i=S_i+s_ij;
                end
            end
            S_i_total(k:k+1, :) = S_i;
            
        end
        
        X_new = c * S_i_total'+ (TargetPosition); % Eq. (2.7) in the paper      
        GrassHopperPositions_temp(i,:)=X_new'; 
    end
    % GrassHopperPositions
    GrassHopperPositions=GrassHopperPositions_temp;
    
    for i=1:size(GrassHopperPositions,1)
        % Relocate grasshoppers that go outside the search space 
        Tp=GrassHopperPositions(i,:)>ub';Tm=GrassHopperPositions(i,:)<lb';GrassHopperPositions(i,:)=(GrassHopperPositions(i,:).*(~(Tp+Tm)))+ub'.*Tp+lb'.*Tm;
        
        % Calculating the objective values for all grasshoppers
        if flag == 1
            GrassHopperFitness(1,i)=fobj(GrassHopperPositions(i,1:end-1));
        else
            GrassHopperFitness(1,i)=fobj(GrassHopperPositions(i,:));
        end
        fitness_history(i,l)=GrassHopperFitness(1,i);
        position_history(i,l,:)=GrassHopperPositions(i,:);
        
        Trajectories(:,l)=GrassHopperPositions(:,1);
        
        % Update the target
        if GrassHopperFitness(1,i)<TargetFitness
            TargetPosition=GrassHopperPositions(i,:);
            TargetFitness=GrassHopperFitness(1,i);
        end
    end
        
    Convergence_curve(l)=TargetFitness;
    disp(['In iteration #', num2str(l), ' , target''s objective = ', num2str(TargetFitness)])
    
    l = l + 1;
end

 

三、執行結果

四、備註

版本：2014a
完整程式碼或代寫加1564658423