# [R] Multi-objective optimization

Daniel Lakeland dlakelan at street-artists.org
Thu Oct 18 01:24:02 CEST 2007

```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

```