function[Max,k,BestSolutions]=GassUMDA(PopSize,NumbVar,T,F,CantGen,MaximumFunction,InitValues,Complex,ConstraintCheck) % Gaussian EDA. Use the univariate and multivariate models to approximate continuous distributions      % INPUTS% PopSize: Population size% NumbVar: Number of variables% T: Truncation parameter (when T=0, proportional selection is used)% F: Name of the function that has as an argument a vector or NumbVar variables% CantGen: Maximum number of generations % MaximumFunction:  Maximum of the function that can be used as stop condition when it is known % InitValues: (2 X NumbVar) matrix with minimum and maximum values for each variable (this is for initialization) % % Complex: Determines whether interactions are considered (Complex=1) or not (Complex = 0, univariate case)% ConstraintCheck (=1) Checks whether the constraints defined by InitValues are fulfilled% setting to the maximum value those variables over MAX, and to MIN those that do not reach the minimum% ConstraintCheck (=0) allows to violate these bounds % OUTPUTS% Max: Maximum value found by the algorithm at each generation% k: Generation where the maximum was found, case it were known in advance% BestSolutions: Matrix with the best solution at each generation% EXAMPLE%[Max,k,BestSolutions]=GassUMDA(300,10,0.5,'sum',20,100,[zeros(1,10);5*ones(1,10)],0,1)% In this example the maximum of the function sum is search for in the % interval [0,5]. There are 10 variables.k=1;% Initial random population in the interval of values   NewPop = repmat(InitValues(1,:),PopSize,1)+(rand(PopSize,NumbVar).*repmat(InitValues(2,:)-InitValues(1,:),PopSize,1)); while( (k==1) | (k<=CantGen & Max(k-1)<MaximumFunction) )              Pop=NewPop;              % Population is evaluated using function F        for i=1:PopSize        FunVal(i) = feval(F,Pop(i,:));       end              % Solutions are sorted according to the function value        [Val,Ind]= sort(FunVal);         Max(k) = Val(PopSize);   %Maximum value of the population       BestSolutions(k,:) = Pop(Ind(PopSize),:); % Best solution            if T==0          %Proportional selection is applied       [Index]=PropSelection(PopSize,FunVal);       SelPop=Pop(Index,:);           else        % Truncation selection is applied       SelPop=Pop(Ind(PopSize:-1:PopSize-floor(T*PopSize)+1),:);    end           % The probabilistic model is calculated        vars_mean = mean(SelPop);   % mean vector       vars_cov = cov(SelPop);    %  covariance matrix         % The new population is calculated sampling from the model according to its complexity       if Complex==0       vars_sigmas = sqrt(diag(vars_cov))';       NewPop =  normrnd(repmat(vars_mean,PopSize,1),repmat(vars_sigmas,PopSize,1));	     else       NewPop = mvnrnd(vars_mean,vars_cov,PopSize);     end        % Fix the  maximum and  minimum values    if (ConstraintCheck==1)       for i=1:NumbVar,          under_val = find(NewPop(:,i)<InitValues(1,i));          NewPop(under_val,i) = InitValues(1,i);          over_val = find(NewPop(:,i)>InitValues(2,i));          NewPop(over_val,i) = InitValues(2,i);       end       end        k=k+1;       endreturn     % Last version 9/22/2005. Roberto Santana (rsantana@si.ehu.es)