2018年ASOC SCI1区TOP，混合灰狼算法HBBOG，深度解析+性能实测

---

1.摘要

为提升生物地理优化算法（BBO）的通用性与性能，本文提出一种混合灰狼算法（HBBOG）。HBBOG算法首先对BBO去除传统变异算子并引入差分变异机制，提高全局搜索能力；同时采用多重迁移操作，增强局部搜索能力。GWO则引入对立学习策略，以避免陷入局部最优。HBBOG算法通过单维与全维交替策略将改进后的BBO与GWO进行有机融合，兼顾了算法的全局探索与局部开发能力。

2.算法原理回顾

【智能算法】灰狼算法（GWO）原理及实现

BBO：生物地理优化算法

3.改进策略

差分变异策略

差分进化（DE）是一种鲁棒性较强的进化算法，它利用当前种群中的距离和方向信息来引导后续搜索。DE中的差分操作具有良好的全局搜索能力，论文去除了BBO中变异算子，将一种更高效的差分变异操作融合到BBO的迁移算子：
$$\begin{array}{rl}& H_i(SI{V}_j)⟵H_i(SI{V}_j)+{\alpha }_d\ast (H_{best}(SI{V}_j)-H_i(SI{V}_j)\\ & +H_{rn1}(SI{V}_j)-H_{rn2}(SI{V}_j))\end{array}$$

差分变异通过引入多个栖息地之间的差分信息，增强了个体的多样性和种群的全局探索能力。个体不仅结合自身信息，还融合了最优解与其他栖息地之间的差分结果，借助加权机制实现更丰富的信息更新。

示例学习方法

为提升迁移操作的效率与引导性，论文不采用BBO中的轮盘赌策略进行选择，示例学习方法依据个体适应度（HSI）对种群进行排序，将每个个体前面适应度更优的个体视为其示例。
$$SI=ceil((i-1)\ast rand)$$

多重迁移算子

为了在增强BBO全局搜索能力的同时实现探索与开发的平衡，还需提升其局部搜索能力。在BBO的迁移算子中引入了多重迁移操作，以替代原有的迁移机制：
$$H_i(SI{V}_j)⟵H_{SI}(SI{V}_j)+{\alpha }_h\ast (0.5-rand)\ast (H_i(SI{V}_j)-H_{SI}(SI{V}_j))$$
$${\alpha }_h=2\sqrt{t/MaxDT}$$

单维和全维交替策略

在大多数进化算法中，更新通常采用全维度方式，具备较快的收敛速度，适合局部搜索。在人工蜂群算法及其变种中，采用的是单维度更新方式，能更有效地保持种群多样性，适用于全局搜索。单维和全维交替策略通过随机维度选择与维度循环机制灵活切换。

流程图

4.结果展示

5.参考文献

[1] Zhang X, Kang Q, Cheng J, et al. A novel hybrid algorithm based on biogeography-based optimization and grey wolf optimizer[J]. Applied Soft Computing, 2018, 67: 197-214.

