1 简介
灰狼群体具有严格的社会支配等级且其等级划分呈金字塔形式，在捕捉猎物时，灰狼是通过相交流共享的体制来模拟的。其他智能算法类似的是，每一个可能解都由每头灰狼的位置来对应。种群的发展需要不断地更新，为了选出 3 只头狼，种群内的狼将被逐一进行评价，在这个过程中，算法起到评价的作用。接下来前进的方向将由这 3只头狼的位置所决定。由于灰狼算法参数较少，收敛较快，所以广泛应用于众多领域，尤其是实际工程领域应用最广。在该算法中，狼群通过竞选选出α 狼作为头狼，就意味着 α 狼将处于金字塔顶端的位置，同时 α 狼群做的所有决定都将代表整个狼群，但这并非表示狼群是全部专制的，在某种程度上也有一定的民主，比如狼群中有时也会存在其他的狼。当有任务需要执行时，α 狼将发号施令，其余狼群只需配合执行即可，因此 α 狼也就当之无愧的成为了狼群中最主要的狼。当狼群需要交配时，只能选择在自己的群体中进行交配。值得一提的是，α 狼之所以成为最主要的狼，其原因并不在于 α狼是最强的，而在于它拥有其他狼所不具备的优越的组织管理的能力。在狼群中 β 狼的地位近乎于 α 狼，这一点可以从狼群执行的其他群体活动中看出，β 狼是第二决策者。 β 狼在活动中都需要听从α 狼的指挥，同时其他更低级别的狼群也要听从它的指挥。在灰狼群体中，位于第三等级是 δ 狼，在严格的等级制度中，δ 狼必须遵从 α 狼和 β 狼的命令，δ 狼不是最低一级，在它的下一级还存在着 ω 狼，ω 狼在整个群体中担任侦查和围捕猎物的责任，也是灰狼群体中等级最低的。虽然它们看起来无足轻重，但一旦失去它们这一群体，整个灰狼种群都将面临着基层缺失的危险，所以也可以看出它们是狼群的重要组成部分。
2 部分代码
%___________________________________________________________________%
% Multi-Objective Grey Wolf Optimizer (MOGWO) %
% Source codes demo version 1.0 %
%
clear all
clc
drawing_flag = 1;
TestProblem='UF2';
nVar=10;
fobj = cec09(TestProblem);
xrange = xboundary(TestProblem, nVar);
% Lower bound and upper bound
lb=xrange(:,1)';
ub=xrange(:,2)';
VarSize=[1 nVar];
GreyWolves_num=100;
MaxIt=1000; % Maximum Number of Iterations
Archive_size=100; % Repository Size
alpha=0.1; % Grid Inflation Parameter
nGrid=10; % Number of Grids per each Dimension
beta=4; %=4; % Leader Selection Pressure Parameter
gamma=2; % Extra (to be deleted) Repository Member Selection Pressure
% Initialization
GreyWolves=CreateEmptyParticle(GreyWolves_num);
for i=1:GreyWolves_num
GreyWolves(i).Velocity=0;
GreyWolves(i).Position=zeros(1,nVar);
for j=1:nVar
GreyWolves(i).Position(1,j)=unifrnd(lb(j),ub(j),1);
end
GreyWolves(i).Cost=fobj(GreyWolves(i).Position')';
GreyWolves(i).Best.Position=GreyWolves(i).Position;
GreyWolves(i).Best.Cost=GreyWolves(i).Cost;
end
GreyWolves=DetermineDomination(GreyWolves);
Archive=GetNonDominatedParticles(GreyWolves);
Archive_costs=GetCosts(Archive);
G=CreateHypercubes(Archive_costs,nGrid,alpha);
for i=1:numel(Archive)
[Archive(i).GridIndex Archive(i).GridSubIndex]=GetGridIndex(Archive(i),G);
end
% MOGWO main loop
for it=1:MaxIt
a=2-it*((2)/MaxIt);
for i=1:GreyWolves_num
clear rep2
clear rep3
% Choose the alpha, beta, and delta grey wolves
Delta=SelectLeader(Archive,beta);
Beta=SelectLeader(Archive,beta);
Alpha=SelectLeader(Archive,beta);
% If there are less than three solutions in the least crowded
% hypercube, the second least crowded hypercube is also found
% to choose other leaders from.
if size(Archive,1)>1
counter=0;
for newi=1:size(Archive,1)
if sum(Delta.Position~=Archive(newi).Position)~=0
counter=counter+1;
rep2(counter,1)=Archive(newi);
end
end
Beta=SelectLeader(rep2,beta);
end
% This scenario is the same if the second least crowded hypercube
% has one solution, so the delta leader should be chosen from the
% third least crowded hypercube.
if size(Archive,1)>2
counter=0;
for newi=1:size(rep2,1)
if sum(Beta.Position~=rep2(newi).Position)~=0
counter=counter+1;
rep3(counter,1)=rep2(newi);
end
end
Alpha=SelectLeader(rep3,beta);
end
% Eq.(3.4) in the paper
c=2.*rand(1, nVar);
% Eq.(3.1) in the paper
D=abs(c.*Delta.Position-GreyWolves(i).Position);
% Eq.(3.3) in the paper
A=2.*a.*rand(1, nVar)-a;
% Eq.(3.8) in the paper
X1=Delta.Position-A.*abs(D);
% Eq.(3.4) in the paper
c=2.*rand(1, nVar);
% Eq.(3.1) in the paper
D=abs(c.*Beta.Position-GreyWolves(i).Position);
% Eq.(3.3) in the paper
A=2.*a.*rand()-a;
% Eq.(3.9) in the paper
X2=Beta.Position-A.*abs(D);
% Eq.(3.4) in the paper
c=2.*rand(1, nVar);
% Eq.(3.1) in the paper
D=abs(c.*Alpha.Position-GreyWolves(i).Position);
% Eq.(3.3) in the paper
A=2.*a.*rand()-a;
% Eq.(3.10) in the paper
X3=Alpha.Position-A.*abs(D);
% Eq.(3.11) in the paper
GreyWolves(i).Position=(X1+X2+X3)./3;
% Boundary checking
GreyWolves(i).Position=min(max(GreyWolves(i).Position,lb),ub);
GreyWolves(i).Cost=fobj(GreyWolves(i).Position')';
end
GreyWolves=DetermineDomination(GreyWolves);
non_dominated_wolves=GetNonDominatedParticles(GreyWolves);
Archive=[Archive
non_dominated_wolves];
Archive=DetermineDomination(Archive);
Archive=GetNonDominatedParticles(Archive);
for i=1:numel(Archive)
[Archive(i).GridIndex Archive(i).GridSubIndex]=GetGridIndex(Archive(i),G);
end
if numel(Archive)>Archive_size
EXTRA=numel(Archive)-Archive_size;
Archive=DeleteFromRep(Archive,EXTRA,gamma);
Archive_costs=GetCosts(Archive);
G=CreateHypercubes(Archive_costs,nGrid,alpha);
end
disp(['In iteration ' num2str(it) ': Number of solutions in the archive = ' num2str(numel(Archive))]);
save results
% Results
costs=GetCosts(GreyWolves);
Archive_costs=GetCosts(Archive);
if drawing_flag==1
hold off
plot(costs(1,:),costs(2,:),'k.');
hold on
plot(Archive_costs(1,:),Archive_costs(2,:),'rd');
legend('Grey wolves','Non-dominated solutions');drawnow
end
end
3 仿真结果
4 参考文献
[1]孟安波, and 林艺城. "一种基于多目标的改进灰狼优化算法.", CN107067121A. 2017.
