cga.m

% Continuous Genetic Algorithm
%
% minimizes the objective function designated in ff
% Before beginning, set all the parameters in parts
% I, II, and III
% Haupt & Haupt
% 2003
clear
%_______________________________________________________
% I Setup the GA
ff='scales'; % objective function
npar=10; % number of optimization variables
varhi=pi; varlo=0; % variable limits
%_______________________________________________________
% II Stopping criteria
maxit=10; % max number of iterations
mincost=-9999999; % minimum cost
%_______________________________________________________
% III GA parameters
popsize=100; % set population size
mutrate=0.9; % set mutation rate
selection=0.5; % fraction of population kept
Nt=npar; % continuous parameter GA Nt=#variables
keep=floor(selection*popsize); % #population members that survive
nmut=ceil((popsize-1)*Nt*mutrate); % total number of mutations
M=ceil((popsize-keep)/2); % number of matings
%_______________________________________________________
% Create the initial population
iga=0; % generation counter initialized
par=(varhi-varlo)*rand(popsize,npar)+varlo; % random




cost=scales(par); % calculates population cost using ff
[rr, cc] =size(par);
for ii=1:rr
    cost(ii) = scales(par(ii,:));
end




[cost,ind]=sort(cost); % min cost in element 1
par=par(ind,:); % sort continuous
minc(1)=min(cost); % minc contains min of
meanc(1)=mean(cost); % meanc contains mean of population
%_______________________________________________________
% Iterate through generations
while iga<maxit
    iga=iga+1; % increments generation counter
    %_______________________________________________________
    % Pair and mate
    M=ceil((popsize-keep)/2); % number of matings
    prob=flipud([1:keep]'/sum([1:keep])); % weights chromosomes
    odds=[0 cumsum(prob(1:keep))']; % probability distribution function
    pick1=rand(1,M); % mate #1
    pick2=rand(1,M); % mate #2
    % ma and pa contain the indicies of the chromosomes that will mate
    ic=1;
    while ic<=M
        for id=2:keep+1
            if pick1(ic)<=odds(id) & pick1(ic)>odds(id-1)
                ma(ic)=id-1;
            end
            if pick2(ic)<=odds(id) & pick2(ic)>odds(id-1)
                pa(ic)=id-1;
            end
        end
        ic=ic+1;
    end
    %_______________________________________________________
    % Performs mating using single point crossover
    ix=1:2:keep; % index of mate #1
    xp=ceil(rand(1,M)*Nt); % crossover point
    r=rand(1,M); % mixing parameter
    for ic=1:M
        xy=par(ma(ic),xp(ic))-par(pa(ic),xp(ic)); % ma and pa
        % mate
        par(keep+ix(ic),:)=par(ma(ic),:); % 1st offspring
        par(keep+ix(ic)+1,:)=par(pa(ic),:); % 2nd offspring
        par(keep+ix(ic),xp(ic))=par(ma(ic),xp(ic))-r(ic).*xy;
        % 1st
        par(keep+ix(ic)+1,xp(ic))=par(pa(ic),xp(ic))+r(ic).*xy;
        % 2nd
        if xp(ic)<npar % crossover when last variable not selected
            par(keep+ix(ic),:)=[par(keep+ix(ic),1:xp(ic)) par(keep+ix(ic)+1,xp(ic)+1:npar)];
            par(keep+ix(ic)+1,:)=[par(keep+ix(ic)+1,1:xp(ic)) par(keep+ix(ic),xp(ic)+1:npar)];
        end % if
    end
    %_______________________________________________________
    % Mutate the population
    mrow=sort(ceil(rand(1,nmut)*(popsize-1))+1);
    mcol=ceil(rand(1,nmut)*Nt);
    for ii=1:nmut
        par(mrow(ii),mcol(ii))=(varhi-varlo)*rand+varlo;
        % mutation
    end % ii
    %_______________________________________________________
    % The new offspring and mutated chromosomes are evaluated
    %cost=feval(ff,par);
    [rr, cc] =size(par);
    for ii=2:rr
        cost(ii) = feval(ff,par(ii,:));
    end
    
    
    
    
    
    %_______________________________________________________
    % Sort the costs and associated parameters
    [cost,ind]=sort(cost);
    par=par(ind,:);
    %_______________________________________________________
    % Do statistics for a single nonaveraging run
    minc(iga+1)=min(cost);
    meanc(iga+1)=mean(cost);
    %_______________________________________________________
    % Stopping criteria
    if iga>maxit | cost(1)<mincost
        break
    end
    [iga cost(1)]
end %iga
%_______________________________________________________
% Displays the output
day=clock;
disp(datestr(datenum(day(1),day(2),day(3),day(4),day(5),day(6)),0))
disp(['optimized function is ' ff])
format short g
disp(['popsize = ' num2str(popsize) ' mutrate = ' num2str(mutrate) ' # par = ' num2str(npar)])
disp(['#generations=' num2str(iga) ' best cost=' num2str(cost(1))])
disp(['best solution'])
disp([num2str(par(1,:))])
disp('continuous genetic algorithm')
figure(24)
iters=0:length(minc)-1;
plot(iters,minc,iters,meanc,'-');
xlabel('generation');ylabel('cost');
title(['Continuous Genetic Algorithm; Function: ' ff]);
%text(0,minc(1),'best');text(1,minc(2),'population average')
legend('best', 'population average');