【优化求解】基于蝗虫算法求解单目标问题附matlab代码

1 简介

蝗虫算法( Grasshopper Optimization Algorithm，GOA ) 是由 Saremi 等[1]于2017 年提出的一种元启发式仿生优化算法。具体原理如下：

2 部分代码

%_____________________________

% Multi-objective Grasshopper Optimization Algorithm (MOGOA) source codes version 1.0

clc;

clear;

close all;

% Change these details with respect to your problem%%%%%%%%%%%%%%

ObjectiveFunction=@ZDT1;

dim=5;

lb=0;

ub=1;

obj_no=2;

if size(ub,2)==1

ub=ones(1,dim)*ub;

lb=ones(1,dim)*lb;

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

flag=0;

if (rem(dim,2)~=0)

dim = dim+1;

ub = [ub, 1];

lb = [lb, 0];

flag=1;

end

max_iter=100;

N=200;

ArchiveMaxSize=100;

Archive_X=zeros(100,dim);

Archive_F=ones(100,obj_no)*inf;

Archive_member_no=0;

%Initialize the positions of artificial whales

GrassHopperPositions=initialization(N,dim,ub,lb);

TargetPosition=zeros(dim,1);

TargetFitness=inf*ones(1,obj_no);

cMax=1;

cMin=0.00004;

%calculate the fitness of initial grasshoppers

for iter=1:max_iter

for i=1:N

Archive_mem_ranks=RankingProcess(Archive_F, ArchiveMaxSize, obj_no);

[Archive_X, Archive_F, Archive_mem_ranks, Archive_member_no]=HandleFullArchive(Archive_X, Archive_F, Archive_member_no, Archive_mem_ranks, ArchiveMaxSize);

else

Archive_mem_ranks=RankingProcess(Archive_F, ArchiveMaxSize, obj_no);

end

Archive_mem_ranks=RankingProcess(Archive_F, ArchiveMaxSize, obj_no);

index=RouletteWheelSelection(1./Archive_mem_ranks);

if index==-1

index=1;

end

TargetFitness=Archive_F(index,:);

TargetPosition=Archive_X(index,:)';

c=cMax-iter*((cMax-cMin)/max_iter); % Eq. (3.8) in the paper

for i=1:N

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));

r_ij_vec=(temp(k:k+1,j)-temp(k:k+1,i))/(Dist+eps);

xj_xi=2+rem(Dist,2);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Eq. (3.2) in the paper

s_ij=((ub(k:k+1)' - lb(k:k+1)') .c/2)S_func(xj_xi).*r_ij_vec;

S_i=S_i+s_ij;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

end

S_i_total(k:k+1, :) = S_i;

end

X_new=c*S_i_total'+(TargetPosition)'; % Eq. (3.7) in the paper

GrassHopperPositions_temp(i,:)=X_new';

end

% GrassHopperPositions

GrassHopperPositions=GrassHopperPositions_temp';

display(['At the iteration ', num2str(iter), ' there are ', num2str(Archive_member_no), ' non-dominated solutions in the archive']);

end

if (flag==1)

TargetPosition = TargetPosition(1:dim-1);

end

figure

Draw_ZDT1();

hold on

plot(Archive_F(:,1),Archive_F(:,2),'ro','MarkerSize',8,'markerfacecolor','k');

legend('True PF','Obtained PF');

title('MOGOA');

set(gcf, 'pos', [403 466 230 200])

img =gcf; %获取当前画图的句柄

print(img, '-dpng', '-r600', './img.png') %即可得到对应格式和期望dpi的图像

3 仿真结果

4 参考文献

[1]潘峰, and 孙红霞. "基于蝗虫算法的图像多阈值分割方法." 电子测量与仪器学报 033.001(2019):149-155.

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