人工原生动物优化器(Artificial Protozoa Optimizer，APO)是发表在中科院一区期刊‘Knowledge-Based Systems’期刊上“Artificial Protozoa Optimizer (APO): A novel bio-inspired metaheuristic algorithm for engineering optimization”这篇文章上的算法。
01.引言
人工原生动物优化器(Artificial Protozoa Optimizer，APO)通过模拟原生动物的觅食、休眠和繁殖行为来模拟原生动物的生存机制。对APO进行数学建模并实现，以执行元启发式算法的优化过程。通过实验仿真验证了APO的性能，并与32种最先进的算法进行了比较。对提出的APO与最先进算法的两两比较采用Wilcoxon符号秩检验，对多重比较采用Friedman检验。首先，使用2022年IEEE进化计算大会基准的12个功能对APO进行了测试。从实用性出发，将该方法应用于具有约束条件的连续空间中求解五种常见的工程设计问题。并将该算法应用于具有约束条件的离散空间中的多级图像分割问题。实验证明，该算法对优化问题具有较强的竞争性。
- APO算法的数学模型基于觅食、休眠和繁殖性能。自养觅食和休眠有助于探索，异养觅食和繁殖有助于开发。
- APO在2022年IEEE进化计算大会基准的单模态、多模态、混合和组合函数下实现和评估。实验结果表明，该算法优于32种最先进的算法。
- APO的有效性通过具有挑战性的现实问题进行了测试，包括五个工程设计和多级图像分割任务。
02.代码流程
03.部分代码
% Artificial Protozoa Optimizer (APO): A novel bio-inspired metaheuristic algorithm for engineering optimization
function [bestProtozoa,bestFit,recordtime] = APO_func(fhd,dim,pop_size,iter_max,Xmin,Xmax,varargin)
% random seeds
stm = RandStream('swb2712','Seed',sum(100*clock));
RandStream.setGlobalStream(stm);
% global best
targetbest = [300;400;600;800;900;1800;2000;2200;2300;2400;2600;2700];
Fidvec = cell2mat(varargin);
Fid = Fidvec(1);
runid = Fidvec(2);
name_convergence_curve = ['APO_Fid_',num2str(Fid),'_',num2str(dim),'D','.dat'];
f_out_convergence = fopen(name_convergence_curve,'a');
ps = pop_size; % ps denotes protozoa size
np = 1; % np denotes neighbor pairs np_max can be set in floor((ps-1)/2)
pf_max = 0.1; % pf_max denotes proportion fraction maximum
% set points to plot convergence_curve
if runid ==1
for i=1:51 % 51 points to plot
if i==1
iteration=1;
fprintf(f_out_convergence,'%s:%s\t','iter_F',num2str(Fid));
else
iteration=iter_max/50*(i-1);
end
fprintf(f_out_convergence,'%d\t',iteration);
end
fprintf(f_out_convergence,'\n');
end
%
tic;
protozoa=zeros(ps,dim); % protozoa
newprotozoa=zeros(ps,dim); % new protozoa
epn=zeros(np,dim); % epn denotes effect of paired neighbors
% initilization
for i = 1:ps
protozoa(i,:) = Xmin + rand(1,dim).*(Xmax-Xmin);
end
% evaluate fitness value
protozoa_Fit = feval(fhd,protozoa',varargin{:});
% find the bestProtozoa and bestFit
[bestval,bestid] = min(protozoa_Fit);
bestProtozoa = protozoa(bestid,:); % bestProtozoa
bestFit = bestval; % bestFit
fprintf(f_out_convergence,'%s\t%.15f\t',num2str(runid),bestFit-targetbest(Fid));
%% Main loop
for iter=2:iter_max
[protozoa_Fit,index] = sort(protozoa_Fit);
protozoa= protozoa(index,:);
pf = pf_max*rand; % proportion fraction
ri=randperm(ps,ceil(ps*pf)); % rank index of protozoa in dormancy or reproduction forms
for i=1:ps
if ismember(i,ri) % protozoa is in dormancy or reproduction form
