【元启发式优化算法】秃鹰搜索优化算法(BEO)

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已于 2025-02-17 18:24:57 修改

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分类专栏：智能优化算法文章标签：算法人工智能

于 2025-02-17 18:22:53 首次发布

本文链接：https://blog.csdn.net/yuchunyu12/article/details/145689096

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01.引言

秃鹰搜索算法(BES)通过模拟秃鹰捕鱼的三阶段智能行为实现优化：首先在空间选择阶段定位猎物密集区域，接着在搜索阶段进行精细勘探，最后基于最优位置发起定向俯冲捕猎。研究者采用多维度验证框架，通过基准测试、横向性能对比以及包含均值分析、Wilcoxon检验的统计评估，证实BES在收敛速度、优化精度等指标上显著优于传统方法和其他元启发式算法，尤其在复杂优化问题中展现出卓越的全局搜索能力与稳定性。

02.优化算法的流程

秃鹰搜索算法(BES)作为一种基于群体智能的元启发式优化算法，其流程遵循典型的优化框架：算法初始化阶段随机生成候选解集（秃鹰种群），通过仿生行为规则逐步逼近最优解。核心流程分为仿生驱动的三阶段迭代机制：空间选择阶段通过适应度评估定位高潜力搜索区域，实现全局探索；空间搜索阶段在选定区域内执行螺旋式局部勘探，平衡广度与深度搜索；俯冲捕猎阶段基于前两阶段的最优解进行定向加速收敛，完成精准利用。算法通过迭代更新秃鹰位置向量，数学上表现为候选解在多维空间中的动态调整，其位置更新公式整合了随机扰动因子与历史最优引导项，有效协调探索与开发的矛盾。终止条件通常设置为达到最大迭代次数或收敛精度阈值，最终输出全局最优解。BES通过模拟秃鹰捕猎的生态行为，构建了从粗粒度区域筛选到细粒度精准捕杀的递进式优化机制。

其伪代码如下：

3.论文中算法对比图

04.部分代码

function [Best_score,Best_x,cg_curve]=BES(nPop,MaxIt,low,high,dim,fobj)
%nPop: size of population 
%MaxIt:number of iterations 
%low, high : space of Decision variables
%dim : number of Decision variables
%fobj : funcation 
st=cputime;
% Initialize Best Solution
BestSol.cost = inf;
for i=1:nPop
    pop.pos(i,:) = low+(high-low).*rand(1,dim);
     pop.cost(i)=fobj(pop.pos(i,:));
    if pop.cost(i) < BestSol.cost
        BestSol.pos = pop.pos(i,:);
        BestSol.cost = pop.cost(i);
    end
end
 disp(num2str([0 BestSol.cost]))
for t=1:MaxIt
    %%               1- select_space 
 [pop BestSol s1(t)]=select_space(fobj,pop,nPop,BestSol,low,high,dim);
    %%                2- search in space
    [pop BestSol s2(t)]=search_space(fobj,pop,BestSol,nPop,low,high);
    %%                3- swoop
  [pop BestSol s3(t)]=swoop(fobj,pop,BestSol,nPop,low,high);
        Convergence_curve(t)=BestSol.cost;
        disp(num2str([t BestSol.cost]))
    ed=cputime;
    timep=ed-st;
   Best_score=BestSol.cost ;Best_x=BestSol.pos;cg_curve= Convergence_curve;
end
function [pop BestSol s1]=select_space(fobj,pop,npop,BestSol,low,high,dim)
Mean=mean(pop.pos);
% Empty Structure for Individuals
empty_individual.pos = [];
empty_individual.cost = [];
lm= 2;
s1=0;
for i=1:npop
    newsol=empty_individual;
    newsol.pos= BestSol.pos+ lm*rand(1,dim).*(Mean - pop.pos(i,:));
    newsol.pos = max(newsol.pos, low);
    newsol.pos = min(newsol.pos, high);
    newsol.cost=fobj(newsol.pos);
    if newsol.cost<pop.cost(i)
       pop.pos(i,:) = newsol.pos;
       pop.cost(i)= newsol.cost;
       s1=s1+1;
         if pop.cost(i) < BestSol.cost
          BestSol.pos= pop.pos(i,:);
         BestSol.cost=pop.cost(i); 
         end
    end
end
end
function [pop best s1]=search_space(fobj,pop,best,npop,low,high)
Mean=mean(pop.pos);
a=10;
R=1.5;
% Empty Structure for Individuals
empty_individual.pos = [];
empty_individual.cost = [];
s1=0;
for i=1:npop-1
    A=randperm(npop);
pop.pos=pop.pos(A,:);
pop.cost=pop.cost(A);
        [x y]=polr(a,R,npop);
    newsol=empty_individual;
   Step = pop.pos(i,:) - pop.pos(i+1,:);
   Step1=pop.pos(i,:)-Mean;
   newsol.pos = pop.pos(i,:) +y(i)*Step+x(i)*Step1;
    newsol.pos = max(newsol.pos, low);
    newsol.pos = min(newsol.pos, high);
    newsol.cost=fobj(newsol.pos);
    if newsol.cost<pop.cost(i)
       pop.pos(i,:) = newsol.pos;
       pop.cost(i)= newsol.cost;
              s1=s1+1;
                  if pop.cost(i) < best.cost
                 best.pos= pop.pos(i,:);
                best.cost=pop.cost(i); 
            end
    end
end
end
function [pop best s1]=swoop(fobj,pop,best,npop,low,high)
Mean=mean(pop.pos);
a=10;
R=1.5;
% Empty Structure for Individuals
empty_individual.pos = [];
empty_individual.cost = [];
s1=0;
for i=1:npop
    A=randperm(npop);
pop.pos=pop.pos(A,:);
pop.cost=pop.cost(A);
        [x y]=swoo_p(a,R,npop);
    newsol=empty_individual;
   Step = pop.pos(i,:) - 2*Mean;
   Step1= pop.pos(i,:)-2*best.pos;
   newsol.pos = rand(1,length(Mean)).*best.pos+x(i)*Step+y(i)*Step1;
    newsol.pos = max(newsol.pos, low);
    newsol.pos = min(newsol.pos, high);
    newsol.cost=fobj(newsol.pos);
    if newsol.cost<pop.cost(i)
       pop.pos(i,:) = newsol.pos;
       pop.cost(i)= newsol.cost;
              s1=s1+1;
                  if pop.cost(i) < best.cost
                 best.pos= pop.pos(i,:);
                best.cost=pop.cost(i); 
            end
    end
end
end
function [xR yR]=swoo_p(a,R,N)
th = a*pi*exp(rand(N,1));
r  =th; %R*rand(N,1);
xR = r.*sinh(th);
yR = r.*cosh(th);
 xR=xR/max(abs(xR));
 yR=yR/max(abs(yR));
end
 
 function [xR yR]=polr(a,R,N)
%// Set parameters
th = a*pi*rand(N,1);
r  =th+R*rand(N,1);
xR = r.*sin(th);
yR = r.*cos(th);
 xR=xR/max(abs(xR));
 yR=yR/max(abs(yR));
 end
end