【智能优化算法】人工原生动物优化器(APO)

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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 seedsstm = RandStream('swb2712','Seed',sum(100*clock));RandStream.setGlobalStream(stm);
% global besttargetbest = [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 sizenp = 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_curveif  runid ==1for i=1:51 % 51 points to plotif i==1iteration=1;fprintf(f_out_convergence,'%s:%s\t','iter_F',num2str(Fid));elseiteration=iter_max/50*(i-1);endfprintf(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:psprotozoa(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; % bestFitfprintf(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 fractionri=randperm(ps,ceil(ps*pf)); % rank index of protozoa in dormancy or reproduction forms   for i=1:psif ismember(i,ri) %  protozoa is in dormancy or reproduction form  pdr=1/2*(1+cos((1-i/ps)*pi)); % probability of dormancy and reproductionif rand<pdr  % dormancy formnewprotozoa(i,:)=  Xmin + rand(1,dim).*(Xmax-Xmin); else  % reproduction formflag=[1,-1];  % +- (plus minus) Flag=flag(ceil(2*rand));  Mr=zeros(1,dim); % Mr is a mapping vector in reproductionMr(1,randperm(dim,ceil(rand*dim)))=1;newprotozoa(i,:)= protozoa(i,:) + Flag*rand*(Xmin+rand(1,dim).*(Xmax-Xmin)).*Mr; endelse  % protozoa is foraging formf= rand*(1+cos(iter/iter_max*pi)); % foraging factorMf=zeros(1,dim);  % Mf is a mapping vector in foragingMf(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 protozoafor k=1:np % np denotes neighbor pairs  if i==1km=i; % km denotes the k- (k minus)kp=i+randperm(ps-i,1); % kp denotes the k+ (k plus)elseif i==pskm=randperm(ps-1,1);kp=i;elsekm=randperm(i-1,1);kp=i+randperm(ps-i,1);end% wa denotes weight factor in the autotroph formswa=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==1imk=i;   % imk denotes i-k (i minus k)ipk=i+k; % ipk denotes i+k (i plus k)elseif i==psimk=ps-k;ipk =i;elseimk=i-k;ipk=i+k;end% neighbor limit range in [1,ps]if  imk<1imk=1;elseif ipk>psipk=ps;end% denotes weight factor in the heterotroph formwh=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;              endendendnewprotozoa = ((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)==0fprintf(f_out_convergence,'%.15f\t',bestFit-targetbest(Fid));end    endrecordtime = toc;fprintf(f_out_convergence,'\n');fclose(f_out_convergence);
end