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⛄ 内容介绍
本研究提出了一种稳健的方法，使用基于帕累托的归档机制和基于拥挤距离的归档处理机制来提高多目标进化算法 (MOEA) 的搜索性能。所提出方法的目的是在目标和决策空间中提供可持续的多样性，并在两个空间中建立稳定的开发-探索平衡。为此：1) 定义了参考空间组合，2) 开发了由参考空间组合组成的策略以提高拥挤距离计算的性能，以及 3) 提出了一种动态切换机制来实现这些策略。在所提出的 DSC 方法中，非支配解在三个不同的参考空间中表示：决策空间、目标空间、以及这两个空间的统一结果。创建了这三个空间的二进制组合，并开发了使用不同参考空间的策略。切换机制旨在动态地实施这些策略。参考由该切换机制选择的空间向量执行拥挤距离计算。所提出的 DSC 方法在多模态多目标优化问题 (MMOP) 和结合交流最优功率流 (AC-OPF) 和交流/直流最优功率流 (AC/DC-OPF) 的实际工程问题上进行了测试. 根据实验研究结果，与竞争对手相比，所提出的 DSC-MOAGDE 算法在 MMOP 上的成功率提高了约 30%。同样，所提出的方法能够将成本优化 6.66%、24.15%、52。
⛄ 部分代码
function [bestFitness]=MOAGDE_SingerMap_Cr3(NP,funnum)
[fname,D, n_obj, L, H] = terminate_problem(funnum);
GEN = 50;
problemName = strcat("@",fname);
ObjectiveFunction=eval(problemName);
X = zeros(D,1); % trial vector
Pop = zeros(D,NP); % population
Fit = zeros(NP,n_obj); % fitness of the population
r = zeros(3,1); % randomly selected indices
Archive_member_no = 0;
bestFitness=inf*ones(1,n_obj);
Archive_X=zeros(NP,D);
Archive_F=ones(NP,n_obj)*inf;
ArchiveMaxSize = NP;
% *********************** %
% ** CREATE POPULATION ** %
% *********************** %
for j = 1:NP % initialize each individual
Pop(:,j) = L + (H-L).*rand(1,D); % within b.constraints
end
Cr_All=zeros(1,2);
NW=zeros(1,2);
global chaosMap
SingerMap(GEN+10)
for g = 1:GEN % for each generation
for i=1:NP %Calculate all the objective values first
Fit(i,:)=ObjectiveFunction(Pop(:,i)');
if dominates(Fit(i,:),bestFitness)
bestFitness=Fit(i,:);
end
end
[Archive_X, Archive_F, Archive_member_no]=UpdateArchive(Archive_X, Archive_F, Pop', Fit, Archive_member_no);
if Archive_member_no>ArchiveMaxSize
Archive_X_F = [Archive_X Archive_F];
Norm_Archive_X_F = Normalize(Archive_X_F);
Norm_Archive_X = Normalize(Archive_X);
if(rand()>chaosMap(g))
Archive_mem_ranks_X=RankingProcess(Norm_Archive_X, ArchiveMaxSize, D);
[Archive_X, Archive_F, ~, Archive_member_no]=HandleFullArchive(Archive_X, Archive_F, Archive_member_no, Archive_mem_ranks_X, ArchiveMaxSize);
else
Archive_mem_ranks_X_F=RankingProcess(Norm_Archive_X_F, ArchiveMaxSize, (n_obj+D));
[Archive_X, Archive_F, ~, Archive_member_no]=HandleFullArchive(Archive_X, Archive_F, Archive_member_no, Archive_mem_ranks_X_F, ArchiveMaxSize);
end
end
Norm_Archive_X = Normalize(Archive_X);
Archive_mem_ranks_X=RankingProcess(Norm_Archive_X, Archive_member_no, D);
index=RouletteWheelSelection(1./Archive_mem_ranks_X);
if index==-1
index=1;
end
% Update the best Organism
bestSolution=Archive_X(index,:);
bestFitness=Archive_F(index,:);
Norm_Archive_F = Normalize(Archive_F);
Archive_mem_ranks_F=RankingProcess(Norm_Archive_F, Archive_member_no, n_obj);
