以下是使用拉普拉斯核函数优化levy飞行并改进GOA2算法的Matlab完整代码：

function [z] = levy(n,m,beta)
    
    num = gamma(1+beta)sin(pibeta/2); % used for Numerator 
    den = gamma((1+beta)/2)beta2^((beta-1)/2); % used for Denominator
    sigma_u = (num/den)^(1/beta); % Standard deviation
    u = random(‘Normal’,0,sigma_u,n,m); 
    v = random(‘Normal’,0,1,n,m);
    z =u./(abs(v).^(1/beta));
  
end

% Laplacian kernel function for GOA2 algorithm
function [Klap] = laplacianKernel(X, c, s)
    % X: M * N matrix (M observations, N dimensions)
    % c: centers of kernel function (clusters) 
    % s: width of kernel function (scaling parameter)
    
    % Number of centers (clusters)
    Nc = size(c, 1);
    M = size(X, 1);
    Klap = zeros(M, Nc);
    
    for i = 1:Nc
        d = sqrt(sum((X - repmat(c(i, :), M, 1)).^2, 2));
        Klap(:, i) = exp(-d./s);
    end
end

function [Top_gazelle_fit,Top_gazelle_pos,Convergence_curve] = GOA2(SearchAgents_no,Max_iter,lb,ub,dim,fobj)

    % Laplacian kernel parameters
    Nc = 10; % number of centers/clusters
    s = 1; % scaling parameter of kernel function
    beta = 2; % shape parameter for Levy distribution
    
    % Generate initial population
    Positions = initialization(SearchAgents_no, dim, ub, lb);
    
    % Initialize variables
    Top_gazelle_pos = zeros(1, dim);
    Top_gazelle_fit = inf;
    Convergence_curve = zeros(1, Max_iter);
    stepsize = zeros(SearchAgents_no, dim);
    fitness = inf(SearchAgents_no, 1);
    
    % Run algorithm for Max_iter iterations
    for iter = 1:Max_iter
        % Evaluate each search agent
        for i = 1:SearchAgents_no  
            Flag4ub = Positions(i, :) > ub;
            Flag4lb = Positions(i, :) < lb;    
            Positions(i, :) = (Positions(i, :) .(~(Flag4ub+Flag4lb))) + ub . Flag4ub + lb .* Flag4lb;                    
            fitness(i, 1) = fobj(Positions(i, :));                
            if fitness(i, 1) < Top_gazelle_fit 
                Top_gazelle_fit = fitness(i, 1); 
                Top_gazelle_pos = Positions(i, :);
            end          
         end
        
        % Update kernel centers
        c = rand(Nc, dim) .* repmat(ub - lb, Nc, 1) + repmat(lb, Nc, 1);
        Klap = laplacianKernel(Positions, c, s);
        
        % Keep track of fitness values (used for elitism)
        if iter == 1
            fit_old = fitness;    
            Prey_old = Positions;
        end
     
        % Update search agents
        Inx = (fit_old < fitness);
        Indx = repmat(Inx, 1, dim);
        Positions = Indx .* Prey_old + ~Indx .* Positions;
        fitness = Inx .* fit_old + ~Inx .* fitness;
        
        % Update fitness and position history
        fit_old = fitness;    
        Prey_old = Positions;
        
        % Update top gazelle position
        Elite = repmat(Top_gazelle_pos, SearchAgents_no, 1);  
        CF = (1 - iter / Max_iter) ^ (2 * iter / Max_iter);  
        RL = levy(SearchAgents_no, dim, beta);   
        RB = randn(SearchAgents_no, dim);          
        for i = 1:size(Positions, 1)
            for j = 1:size(Positions, 2)        
                R = rand();
                r = rand();
                if mod(iter, 2) == 0
                    mu = -1;
                else
                    mu = 1;
                end
                % Update search agent position
                if r > 0.5 
                    stepsize(i, j) = RB(i, j) .* (Elite(i, j) - RB(i, j) .* Positions(i, j));                    
                    Positions(i, j) = Positions(i, j) + Klap(i, :) * s * R * stepsize(i, j); 
                % Update search agent position using kernel function
                else 
                    if i > size(Positions, 1) / 2
                        stepsize(i, j) = RB(i, j) .* (RL(i, j) .* Elite(i, j) - Positions(i, j));
                        Positions(i, j) = c(i, j) + Klap(i, :) * mu * CF * stepsize(i, j); 
                    else
                        stepsize(i, j) = RL(i, j) .* (Elite(i, j) - RL(i, j) .* Positions(i, j));                     
                        Positions(i, j) = Positions(i, j) + Klap(i, :) * mu * R * stepsize(i, j);  
                    end 
                end  
            end                                         
        end    
      
        % Keep search agents within boundary
        for i = 1:size(Positions, 1)
            Flag4ub = Positions(i, :) > ub;  
            Flag4lb = Positions(i, :) < lb;  
            Positions(i, :) = Positions(i, :) .(~(Flag4ub + Flag4lb)) + ub . Flag4ub + lb .* Flag4lb;
        end
        
        % Update top gazelle position