Wednesday, May 05, 2010

Rosenbrock Function And The Steepest Descent

It's interesting how the steepest descent method sweats a lot if not correctly set up inside the "right" parameters' interval of the Rosenbrock Function:

It's a well known testbed optimization function and evolutionary algorithms can find its optimum with no problems at all -- surely, as long as you try a traditional parameters' setting that any introductory Evolutionary Computation book gives you.

Using the steepest descent and setting it up as:

x = 2

y = 2

Step Size = 0.001

Stop Criterion = 10-6

I got the following results (see the image below):

Pay attention to the path the steepest descent takes until finding the optimum at x = 1 and y = 1. It is said that an evolution strategy would follow a similar path if its population could be infinite. Since, so far, there are no real computers with infinite memory, such assumption cannot be verified in the real world.

During a second run I set the parameters x = 5 and y = 5. The optimization path run very far away from the previous one! And from the optimum too!

Labels: , , , , , , , , ,


Anonymous Anonymous said...

"It is said that an evolution strategy would follow a similar path if its population could be infinite. "

This is only true if also (i) the step-size is 'set' to zero and (ii) it uses an isotropic sample distribution. For non-zero step-size, there are two possibilities with infinite population size: (i) finite parent number (truncation ratio zero), in which case an ES steps right into the optimum. (ii) the usual truncation ratio. Then, as with finite population size, the behavior depends essentially (i) on the step-size and (ii) on the shape of the mutation distribution. When using the distribution which is optimal in the finite case, infinite population will not change a lot.

02 December, 2010 14:55  
Blogger Joshua Smith said...

Its interesting. Turn your attention on auto insurance rates by zip code to help you to save on home policy.

02 November, 2011 10:14  
Blogger Right here waiting said...

The bravery of each bull is then rated with care according to the number of times he demonstrates his willingness to charge in spite of the sting of the blade Runescape gp, Henceforth will I recognize that each day I am tested by life in like manner. If I persist, if I continue to try, if I continue to charge forward, I will succeed rs gp, Your future depends on your dreams Runescape2 Gold. So go to sleep. Do not keep anything for a special occasion..

16 May, 2013 23:32  

Post a Comment

Links to this post:

Create a Link

<< Home

Charles Darwin Has A Posse Check Google Page Rank