Norm_Fit = Normalize(Fit);
allRank=RankingProcess(Norm_Fit, ArchiveMaxSize, n_obj);
CrPriods_Index=zeros(1,NP);
Sr=zeros(1,2);
CrPriods_Count=zeros(1,2);
for j = 1:NP % for each individual
%%%%%%%%ADAPTIVE CR RULE %%%%%%%%%%%%%%%%%%%%%%%%%
Ali = rand;
if(g<=1) % Do for the first Generation
if (Ali<=1/2)
CR=0.05+0.1*rand(1,1);
CrPriods_Index(j)=1;
else
CR=0.9+0.1*rand(1,1);
CrPriods_Index(j)=2;
end
CrPriods_Count(CrPriods_Index(j))=CrPriods_Count(CrPriods_Index(j)) + 1;
else
if (Ali<=NW(1))
CR=0.05+0.1*rand(1,1);
CrPriods_Index(j)=1;
else
CR=0.9+0.1*rand(1,1);
CrPriods_Index(j)=2;
end
CrPriods_Count(CrPriods_Index(j))=CrPriods_Count(CrPriods_Index(j)) + 1;
end
%%%%%%%%%%%%%%%%%END OF CR RULE%%%%%%%%%%%%%%%%%%%%%%%%%%%
indexs_Archive = [];
while(size(indexs_Archive) < 3)
index=RouletteWheelSelection(1./Archive_mem_ranks_F);
if ismember(index,indexs_Archive) == 0
indexs_Archive = [indexs_Archive index];
end
end
indexs_Pop = [];
while(size(indexs_Pop) < 3)
index=RouletteWheelSelection(1./allRank);
if ismember(index,indexs_Pop) == 0
indexs_Pop = [indexs_Pop index];
end
end
r(1) = indexs_Pop(1);
r(2) = indexs_Archive(1);
r(3) = indexs_Pop(2);
F=0.1+0.9*rand(1,1);
Archive_Pop = Archive_X';
Rnd = floor(rand()*D) + 1;
for i = 1:D
if ( rand()<CR ) || ( Rnd==i )
X(i)=Pop(i,r(3))+F*(Pop(i,r(1))-(Archive_Pop(i,r(2))));
else
%X(i) = Pop(i,j);
X(i) = bestSolution(i);
end
end
% end%end of All cases
% verify boundary constraints
% verify boundary constraints
for i = 1:D
if (X(i)<L(i))||(X(i)>H(i))
X(i) = L(i) + (H(i)-L(i))*rand();
end
end
% select the best individual
% between trial and current ones
% calculate fitness of trial individual
XPf=ObjectiveFunction(X');
% if trial is better or equal than current
% CRRatio(find(A==CRs(j)))=CRRatio(find(A==CRs(j)))+1-(min(f,Fit(j))/max(f,Fit(j)));
Sr (CrPriods_Index(j)) = Sr(CrPriods_Index(j)) +1;
Pop(:,j) = X; % replace current by trial
Fit(j,:) = XPf ;
% if trial is better than the best
end
CrPriods_Count(CrPriods_Count==0)=0.0001;
Sr=Sr./CrPriods_Count;
%%%%%%%%%%%%%%%%USING SR ONLY%%%%%%%%%%5
if(sum(Sr)==0)
W=[1/2 1/2];
else
W=Sr/sum(Sr);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%5
NW=(NW*(g-1)+W)/g;
Cr_All=Cr_All+CrPriods_Count;
display(['At the iteration ', num2str(g), ' best fitness ', num2str(bestFitness)]);
end
end
⛄ 运行结果
⛄ 参考文献
KAHRAMAN, H. T., AKBEL, M., DUMAN, S., KATI, M., SAYAN, H. H. (2022). Unified Space Approach-based Dynamic Switched Crowding (DSC): A New Method for Designing Pareto-based Multi/Many-Objective Algorithms, Swarm and Evolutionary Computation, 101196, https://doi.org/10.1016/j.swevo.2022.101196
