Alberto Monteiro wrote: > Duncan Murdoch 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 > > Yes, but there's an alternative interpretation:
maximize g(x,y) over y _subject to_ f(x,y) being maximized over x => maximize g(y,y) over y => y = x = 1.5 (this sort of optimization problem arises naturally if you want a least-squares fit to a function given by a partial differential equation and solve the latter using some minimization method). -- O__ ---- Peter Dalgaard Øster Farimagsgade 5, Entr.B c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918 ~~~~~~~~~~ - ([EMAIL PROTECTED]) FAX: (+45) 35327907 ______________________________________________ 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.
