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From: "Steven_Lord" <slord@mathworks.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Optimizing a selection problem
Date: Sun, 10 Oct 2010 01:37:54 -0400
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"Jordan " <j333poppenk@removethethrees.princeton.edu> wrote in message 
news:i8p0oc$fbe$1@fred.mathworks.com...
> Dear Matlab users,
>
> I am new to optimization problems and hope that someone may be able to 
> help me find a solution.
>
> I have two groups of 100 people, all of whom have two features (age and 
> education). I would like to match up each individual with a similar person 
> from the other group.
>
> It is simple enough to start by picking the best matches from the group, 
> but of course you are punished for this with bad pairings once you get to 
> the bottom of the pool with ill-fitting leftovers. Optimizing pairings 
> across the entire group for the minimum overall difference in age and 
> education is a difficult problem that I need Matlab to solve.
>
> Can anyone point me towards an appropriate function or algorithm? The 
> optimization toolbox seems to be geared towards continuous functions, 
> whereas this is quite a different problem. Sampling the entire set of 
> possibilities does not seem practical owing to large combinatorials.

This sounds to me like the assignment variety of the (mathematical) marriage 
problem:

http://en.wikipedia.org/wiki/Marriage_problem

There are probably implementations of the Hungarian algorithm on the File 
Exchange; if not it's not that difficult an algorithm to implement, if I 
remember correctly.

-- 
Steve Lord
slord@mathworks.com
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