[R] Multi-objective optimization

[Duncan Murdoch]

On 10/17/2007 1:54 PM, 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?

I don't think the problem is well posed.  For example, what's the 
solution if f(x,y) = -(x-y)^2 and g(x,y) = -(x-2)^2-(y-1)^2?  The first 
is maximized at x=y, the second at x=2, y=1, so in order to choose a 
solution you need to specify what sort of tradeoff to use to combine the 
two objectives.

Duncan Murdoch