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 Alberto Monteiro ______________________________________________ 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.