pdr=1/2*(1+cos((1-i/ps)*pi)); % probability of dormancy and reproduction
if rand<pdr % dormancy form
newprotozoa(i,:)= Xmin + rand(1,dim).*(Xmax-Xmin);
else % reproduction form
flag=[1,-1]; % +- (plus minus)
Flag=flag(ceil(2*rand));
Mr=zeros(1,dim); % Mr is a mapping vector in reproduction
Mr(1,randperm(dim,ceil(rand*dim)))=1;
newprotozoa(i,:)= protozoa(i,:) + Flag*rand*(Xmin+rand(1,dim).*(Xmax-Xmin)).*Mr;
end
else % protozoa is foraging form
f= rand*(1+cos(iter/iter_max*pi)); % foraging factor
Mf=zeros(1,dim); % Mf is a mapping vector in foraging
Mf(1,randperm(dim,ceil(dim*i/ps)))=1;
pah= 1/2*(1+cos(iter/iter_max*pi)); % probability of autotroph and heterotroph
if rand<pah % protozoa is in autotroph form
j= randperm(ps,1); % j denotes the jth randomly selected protozoa
for k=1:np % np denotes neighbor pairs
if i==1
km=i; % km denotes the k- (k minus)
kp=i+randperm(ps-i,1); % kp denotes the k+ (k plus)
elseif i==ps
km=randperm(ps-1,1);
kp=i;
else
km=randperm(i-1,1);
kp=i+randperm(ps-i,1);
end
% wa denotes weight factor in the autotroph forms
wa=exp(-abs(protozoa_Fit(1,km)/(protozoa_Fit(1,kp)+eps)));
% epn denotes effect of paired neighbors
epn(k,:)=wa*(protozoa(km,:)-protozoa(kp,:));
end
newprotozoa(i,:)= protozoa(i,:)+ f*(protozoa(j,:)-protozoa(i,:)+1/np*sum(epn,1)).*Mf;
else % protozoa is in heterotroph form
for k=1:np % np denotes neighbor pairs
if i==1
imk=i; % imk denotes i-k (i minus k)
ipk=i+k; % ipk denotes i+k (i plus k)
elseif i==ps
imk=ps-k;
ipk =i;
else
imk=i-k;
ipk=i+k;
end
% neighbor limit range in [1,ps]
if imk<1
imk=1;
elseif ipk>ps
ipk=ps;
end
% denotes weight factor in the heterotroph form
wh=exp(-abs(protozoa_Fit(1,imk)/(protozoa_Fit(1,ipk)+eps)));
epn(k,:)=wh*(protozoa(imk,:)-protozoa(ipk,:));
end
flag=[1,-1]; % +- (plus minus)
Flag=flag(ceil(2*rand));
Xnear=(1+Flag*rand(1,dim)*(1-iter/iter_max)).* protozoa(i,:);
newprotozoa(i,:)=protozoa(i,:)+f*(Xnear-protozoa(i,:)+1/np*sum(epn,1)).*Mf;
end
end
end
newprotozoa = ((newprotozoa>=Xmin)&(newprotozoa<=Xmax)).*newprotozoa...
+(newprotozoa<Xmin).*Xmin+(newprotozoa>Xmax).*Xmax;
newprotozoa_Fit= feval(fhd,newprotozoa',varargin{:});
bin = (protozoa_Fit > newprotozoa_Fit)';
protozoa(bin==1,:) = newprotozoa(bin==1,:);
protozoa_Fit(bin==1) = newprotozoa_Fit(bin==1);
[bestFit,bestid] = min(protozoa_Fit);
bestProtozoa = protozoa(bestid,:);
if mod(iter,iter_max/50)==0
fprintf(f_out_convergence,'%.15f\t',bestFit-targetbest(Fid));
end
end
recordtime = toc;
fprintf(f_out_convergence,'\n');
fclose(f_out_convergence);
end04.代码效果图
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