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| Re: TNMIN limits [message #57173 is a reply to message #57121] |
Tue, 04 December 2007 11:55  |
Brian Larsen
Messages: 270
Registered: June 2006
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Senior Member |
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> Hi Brian;
> Would you please compare GA(genetic algorithm) with amoeba or SA
> method? Which on is faster? Which one is reliable? Is in the amoeba
> method any divergence problems exist like in GA or SA?
> Cheers
> Dave
> Hi Brian;
> Would you please compare GA(genetic algorithm) with amoeba or SA
> method? Which on is faster? Which one is reliable? Is in the amoeba
> method any divergence problems exist like in GA or SA?
> Cheers
> Dave
Dave, this is no small feat... What I now comes from Numerical
recipes
http://www.nr.com/oldverswitcher.html
and from some experiences both research based and coursework...
In general the more information the algorithm requires the faster it
is. After all you could always get the right answer if you tested
every possible option (I have done this too). Every algorithm is
trying to get to the right answer in the least number of steps. Think
of this practically, if you want to get to the ocean you walk
downhill. You will certainly get there but certainly not the shortest
way (fewest steps). If you look at a map you can then choose the
shortest path. These are all that way also.
Looking at derivatives is another piece of the map making you need
fewer steps. But with that comes the requirement that the function is
differentiable. For Amoeba you don't assume that so you need more
steps than a faster/smarter algorithm like Conjugate gradient. I
always start my search for the minimum is several places regardless of
the method to assure that I get the same answer. If not then which is
the right answer? Also it is often good to try more than one method
but who has the time? Well if you find the new minimum after the
paper is published then you sure feel dumb.
I like to use amoeba as I understand it well and trust it. I am
willing to take the efficiency hit for not having to think as hard or
code as long. But if you are putting it inside a 10^6 for loop than
you had better find a better algorithm.
GA algorithms are really really slow but work great.
This is a bit from an old course note that I happened to pull up. (NR
= Numerical Recipes in C)
Function minimization in N dimensions
(1) Downhill simplex, a.k.a. amoeba (NR §10.4)
* O(N^2) storage
* robust, simple
* Lecture/handout already prepared
(2) Conjugate gradient (NR §10.6)
* Uses Brent's method (NR §10.3) in 1-D
* O(N) storage ==> large problems
* fast/efficient
* requires derivatives (==> smoothness assumed)
(3) Simulated annealing (NR §10.9)
* most robust and simplest of algorithms!
* often finds global minima, even of rough functions
* O(N) storage ==> large problems
* slow as molasses in January
* independent variables need not be continuous!
Cheers,
Brian
------------------------------------------------------------ --------------
Brian Larsen
Boston University
Center for Space Physics
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