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From: dtj@sumac.cray.com (Dean Johnson)
Newsgroups: comp.software-eng
Subject: Re: Brand New Optimization Methods
Message-ID: <150402.23480@timbuk.cray.com>
Date: 4 Jun 91 23:31:18 GMT
Article-I.D.: timbuk.150402.23480
References: <91154.224250EC13@LIVERPOOL.AC.UK>
Reply-To: dtj@sumac.cray.com (Dean Johnson)
Organization: Cray Research, Inc.
Lines: 53


In article <91154.224250EC13@LIVERPOOL.AC.UK>, EC13@LIVERPOOL.AC.UK writes:
|> I am including here some numerical examples solved using the new entropy-based
|> methods......
|> 
|> 1)In Vector Optimization to generate Pareto set:
|> ------------------------------------------------
|> This example was taken from 'Multicriterion Optimization in Engineering',
|> Osyczka, Ellis Horwood, Chichester, 1984. It is a beam design example.
|> 
|> F1(X) = 0.785{x1 (6400 - x2**2) + (1000 - x1) (10000 - x2**2)} mm^3 ----> Min
|> 
|> F2(X) = 3.298 x 10^(-5) {[(1/(4.096 x 10^6 - x2**4)) - (1/(10^8-x2**4))] * x1^3
|>         + (10^9/(10^8 - x2**4))} mm/N                               ----> Min
|> 
|> S.t.:  g1(X) = 180 - 9.87 x 10^6 * x1 / (4.096*10^7 - x2**4) >=0
|>        g2(X) = 75.2 - x2 >=0
|>        g3(X) = x2 - 40 >=0
|>        x1,x2>=o
|> Using the 1st entropy-based method, which can generate convex solutions only,
|> I was able to obtain 18 solutions while using the 2nd entropy-based method I
|> was able to generate 53 solutions. The results are summarized below:
|> -------------------------------------------------------------------------------
|>         The Entropy-Based Weighted Objectives Function Method (EWOF)
|> -------------------------------------------------------------------------------
|>   No.           X=(x1,x2)                              F(X)=(F1,F2)
|> -------------------------------------------------------------------------------
|>   1             (165.29, 75.2)            (0.2943695e+07, 0.49924662e-03)
|>   2             (183.58, 74.609)          (0.2961524e+07, 0.495371176e-03)
|>   3             (192.75, 74.307)          (0.2970895e+07, 0.493597705e-03)
|>   4             (202.39, 73.986)          (0.2981043e+07, 0.491856365e-03)
|>   5             (212.51, 73.744)          (0.2992045e+07, 0.490157399e-03)
|>   6             (219.88, 73.392)          (0.3000292e+07, 0.489001861e-03)
|>   7             (223.67, 73.262)          (0.3004618e+07, 0.488433288e-03)
|>   8             (152.71, 40.0)            (0.6162431e+07, 0.340317842e-03)
|>   9             (145.21, 40.0)            (0.6183632e+07, 0.340058003e-03)
|>  10             (137.95, 40.0)            (0.6204248e+07, 0.33983076e-03)
|>  11             (132.72, 40.0)            (0.6218924e+07, 0.33968105e-03)
|>  12             (131.05, 40.0)            (0.6223628e+07, 0.33963611e-03)
|>  13             (124.50, 40.0)            (0.624214 e+07, 0.339468941e-03)
|>  14             (110.72, 40.0)            (0.6281057e+07, 0.339171384e-03)
|>  15             (101.02, 40.0)            (0.6308531e+07, 0.339000951e-03)
|>  16             (96.227, 40.0)            (0.6321995e+07, 0.338929007e-03)
|>  17             (74.569, 40.0)            (0.6385737e+07, 0.33867266e-03)
|

Ooooohhhhh.... now that hits the spot! My life is now complete, I can die a 
happy man ;-)
--
	-Dean Johnson
	 Software Berserker/Rabid-Prototyping Specialist
	 Tools, Libraries, and Commands Group
	 Cray Research Inc.	Eagan, MN	(612) 683-5880