6.代码获取

function [Alpha_score,Cbest,Alpha_pos]=HBBOG(f,a,b,d,M,N)%混合差分扰动和趋优迁移的BBO算法
% Hybrid Biogeography Based Optimization with Grey wolf optimization(HBBOG)Alpha_pos=zeros(1,d);
Alpha_score=inf; %change this to -inf for maximization problems
Beta_pos=zeros(1,d);
Beta_score=inf; %change this to -inf for maximization problems
Delta_pos=zeros(1,d);
Delta_score=inf; %change this to -inf for maximization problems
lambdaLower = 0.0; % lower bound for immigration probabilty per gene
lambdaUpper = 1; % upper bound for immigration probabilty per gene
Ib = 1; % max immigration rate for each island
Eb = 1; % max emigration rate, for each island
P = N; % max species count, for each island
dn=d+1;
X=rand(N,d+1);
aa=repmat(a,N,1);
bb=repmat(b,N,1);
X(:,1:d)=aa+(bb-aa).*X(:,1:d);
X(:,d+1)=feval(f, X(:,1:d));fit=X(:,d+1);
X = PopSort(X);
for i=1:Nif fit(i)<Alpha_scoreAlpha_score=fit(i); % Update alphaAlpha_pos=X(i,1:d);endif fit(i)>Alpha_score && fit(i)<Beta_scoreBeta_score=fit(i); % Update betaBeta_pos=X(i,1:d);endif fit(i)>Alpha_score && fit(i)>Beta_score && fit(i)<Delta_scoreDelta_score=fit(i); % Update deltaDelta_pos=X(i,1:d);end
endSpeciesCount=zeros(1);
lambda=zeros(1);
mu=zeros(1);
for j = 1 : Nif X(j,d+1) < infSpeciesCount(j) = P - j;elseSpeciesCount(j) = 0;endlambda(j) = Ib * (1 - SpeciesCount(j) / P);mu(j) = Eb * SpeciesCount(j) / P;    
end
lambdaMin = min(lambda);
lambdaMax = max(lambda);
lambdaScale = lambdaLower + (lambdaUpper - lambdaLower) * (lambda - lambdaMin) / (lambdaMax - lambdaMin);
Cbest=zeros(1,M);
Ped=0.5;a1=4;a2=2;
l=0;
while l<M    p=sqrt(l/M);Positions=X(:,1:d);as=1-l*((1-0)/M);if l<1*M/2for k = 1 : Nalfa=rand^1;j=ceil(rand*d);            if rand < lambdaScale(k)% Pick a habitat from which to obtain a featureSelectIndex=ceil((k-1)*rand);                if rand>pif rand<0.5Positions(k,j) =X(SelectIndex,j);elsecnum=ceil(rand*d);Positions(k,j) =X(SelectIndex,cnum); endelse                    Positions(k,j) =X(SelectIndex,j)+2*p*(0.5-rand)*(X(k,j)-X(SelectIndex,j));endelsernum=ceil(N*rand);while rnum==k,rnum=ceil(N*rand);endrnum1=ceil(N*rand);while rnum1==k ||rnum1==rnum,rnum1=ceil(N*rand);end                Positions(k,j) = X(k,j)+alfa*(X(1,j)-X(k,j)+X(rnum1,j)-X(rnum,j));                              end            end        elseif rand<PedNum=ceil(N*rand);           for i=1:Nif i==Num                   Positions(i,:)=a+(b-Alpha_pos);elseif rand<=0.5k=ceil(rand*d);X1=Alpha_pos(k)-a1*as*(2*rand-1)*abs(2*rand*Alpha_pos(k)-Positions(i,k));X2=Beta_pos(k)-a1*as*(2*rand-1)*abs(2*rand*Beta_pos(k)-Positions(i,k));X3=Delta_pos(k)-a1*as*(2*rand-1)*abs(2*rand*Delta_pos(k)-Positions(i,k));Positions(i,k)=(X1+X2+X3)/3;% Equation (3.7)else                        X1=Alpha_pos-a2*as*(2*rand(1,d)-1).*abs(2*rand(1,d).*Alpha_pos-Positions(i,:));X2=Beta_pos-a2*as*(2*rand(1,d)-1).*abs(2*rand(1,d).*Beta_pos-Positions(i,:));X3=Delta_pos-a2*as*(2*rand(1,d)-1).*abs(2*rand(1,d).*Delta_pos-Positions(i,:));Positions(i,:)=(X1+X2+X3)/3;endendendelse            for k = 1 : Nalfa=rand^1;for j = 1 : dif rand < lambdaScale(k)% Pick a habitat from which to obtain a featureSelectIndex=ceil((k-1)*rand);                       if rand>pif rand<0.5cnum=ceil(rand*d);Positions(k,j) =X(SelectIndex,cnum);elsePositions(k,j) =X(SelectIndex,j);endelsePositions(k,j) =X(SelectIndex,j)+2*as*(0.5-rand)*(X(k,j)-X(SelectIndex,j));endelsernum=ceil(N*rand);while rnum==k,rnum=ceil(N*rand);endrnum1=ceil(N*rand);while rnum1==k ||rnum1==rnum,rnum1=ceil(N*rand);end                        Positions(k,j) = X(k,j)+alfa*(X(1,j)-X(k,j)+X(rnum1,j)-X(rnum,j));                        endendend            end        end   Positions=simplebounds(Positions,aa,bb);    fit=feval(f,Positions);    for i=1:N        fitness=fit(i);if X(i,d+1)>fitnessX(i,d+1)=fitness;X(i,1:d)=Positions(i,:);end        % Update Alpha, Beta, and Deltaif fitness<Alpha_scoreAlpha_score=fitness; % Update alphaAlpha_pos=Positions(i,:);endif fitness>Alpha_score && fitness<Beta_scoreBeta_score=fitness; % Update betaBeta_pos=Positions(i,:);endif fitness>Alpha_score && fitness>Beta_score && fitness<Delta_scoreDelta_score=fitness; % Update deltaDelta_pos=Positions(i,:);end        endX = PopSort(X);l=l+1;Cbest(l)=X(1,dn);
end
Alpha_score=X(1,dn);
Alpha_pos=X(1,1:d);function s=simplebounds(s,Lb,Ub)
% Apply the lower bound
ns_tmp=s;
I=ns_tmp<Lb;
ns_tmp(I)=Lb(I);% Apply the upper bounds
J=ns_tmp>Ub;
ns_tmp(J)=Ub(J);
% Update this new move
s=ns_tmp;

7.读者交流