【智能优化算法】白鲨智能优化算法(White Shark Optimizer,WSO)

白鲨智能优化算法(White Shark Optimizer,WSO)是期刊“KNOWLEDGE-BASED SYSTEMS”（中科院一区期刊 IF=8.6）的2022年智能优化算法

01.引言

白鲨智能优化算法(White Shark Optimizer,WSO)的核心理念和基础灵感来自大白鲨的行为，包括它们在导航和觅食时非凡的听觉和嗅觉。行为的这些方面被数学建模，以适应对WSO的探索和利用之间的充分平衡，并协助搜索代理探索和利用搜索空间的每个潜在区域，以实现优化。WSO的搜索代理会根据目前最佳的解决方案随机更新自己的位置，最终得到最优的结果。在CEC-2017测试套件的29个测试功能的基础上，对WSO的性能进行了多个维度的综合基准测试。进一步将WSO应用于CEC-2011进化算法竞赛的基准问题，证明其可靠性和对现实问题的适用性。对计算结果和收敛结果进行了全面分析，以阐明WSO的有效性和稳定性水平。基于生成的解，将WSO在几种统计方法下的性能得分与9种成熟的元启发式方法进行比较。Friedman和Holm对结果的测试表明，与其他现有的元启发式方法相比，WSO在全局最优性、避免局部最小值和解决方案质量方面揭示了合理的解决方案。

02.优化算法的流程

03.论文中算法对比图

04.部分代码

function [fmin0,gbest,ccurve]=WSO(whiteSharks,itemax,lb,ub,dim,fobj)
 
%% Convergence curve
ccurve=zeros(1,itemax);
%% Show the convergence curve
%     figure (1);
%     set(gcf,'color','w');
%     hold on
%     xlabel('Iteration','interpreter','latex','FontName','Times','fontsize',10)
%     ylabel('fitness value','interpreter','latex','FontName','Times','fontsize',10); 
%     grid;
%% Start the WSO  Algorithm
% Generation of initial solutions
WSO_Positions=initialization(whiteSharks,dim,ub,lb);% Initial population
% initial velocity
v=0.0*WSO_Positions; 
%% Evaluate the fitness of the initial population
fit=zeros(whiteSharks,1);
for i=1:whiteSharks
     fit(i,1)=fobj(WSO_Positions(i,:));
end
%% Initalize the parameters of WSO
fitness=fit; % Initial fitness of the random positions of the WSO
 
[fmin0,index]=min(fit);
wbest = WSO_Positions; % Best position initialization
gbest = WSO_Positions(index,:); % initial global position
%% WSO Parameters
    fmax=0.75; %  Maximum frequency of the wavy motion
    fmin=0.07; %  Minimum frequency of the wavy motion   
    tau=4.11;  
       
    mu=2/abs(2-tau-sqrt(tau^2-4*tau));
    pmin=0.5;
    pmax=1.5;
    a0=6.250;  
    a1=100;
    a2=0.0005;
  %% Start the iterative process of WSO 
for ite=1:itemax
    mv=1/(a0+exp((itemax/2.0-ite)/a1)); 
    s_s=abs((1-exp(-a2*ite/itemax))) ;
 
    p1=pmax+(pmax-pmin)*exp(-(4*ite/itemax)^2);
    p2=pmin+(pmax-pmin)*exp(-(4*ite/itemax)^2);
    
 %% Update the speed of the white sharks in water  
     nu=floor((whiteSharks).*rand(1,whiteSharks))+1;
     for i=1:size(WSO_Positions,1)
           rmin=1; rmax=3.0;
          rr=rmin+rand()*(rmax-rmin);
          wr=abs(((2*rand()) - (1*rand()+rand()))/rr);       
          v(i,:)=  mu*v(i,:) +  wr *(wbest(nu(i),:)-WSO_Positions(i,:));
           %% or                
%          v(i,:)=  mu*(v(i,:)+ p1*(gbest-WSO_Positions(i,:))*rand+.... 
%                    + p2*(wbest(nu(i),:)-WSO_Positions(i,:))*rand);          
     end
 
 %% Update the white shark position
     for i=1:size(WSO_Positions,1)
       
        f =fmin+(fmax-fmin)/(fmax+fmin);
         
        a=sign(WSO_Positions(i,:)-ub)>0;
        b=sign(WSO_Positions(i,:)-lb)<0;
         
        wo=xor(a,b);
        % locate the prey based on its sensing (sound, waves)
            if rand<mv
                WSO_Positions(i,:)=  WSO_Positions(i,:).*(~wo) + (ub.*a+lb.*b); % random allocation  
            else   
                WSO_Positions(i,:) = WSO_Positions(i,:)+ v(i,:)/f;  % based on the wavy motion
            end
    end 
    
    %% Update the position of white sharks consides_sng fishing school 
for i=1:size(WSO_Positions,1)
        for j=1:size(WSO_Positions,2)
            if rand<s_s      
                
             Dist=abs(rand*(gbest(j)-1*WSO_Positions(i,j)));
             
                if(i==1)
                    WSO_Positions(i,j)=gbest(j)+rand*Dist*sign(rand-0.5);
                else    
                    WSO_Pos(i,j)= gbest(j)+rand*Dist*sign(rand-0.5);
                    WSO_Positions(i,j)=(WSO_Pos(i,j)+WSO_Positions(i-1,j))/2*rand;
                end   
            end
         
        end       
end
%     
%% Update global, best and new positions
 
    for i=1:whiteSharks 
        % Handling boundary violations
           if WSO_Positions(i,:)>=lb & WSO_Positions(i,:)<=ub%         
            % Find the fitness
              fit(i)=fobj(WSO_Positions(i,:));    
              
             % Evaluate the fitness
            if fit(i)<fitness(i)
                 wbest(i,:) = WSO_Positions(i,:); % Update the best positions
                 fitness(i)=fit(i);   % Update the fitness
            end
            
            %% Finding out the best positions
            if (fitness(i)<fmin0)
               fmin0=fitness(i);
               gbest = wbest(index,:); % Update the global best positions
            end 
            
        end
    end
%% Obtain the results
%   outmsg = ['Iteration# ', num2str(ite) , '  Fitness= ' , num2str(fmin0)];
%   disp(outmsg);
 ccurve(ite)=fmin0; % Best found value until iteration ite
%  if ite>2
%         line([ite-1 ite], [ccurve(ite-1) ccurve(ite)],'Color','b'); 
%         title({'Convergence characteristic curve'},'interpreter','latex','FontName','Times','fontsize',12);
%         xlabel('Iteration');
%         ylabel('Best score obtained so far');
%         drawnow 
%  end 
  
end 
end