人工蜂群算法对Fisher的优化
%人工蜂群算法第一次应用
%experiment.m
clear all %preprocessing预处理
close all
clc
%图像预处理
I=imread(‘E:\lena512.bmp‘);
%R=imread(‘E:\Home.jpg‘);
%R=imread(‘E:\bird.jpg‘);
%R=imread(‘E:\car.bmp‘);
%R=imread(‘peppers.png‘);
%I=imread(‘AT3_1m4_01.tif‘);
%I=imread(‘rice.png‘);
%I=rgb2gray(R);
%二维直方图平面分布图
row=size(I,1);
column=size(I,2);
M=zeros(256,256);%区域平均灰度值图像
for i=1:row
for j=1:column
k=0;
for i1=-1:1
for i2=-1:1
try %边缘区域处理
k=k+I(i+i1,j+i2)/9;
catch
%k=k;
end
end
end%邻域平均值计算
M(I(i,j)+1,k+1)=M(I(i,j)+1,k+1)+1;%记录用以生成像素周边区域平均像素
%M1(i,j)=k;
end %图像循环
end
%人工蜂群算法部分
NP=50; %蜂群规模
FoodNumber=NP/2; %食物源数量
limit=100; %/*A food source which could not be improved through "limit" trials is abandoned by its employed bee*/蜂群规模*维数比较合适
maxCycle=600; %觅食周期数--循环次数
%参数定义
objfun=‘SCFisher‘; %cost function to be optimized 成本函数
D=4; %/*The number of parameters of the problem to be optimized 要优化参数数量*/
ub=ones(1,D)*255; %/*lower bounds of the parameters. 参数下界*/
lb=ones(1,D)*(1);%/*upper bound of the parameters.*/
runtime=1;%/*Algorithm can be run many times in order to see its robustness*/鲁棒性检测
GlobalMins=zeros(1,runtime);
for r=1:runtime
% /*All food sources are initialized */解空间生成
%/*Variables are initialized in the range [lb,ub]. If each parameter has different range, use arrays lb[j], ub[j] instead of lb and ub */
Range = repmat((ub-lb),[FoodNumber 1]);
Lower = repmat(lb, [FoodNumber 1]);
Foods = rand(FoodNumber,D) .* Range + Lower;
Foods=round(Foods);
ObjVal=feval(objfun,Foods,M);
Fitness=calculateFitness(ObjVal);
%reset trial counters
trial=zeros(1,FoodNumber);
%/*The best food source is memorized*/
BestInd=find(ObjVal==min(ObjVal));
BestInd=BestInd(end);
GlobalMin=ObjVal(BestInd);
GlobalParams=Foods(BestInd,:);
iter=1;
while ((iter <= maxCycle)),
%%%%%%%%% EMPLOYED BEE PHASE 雇佣蜂%%%%%%%%%%%%%%%%%%%%%%%%
for i=1:(FoodNumber)
%/*The parameter to be changed is determined randomly*/
Param2Change=fix(rand*D)+1;
%/*A randomly chosen solution is used in producing a mutant solution of the solution i*/
neighbour=fix(rand*(FoodNumber))+1;
%/*Randomly selected solution must be different from the solution i*/
while(neighbour==i)
neighbour=fix(rand*(FoodNumber))+1;
end;
sol=Foods(i,:);
% /*v_{ij}=x_{ij}+\phi_{ij}*(x_{kj}-x_{ij}) */
sol(Param2Change)=Foods(i,Param2Change)+(Foods(i,Param2Change)-Foods(neighbour,Param2Change))*(rand-0.5)*2;
sol=round(sol);
% /*if generated parameter value is out of boundaries, it is shifted onto the boundaries*/
ind=find(sol<lb);
sol(ind)=lb(ind);
ind=find(sol>ub);
sol(ind)=ub(ind);
%evaluate new solution
ObjValSol=feval(objfun,sol,M);
FitnessSol=calculateFitness(ObjValSol);
