What if simultaneously maximizing f(x,y) and g(x,y) is an incompatible objective?
Modifying Duncan's example slightly, What if: f(x,y) = -(x-y)^2 and g(x,y) = -(x-2)^2-(y-x-1)^2? Here: (1) => x = y (2) => y = x + 1 (3) => x = y => no solution! In order for a solution to necessarily exist, one needs to define a scalar function that strikes a compromise between f and g. Ravi. ---------------------------------------------------------------------------- ------- Ravi Varadhan, Ph.D. Assistant Professor, The Center on Aging and Health Division of Geriatric Medicine and Gerontology Johns Hopkins University Ph: (410) 502-2619 Fax: (410) 614-9625 Email: [EMAIL PROTECTED] Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html ---------------------------------------------------------------------------- -------- -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Alberto Monteiro Sent: Wednesday, October 17, 2007 2:30 PM To: Duncan Murdoch; Paul Smith Cc: r-help Subject: Re: [R] Multi-objective optimization 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. ______________________________________________ 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.
