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bga.m
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bga.m
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% Binary 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='f5'; % objective function
npar=10; % number of optimization variables
varhi=100; varlo=0; % variable limits
%_______________________________________________________
% II. Stopping criteria
maxit=10; % max number of iterations
mincost=-9999999; % minimum cost
%_______________________________________________________
% III. GA parameters
popsize=10; % set population size
mutrate=0.5; % set mutation rate
selection=0.5; % fraction of population kept
nbits=19; % number of bits in each parameter
Nt=nbits*npar; % total number of bits in a chormosome
keep=floor(selection*popsize); % #population members that survive
%_______________________________________________________
% Create the initial population
iga=0; % generation counter initialized
pop=round(rand(popsize,Nt)); % random population of 1s and 0s
par=gadecode(pop,varlo,varhi,nbits); % convert binary to continuous values
cost=f5(par); % calculates population
[rr, cc] =size(par);
for ii=1:rr
cost(ii) = f5(par(ii,:));
end
% cost using ff
[cost,ind]=sort(cost); % min cost in element 1
par=par(ind,:);pop=pop(ind,:); % sorts population with lowest cost first
minc(1)=min(cost); % minc contains min of population
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 based upon position in list
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
if pick2(ic)<=odds(id) & pick2(ic)>odds(id-1)
pa(ic)=id-1;
end % if
end % id
ic=ic+1;
end % while
%_______________________________________________________
% Performs mating using single point crossover
ix=1:2:keep; % index of mate #1
xp=ceil(rand(1,M)*(Nt-1)); % crossover point
pop(keep+ix,:)=[pop(ma,1:xp) pop(pa,xp+1:Nt)];
% first offspring
pop(keep+ix+1,:)=[pop(pa,1:xp) pop(ma,xp+1:Nt)];
% second offspring
%_______________________________________________________
% Mutate the population
nmut=ceil((popsize-1)*Nt*mutrate); % total number
% of mutations
mrow=ceil(rand(1,nmut)*(popsize-1))+1; % row to mutate
mcol=ceil(rand(1,nmut)*Nt); % column to mutate
for ii=1:nmut
pop(mrow(ii),mcol(ii))=abs(pop(mrow(ii),mcol(ii))-1);
% toggles bits
end % ii
%_______________________________________________________
% The population is re-evaluated for cost
par(2:popsize,:)=gadecode(pop(2:popsize,:),varlo,varhi,nbits); % decode
cost(2:popsize)=feval(ff,par(2:popsize,:));
[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); % min cost in element 1
par=par(ind,:);pop=pop(ind,:); % sorts population with
% 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('binary genetic algorithm')
disp(['each parameter represented by ' num2str(nbits) ' bits'])
figure(24)
iters=0:length(minc)-1;
plot(iters,minc,iters,meanc,'-');
xlabel('generation');ylabel('cost');
title(['Binary Genetic Algorithm; Function: ' ff]);
text(0,minc(1),'best');text(1,minc(2),'population average')
legend('best', 'population average');