% /*a greedy selection is applied between the current solution i and its mutant*/
if (FitnessSol>Fitness(i)) %/*If the mutant solution is better than the current solution i, replace the solution with the mutant and reset the trial counter of solution i*/
Foods(i,:)=sol;
Fitness(i)=FitnessSol;
ObjVal(i)=ObjValSol;
trial(i)=0;
else
trial(i)=trial(i)+1; %/*if the solution i can not be improved, increase its trial counter*/
end;
end;
%%%%%%%%%%%%%%%%%%%%%%%% CalculateProbabilities %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%/* A food source is chosen with the probability which is proportioal to its quality*/
%/*Different schemes can be used to calculate the probability values*/
%/*For example prob(i)=fitness(i)/sum(fitness)*/
%/*or in a way used in the metot below prob(i)=a*fitness(i)/max(fitness)+b*/
%/*probability values are calculated by using fitness values and normalized by dividing maximum fitness value*/
prob=(0.9.*Fitness./max(Fitness))+0.1;
%%%%%%%%%%%%%%%%%%%%%%%% ONLOOKER BEE PHASE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
i=1;
t=0;
while(t<FoodNumber)
if(rand<prob(i))
t=t+1;
%/*The parameter to be changed is determined randomly*/
Param2Change=fix(rand*D)+1;
%/*A randomly chosen solution is used in producing a mutant solution of the solution i*/
neighbour=fix(rand*(FoodNumber))+1;
%/*Randomly selected solution must be different from the solution i*/
while(neighbour==i)
neighbour=fix(rand*(FoodNumber))+1;
end;
sol=Foods(i,:);
% /*v_{ij}=x_{ij}+\phi_{ij}*(x_{kj}-x_{ij}) */
sol(Param2Change)=Foods(i,Param2Change)+(Foods(i,Param2Change)-Foods(neighbour,Param2Change))*(rand-0.5)*2;
sol=round(sol);
% /*if generated parameter value is out of boundaries, it is shifted onto the boundaries*/
ind=find(sol<lb);
sol(ind)=lb(ind);
ind=find(sol>ub);
sol(ind)=ub(ind);
%evaluate new solution
ObjValSol=feval(objfun,sol,M);
FitnessSol=calculateFitness(ObjValSol);
% /*a greedy selection is applied between the current solution i and its mutant*/
if (FitnessSol>Fitness(i)) %/*If the mutant solution is better than the current solution i, replace the solution with the mutant and reset the trial counter of solution i*/
Foods(i,:)=sol;
Fitness(i)=FitnessSol;
ObjVal(i)=ObjValSol;
trial(i)=0;
else
trial(i)=trial(i)+1; %/*if the solution i can not be improved, increase its trial counter*/
end;
end;
i=i+1;
if (i==(FoodNumber)+1)
i=1;
end;
end;
%/*The best food source is memorized*/
ind=find(ObjVal==min(ObjVal));
ind=ind(end);
if (ObjVal(ind)<GlobalMin)
GlobalMin=ObjVal(ind);
GlobalParams=Foods(ind,:);
end;
%%%%%%%%%%%% SCOUT BEE PHASE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%/*determine the food sources whose trial counter exceeds the "limit" value.
