【智能优化算法】IHAOAVOA（一种改进的混合天鹰优化算法（AO）和非洲秃鹫优化算法(AVOA)）

发表在Mathematical Biosciences and Engineering的文章：IHAOAVOA: An improved hybrid aquila optimizer and African vultures optimization algorithm for global optimization problems.https://www.x-mol.com/paperRedirect/1572654041256222720

01.引言

天鹰优化器（AO）和非洲秃鹰优化算法（AVOA）是两种新开发的元启发式算法，分别模拟自然界中天鹰座和非洲秃鹰的几种智能狩猎行为。AO具有强大的全局探索能力，但其局部开发阶段不够稳定。另一方面，AVOA具有可观的开发能力，但探索机制不足。基于两种算法的特点，本文提出了一种改进的混合AO和AVOA优化器，称为IHAOAVOA，以克服单一算法的不足，为解决全局优化问题提供更高质量的解决方案。首先，将 AO 的探索阶段和 AVOA 的开发阶段结合起来，以保留各自有价值的搜索能力。然后，一种新的复合反对学习（COBL）旨在增加种群多样性并帮助混合算法摆脱局部最优。此外，为了更有效地指导搜索过程，平衡探索和利用，引入适应度-距离平衡（FDB）选择策略来修改核心位置更新公式。通过在 23 个经典基准函数和 IEEE CEC2019 测试套件上与基本 AO、AVOA 和六种最先进的算法进行比较，对所提出的 IHAOAVOA 的性能进行了全面调查和分析。实验结果表明，与其他比较方法相比，IHAOAVOA 在大多数测试函数上都实现了优越的求解精度、收敛速度和局部最优避免。此外，通过解决五个工程设计问题，突出了 IHAOAVOA 的实用性。我们的研究结果表明，在解决实际优化任务时，所提出的技术也具有很强的竞争力和前景。

02.代码流程图

3.部分代码

%___________________________________________________________________________________________________________%
%  IHAOAVOA: An improved hybrid Aquila optimizer and African vultures optimization algorithm(IHAOAVOA) source codes demo 1.0          
%                                                                                                           %
%  Developed in MATLAB R2017a                                                                               %
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%  Author and programmer: Yaning Xiao,Yanling Guo, Hao Cui, Yangwei Wang, Jian Li, Yapeng Zhang             %
%                                                                                                           %
%         e-Mail: xiaoyaning@nefu.edu.cn, nefugyl@hotmail.com                                               %
%                                                                                                           %                                           
%___________________________________________________________________________________________________________%
% The IHAOAVOA Optimization Algorithm
function [ihaoavoa_score,ihaoavoa_pos,ihaoavoa_curve]=IHAOAVOA(N,max_iter,lb,ub,dim,fobj)
    tic
    % initialize Best_vulture1, Best_vulture2
    ihaoavoa_pos=zeros(1,dim);
    ihaoavoa_score=inf;
    Best_vulture2_X=zeros(1,dim);
    Best_vulture2_F=inf;
    %Initialize the first random population of vultures
    X=initialization(N,dim,ub,lb);   
   %%  Controlling parameter   
   %/********AVOA**********/
    p2=0.4;
    p3=0.6;
    alpha=0.8;
    betha=0.2;
    gamma=2.5;
    %/********AO**********/
    avto = 1:dim;
    u = .0265;
    r0 = 10;
    rao = r0 +u*avto;
    omega = .005;
    phi0 = 3*pi/2;
    phi = -omega*avto+phi0;
    x = rao .* sin(phi);  
    y = rao .* cos(phi); 
    %/********LOBL**********/
    k=12000; % Scale Coefficient
    
    t=1; % Loop counter
%%Main loop
while t <= max_iter
    %% Evaluate the fitness
        for i=1:size(X,1)
            % Calculate the fitness of the population
            current_vulture_X = X(i,:);
            current_vulture_F=fobj(current_vulture_X);
            % Update the first best two vultures if needed
            if current_vulture_F<ihaoavoa_score
                ihaoavoa_score=current_vulture_F; % Update the first best bulture
                ihaoavoa_pos=current_vulture_X;
            end
            if current_vulture_F>ihaoavoa_score && current_vulture_F<Best_vulture2_F
                Best_vulture2_F=current_vulture_F; % Update the second best bulture
                Best_vulture2_X=current_vulture_X;
            end
        end
        
        a=unifrnd(-2,2,1,1)*((sin((pi/2)*(t/max_iter))^gamma)+cos((pi/2)*(t/max_iter))-1);
        P1=(2*rand+1)*(1-(t/max_iter))+a;
        %% FDB
        index = fitnessDistanceBalance(X,ihaoavoa_score); 
        %% Update the location
        for i=1:size(X,1)
            current_vulture_X = X(i,:);  % pick the current vulture back to the population
            F=P1*(2*rand()-1);  
            random_vulture_X=random_select(ihaoavoa_pos,Best_vulture2_X,alpha,betha);
          %% Composite opposition-based learning strategy (COBL)
           if rand<0.5
               opposite_X=lb+ub-rand*current_vulture_X;
            else
               opposite_X=(ub + lb)/2 + (ub + lb)/(2*k) - current_vulture_X/k;
            end
            Flag_UB=opposite_X>ub; % check if they exceed (up) the boundaries
            Flag_LB=opposite_X<lb; % check if they exceed (down) the boundaries
            opposite_X=(opposite_X.*(~(Flag_UB+Flag_LB)))+ub.*Flag_UB+lb.*Flag_LB;
            Fnew=fobj(opposite_X);
            if Fnew<fobj(current_vulture_X)
                current_vulture_X=opposite_X;
            end
            if Fnew<ihaoavoa_score
                ihaoavoa_pos=current_vulture_X;
                ihaoavoa_score=Fnew;
            end
            %% Exploration stage:AO
            if abs(F) >= 1 
                if rand <0.5
                    current_vulture_X=ihaoavoa_pos*(1-t/max_iter)+(mean(X(i,:))-ihaoavoa_pos)*rand();
                else
                    current_vulture_X=ihaoavoa_pos.*Levy(dim)+X(index,:)+(y-x)*rand;  
                end
            %% Exploitation stage:AVOA
            elseif abs(F) < 1 
                current_vulture_X = exploitation(current_vulture_X, ihaoavoa_pos, Best_vulture2_X, random_vulture_X, F, p2, p3, dim, ub, lb); % Modified the position-weighted equation
            end
                X(i,:) = current_vulture_X; % place the current vulture back into the population
        end
        t=t+1;
        ihaoavoa_curve(t)=ihaoavoa_score;
        X = boundaryCheck(X, lb, ub);%check the boundary
end
toc
end