On 10/17/07, Alberto Monteiro <[EMAIL PROTECTED]> wrote: > >> 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. > > > I guess the problem was not well _defined_. > > I "interpreted" it as: > > maximize f(x,y) in order to x %means% > (1) for every y, find x = f1(y) such that f(x,y) is max > > maximize g(x,y) in order to y %means% > (2) for every x, find y = g1(x) such that g(x,y) is max > > simultaneously %means% > (3) x = f1(y) and y = g1(x). > > So, for your example, we would have: > (1) => x = y > (2) => y = 1 > (3) => x = y = 1
I apologize for having been not sufficiently clear. Alberto's interpretation corresponds to what I wanted to mean. Can R solve numerically this sort of maximization problems? Paul ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
