[R] Multi-objective optimization

[Daniel Lakeland]

On Wed, Oct 17, 2007 at 06:54:31PM +0100, Paul Smith wrote:
> Dear All,
> 
> Is there any package to do multi-objective optimization? For instance,
> consider the following problem:
> 
> maximize f(x,y) in order to x
> 
> and
> 
> maximize g(x,y) in order to y,
> 
> simultaneously, with x and y being the same both for f and g. Can R do
> it numerically?


R can solve the following problem using optim, perhaps it helps you:

find x,y such that sqrt(g(x,y)^2+f(x,y)^2) is maximized.

Alternatively, you may want the following:

maximize f(x,y) varying both x and y. Then, holding x constant at the
previous value, maximize g(x,y) varying ONLY y.

This can be done in two steps in R. first use optim on f(x,y), then
when x is determined, create a new function (using "function") that
projects g(x,y) onto the fixed x value ie:

function(y) { g(best.x,y)}

and use optim to optimize this new function varying only y.

Hope this helps. 

-- 
Daniel Lakeland
dlakelan at street-artists.org
http://www.street-artists.org/~dlakelan