Optimizing a multi-modal function with a two step anneal method.

February 24, 2013

(This article was first published on PsychoAnalytix Blog, and kindly contributed to R-bloggers)

I have been working on a reliable optimization method for this crazy function.



I noticed that if I had a large variance in the random normal generator, the optimizer would jump all over the place but would not settle down in the best optimum. So I added in a second step that takes the best of the attempted values and uses them as a second set of start values. Then, a second smaller variance is used that does not allow for major jumps. The two step anneal function can be seen below.

    xm = mu[1]
	ym = mu[2]
	fm = f(xm,ym)
	x = rep(NA,n*2)
	y = rep(NA,n*2)
	fx = rep(NA,n*2)
	for(k in 1:2){
		for (i in 1:n){
			dxm = xm+rnorm(1,0,s)
			dym = ym+rnorm(1,0,s)
			fdm = f(dxm, dym)

			t = t*g
			if (runif(1) < (fdm/fm)^(1/t)){
				xm = dxm
				ym = dym
				fm = fdm
			x[(i+(k-1)*n)] = xm
			y[(i+(k-1)*n)] = ym
			fx[(i+(k-1)*n)] = fm
		ii = which(fx==max(fx, na.rm=TRUE))[1]
		best=c(x[ii], y[ii])
	list(x = x, y = y, fx = fx, best = best , fbest = fx[ii], t=t)

To run the function and see the path of the anneal function use this code.


z<-outer(x,y, f.egg)

aa<-twostep.anneal(f.egg, n=1000, sig=c(2, 2), mu=c(5,5), t=2, g=.99)

lines(aa$x, aa$y, col=2)

To leave a comment for the author, please follow the link and comment on their blog: PsychoAnalytix Blog.

R-bloggers.com offers daily e-mail updates about R news and tutorials on topics such as: Data science, Big Data, R jobs, visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more...

If you got this far, why not subscribe for updates from the site? Choose your flavor: e-mail, twitter, RSS, or facebook...

Comments are closed.


Mango solutions

plotly webpage

dominolab webpage

Zero Inflated Models and Generalized Linear Mixed Models with R

Quantide: statistical consulting and training





CRC R books series

Six Sigma Online Training

Contact us if you wish to help support R-bloggers, and place your banner here.

Never miss an update!
Subscribe to R-bloggers to receive
e-mails with the latest R posts.
(You will not see this message again.)

Click here to close (This popup will not appear again)