Newsgroups: comp.ai.genetic
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From: m1mbg00@newfed.frb.gov (Michael B Gordy)
Subject: GA to approximate monotonic increasing function
Message-ID: <DC0sCx.FF2@glendora.uucp>
Sender: usenet@glendora.uucp (Usenet)
Reply-To: m1mbg00@frb.gov
Organization: Federal Reserve Board
Date: Thu, 20 Jul 1995 15:00:32 GMT
Lines: 23

I'm trying to use a genetic algorithm to find the optimal bidding strategy
in a somewhat complex auction.  I've been modeling the unknown function
as a polynomial, and using a genetic algorithm to find the optimal
coefficients.  The main drawback to this approach is that it does not
take advantage of an important a-priori known property of the bidding
function:  B(x) must be monotonic increasing on x in [0,infinity).  
I also known that B(0)=0.  Using the polynomial approach, I can enforce 
that starting point condition by setting the constant term in the
polynomial to zero.

What alternatives are there to modeling the function as a polynomial?
I thought of one other approach, which is to model B(x) as the integral 
from 0 to x of p(y)^2 dy, where p is a polynomial.  This would ensure 
that B(x) is increasing on [0,infinity).  Seems like something more 
elegant might exist, though!


Any suggestions appreciated!

-- Michael Gordy
   Federal Reserve Board


