GenEstim : A simple genetic algorithm for parameters estimation

The GenEstim function presented here uses a very simple genetic algorithm to estimate parameters. The function returns the best estimated set of parameters ($estim), the AIC ($information) at each generation, and the cost of the best model ($bestcost) at each generation.

Results of running the program with a logistic function :

Logis = function(x,p)	p[[1]]/(1+p[[2]]*exp(-p[[3]]*x))
RSS = function(par)	sum((Logis(X,par)-Y)^2)
aic <- function(yvalues,rss,par)
{
	k <- length(par)
	n <- length(yvalues)
	aic <- 2*k+n*log(rss/n)
	return(aic)
}
P	<-	list(2,10,4)
X	<-	seq(from=-5,to=5,by=0.1)
Y	<-	Logis(X,P) + rnorm(length(X),sd=0.1)
plot(X,Y,pch=19,col='grey')
GenEstim	<- function(
		start.pars,
		cost = RSS,
		...,
		numiter = 1e3,
		npop = 1e2)
{
	bestcost <- NULL
	cur.AIC <- NULL
	for(it in 1:numiter)
	{
		pop <- matrix(0,ncol=length(start.pars),nrow=npop)
		for(p in 1:length(start.pars))
		{
			pop[,p] 	<- rnorm(npop,start.pars[[p]],sd=1)
			pop[1,p]	<- start.pars[[p]]
		}
		Costs <- NULL
		for(i in 1:nrow(pop))
		{
			li <- as.list(pop[i,])
			Costs[i] <- cost(li)
		}
		bestcost <- c(bestcost,min(Costs))
		best <-which.min(Costs)
		start.pars <- as.list(pop[best,])
		cur.AIC <- c(cur.AIC,aic(Y,RSS(start.pars),start.pars))
	}
	return(list(estim=start.pars,information=cur.AIC,convergence=bestcost))
}

simul <- GenEstim(list(0,0,0))
x.control <- seq(from=-6,to=6,by=0.1)
lines(x.control,Logis(x.control,simul$estim),col='orange',lwd=3)