### 多目标灰狼优化器简介
多目标灰狼优化器(
Multi-Objective Grey Wolf Optimizer, MOGWO)是一种新颖的元启发式算法，旨在解决复杂的多目标优化问题。MOGWO基于单目标灰狼优化(
Grey Wolf Optimizer, GWO)[^1]发展而来，在保持原有优势的基础上进行了扩展。
#### 原理概述
在自然环境中，灰狼群体通过协作捕食来维持生存和发展。受此现象启发，MOGWO模拟了这种社会结构及其决策过程：
- **领导层形成**：利用外部存档存储Pareto最优解集，并据此构建领导者阶层；
- **位置更新规则**：根据个体适应度调整候选解的位置向量；
- **探索与开发平衡**：动态调节搜索范围以兼顾全局勘探和局部精炼；
这些特性使得MOGWO能够在高维复杂环境下有效地寻找多个冲突目标之间的折衷方案[^2]。
```matlab
function [X,F]=mogwo(SearchAgents_no,Max_iter,lb,ub,dim,fobj)
Alpha_pos=zeros(1,dim);
Alpha_score=inf;
Beta_pos=zeros(1,dim);
Beta_score=inf;
Delta_pos=zeros(1,dim);
Delta_score=inf;
Positions=rand(SearchAgents_no,dim).*(ub
-lb)+lb;
Convergence_curve=zeros(1,Max_iter);
t=1;% Loop counter
while t<=Max_iter
for i=1
:size(Positions,1)
Flag4ub=Positions(i,
:)>ub;
Flag4lb=Positions(i,
:)<lb;
Positions(i,
:)=(Positions(i,
:).*(~(Flag4ub+Flag4lb)))+...
ub.*Flag4ub+lb.*Flag4lb;
fitness=fobj(Positions(i,
:));
if isnan(fitness)||isinf(fitness)
fitness=inf;
end
F(t,i)=fitness;
% Update the three best search agents
if fitness<Alpha_score
Alpha_score=fitness; %#ok<*NASGU>
Alpha_pos=Positions(i,
:);
elseif fitness<Beta_score && fitness>=Alpha_score
Beta_score=fitness;
Beta_pos=Positions(i,
:);
elseif fitness<Delta_score && fitness>=Beta_score
Delta_score=fitness;
Delta_pos=Positions(i,
:);
end
end
a=2
-t*((2)/Max_iter);% Parameter a decreases linearly from 2 to 0
for i=1
:size(Positions,1)
r1=rand(size(Positions(i,
:),1));% random number in [0,1]
r2=rand(size(Positions(i,
:),1));% random number in [0,1]
A1=2*a*r1
-a;% Equation (3.3)
C1=2*r2;% Equation (3.4)
D_alpha=abs(C1*Alpha_pos
-Positions(i,
:));% Equation (3.5)
-part 1
X1=Alpha_pos
-A1*D_alpha;% Equation (3.6)
-part 1
r1=rand(size(Positions(i,
:),1));% random number in [0,1]
r2=rand(size(Positions(i,
:),1));% random number in [0,1]
A2=2*a*r1
-a;% Equation (3.3)
C2=2*r2;% Equation (3.4)
D_beta=abs(C2*Beta_pos
-Positions(i,
:));% Equation (3.5)
-part 2
X2=Beta_pos
-A2*D_beta;% Equation (3.6)
-part 2
r1=rand(size(Positions(i,
:),1));% random number in [0,1]
r2=rand(size(Positions(i,
:),1));% random number in [0,1]
A3=2*a*r1
-a;% Equation (3.3)
C3=2*r2;% Equation (3.4)
D_delta=abs(C3*Delta_pos
-Positions(i,
:));% Equation (3.5)
-part 3
X3=Delta_pos
-A3*D_delta;% Equation (3.6)
-part 3
Positions(i,
:)=(X1+X2+X3)./3;% Equation (3.7)
end
Convergence_curve(t)=Alpha_score;
t=t+1;
end
[f_min,index_fmin]=min(F(end,
:));
X=Positions(index_fmin,
:);
end
```
上述MATLAB代码实现了基本框架下的MOGWO流程，具体参数设置可根据实际应用场景灵活调整[^3]。
多目标改进灰狼算法求解最优潮流问题
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