1 简介

随着人类社会的进步,科学技术的发展日新月异.模拟人脑神经网络的人工神经网络已取得了长足的发展.经过半个多世纪的发展,人工神经网络在计算机科学,人工智能,智能控制等方面得到了广泛的应用. 当代社会是一个讲究效率的社会,科技更新领域也是如此.在人工神经网络研究领域,算法的优化显得尤为重要,对提高网络整体性能举足轻重.BP神经网络模型是目前应用最为广泛的一种神经网络模型,对于解决非线性复杂问题具有重要的意义.但是BP神经网络有其自身的一些不足(收敛速度慢和容易陷入局部极小值问题),在解决某些现实问题的时候显得力不从心.针对这个问题,本文利用遗传算法的并行全局搜索的优势,能够弥补BP网络的不足,为解决大规模复杂问题提供了广阔的前景.本文将鲸鱼算法与BP网络有机地结合起来,提出了一种新的网络结构,在稳定性,学习性和效率方面都有了很大的提高. 基于以上的研究目的,本文首先设计了BP神经网络结构,在此基础上,应用鲸鱼算法进行优化,达到了加快收敛速度和全局寻优的效果.本文借助MATLAB平台,对算法的优化内容进行了仿真实验,得出的效果也符合期望值,实现了对BP算法优化的目的.

2 部分代码

%_________________________________________________________________________%
%  Whale Optimization Algorithm (WOA) source codes demo 1.0               %
%                                                                         %
%                                                                         %
%_________________________________________________________________________%
% You can simply define your cost in a seperate file and load its handle to fobj 
% The initial parameters that you need are:
%__________________________________________
% fobj = @YourCostFunction
% dim = number of your variables
% Max_iteration = maximum number of generations
% SearchAgents_no = number of search agents
% lb=[lb1,lb2,...,lbn] where lbn is the lower bound of variable n
% ub=[ub1,ub2,...,ubn] where ubn is the upper bound of variable n
% If all the variables have equal lower bound you can just
% define lb and ub as two single number numbers
% To run ALO: [Best_score,Best_pos,cg_curve]=ALO(SearchAgents_no,Max_iteration,lb,ub,dim,fobj)
% The Whale Optimization Algorithm
function [Leader_score,Leader_pos,Convergence_curve]=WOA(SearchAgents_no,Max_iter,lb,ub,dim,fobj,handles,value)
% initialize position vector and score for the leader
Leader_pos=zeros(1,dim);
Leader_score=inf; %change this to -inf for maximization problems
%Initialize the positions of search agents
Positions=initialization(SearchAgents_no,dim,ub,lb);
Convergence_curve=zeros(1,Max_iter);
t=0;% Loop counter
% Main loop
while t<Max_iter
    for i=1:size(Positions,1)
        % Return back the search agents that go beyond the boundaries of the search space
        Flag4ub=Positions(i,:)>ub;
        Flag4lb=Positions(i,:)<lb;
        Positions(i,:)=(Positions(i,:).*(~(Flag4ub+Flag4lb)))+ub.*Flag4ub+lb.*Flag4lb;
        % Calculate objective function for each search agent
        fitness=fobj(Positions(i,:));
        All_fitness(1,i)=fitness;
        % Update the leader
        if fitness<Leader_score % Change this to > for maximization problem
            Leader_score=fitness; % Update alpha
            Leader_pos=Positions(i,:);
        end
    end
    a=2-t*((2)/Max_iter); % a decreases linearly fron 2 to 0 in Eq. (2.3)
    % a2 linearly dicreases from -1 to -2 to calculate t in Eq. (3.12)
    a2=-1+t*((-1)/Max_iter);
    % Update the Position of search agents 
    for i=1:size(Positions,1)
        r1=rand(); % r1 is a random number in [0,1]
        r2=rand(); % r2 is a random number in [0,1]
        A=2*a*r1-a;  % Eq. (2.3) in the paper
        C=2*r2;      % Eq. (2.4) in the paper
        b=1;               %  parameters in Eq. (2.5)
        l=(a2-1)*rand+1;   %  parameters in Eq. (2.5)
        p = rand();        % p in Eq. (2.6)
        for j=1:size(Positions,2)
            if p<0.5   
                if abs(A)>=1
                    rand_leader_index = floor(SearchAgents_no*rand()+1);
                    X_rand = Positions(rand_leader_index, :);
                    D_X_rand=abs(C*X_rand(j)-Positions(i,j)); % Eq. (2.7)
                    Positions(i,j)=X_rand(j)-A*D_X_rand;      % Eq. (2.8)
                elseif abs(A)<1
                    D_Leader=abs(C*Leader_pos(j)-Positions(i,j)); % Eq. (2.1)
                    Positions(i,j)=Leader_pos(j)-A*D_Leader;      % Eq. (2.2)
                end
            elseif p>=0.5
                distance2Leader=abs(Leader_pos(j)-Positions(i,j));
                % Eq. (2.5)
                Positions(i,j)=distance2Leader*exp(b.*l).*cos(l.*2*pi)+Leader_pos(j);
            end
        end
    end
    t=t+1;
    Convergence_curve(t)=Leader_score;
    if t>2
        line([t-1 t], [Convergence_curve(t-1) Convergence_curve(t)],'Color','b')
        xlabel('Iteration');
        ylabel('Best score obtained so far');        
        drawnow
    end
    set(handles.itertext,'String', ['The current iteration is ', num2str(t)])
    set(handles.optimumtext,'String', ['The current optimal value is ', num2str(Leader_score)])
    if value==1
        hold on
        scatter(t*ones(1,SearchAgents_no),All_fitness,'.','k')
    end
end

3 仿真结果

4 参考文献

[1]任谢楠. 基于遗传算法的BP神经网络的优化研究及MATLAB仿真[D]. 天津师范大学, 2014.

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