%In Basic ABC, only one scout is allowed to occur in each cycle*/
ind=find(trial==max(trial));
ind=ind(end);
if (trial(ind)>limit)
Bas(ind)=0;
sol=(ub-lb).*rand(1,D)+lb;
sol=round(sol);
ObjValSol=feval(objfun,sol,M);
FitnessSol=calculateFitness(ObjValSol);
Foods(ind,:)=sol;
Fitness(ind)=FitnessSol;
ObjVal(ind)=ObjValSol;
end;
%fprintf(‘iter=%d ObjVal=%g\n‘,iter,GlobalMin);
iter=iter+1;
end % End of ABC
GlobalMins(r)=GlobalMin;
end; %end of runs
%fprintf(‘pos=%g\n‘,mean(pos,2));
fprintf(‘mean=%g\n‘,mean(GlobalMins));
save all
%人工蜂群算法部分结束
%根据阈值进行图像分割
BestValue=[(GlobalParams(1)+GlobalParams(3))/2 (GlobalParams(2)+GlobalParams(4))/2];
if BestValue(1)>BestValue(2)
cach=BestValue(1);
BestValue(1)=BestValue(2);
BestValue(2)=cach;
end
for i=1:row
for j=1:column
if(I(i,j)>=BestValue(1)&&I(i,j)<=BestValue(2))
K(i,j)=255;
else
K(i,j)=0;
end
end
end
figure;
subplot(121);imshow(I);
subplot(122);imshow(K);
二维Fisher算法
%SCFisher.m
function ObjVal = SCFisher( Chrom,M)
%代价函数
FoodNumber=size(Chrom,1);
ObjVal=zeros(1,FoodNumber);
for fn=1:FoodNumber
s1=Chrom(fn,1);
s2=Chrom(fn,2);
t1=Chrom(fn,3);
t2=Chrom(fn,4);
%二维直方图预处理
%求解H（i）
H=zeros(1,256);
for i=1:256
sum=0;
for j=1:256
sum=sum+M(i,j);
end
H(i)=sum;
end
%求解W（j）
W=zeros(1,256);
for j=1:256
sum=0;
for i=1:256
sum=sum+M(i,j);
end
W(j)=sum;
end
%μi0的计算
sum0=0;
sum1=0;
for s=s1:s2
sum0=sum0+(s)*H(s);
sum1=sum1+H(s);
end
ui0=sum0/sum1;
%μj0的计算
sum0=0;
sum1=0;
for t=t1:t2
sum0=sum0+(t)*W(t);
sum1=sum1+W(t);
end
uj0=sum0/sum1;
%μi1的计算
sum0=0;
sum1=0;
for s=1:s1
sum0=sum0+(s)*H(s);
sum1=sum1+H(s);
end
for s=s2:256
sum0=sum0+(s)*H(s);
sum1=sum1+H(s);
end
ui1=sum0/sum1;
%μj1的计算
sum0=0;
sum1=0;
for t=1:t1
sum0=sum0+(t)*W(t);
sum1=sum1+W(t);
end
for t=t2:256
sum0=sum0+(t)*W(t);
sum1=sum1+W(t);
end
uj1=sum0/sum1;
%σi02的计算
qi0=0;
for s=s1:s2
mul=(s-ui0)*(s-ui0)*H(s);
qi0=qi0+mul;
end
%σj02的计算
qj0=0;
for t=t1:t2
mul=(t-uj0)*(t-uj0)*W(t);
qj0=qj0+mul;
end
%σi12的计算
qi1=0;
for s=1:s1
mul=(s-ui1)*(s-ui1)*H(s);
qi1=qi1+mul;
end
for s=s2:256
mul=(s-ui1)*(s-ui1)*H(s);
qi1=qi1+mul;
end
%σj12的计算
qj1=0;
for t=1:t1
mul=(t-uj1)*(t-uj1)*W(t);
qj1=qj1+mul;
end
for t=t2:256
mul=(t-uj1)*(t-uj1)*W(t);
qj1=qj1+mul;
end
%Jf(s,t)
ujf=([ui0,uj0]-[ui1,uj1])*([ui0,uj0]-[ui1,uj1])‘;
djf=qi0+qj0+qi1+qj1;
%Jf=ujf/djf;
ObjVal(fn)=djf/ujf;
%ObjVal(fn)=ujf/djf;
end
end
评估函数
%calculateFitness.m
function fFitness=calculateFitness(fObjV)
fFitness=zeros(size(fObjV));
ind=find(fObjV>=0);
fFitness(ind)=1./(fObjV(ind)+1);
ind=find(fObjV<0);
fFitness(ind)=1+abs(fObjV(ind));
原文：https://www.cnblogs.com/zhoushuaiyi/p/14670717.html