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: Evolution Strategy, Evolutionary Algorithm, Evolutionary Computation, Genetic Algorithm, Gradient Method, Optimization, Optimization Path, Optimum Seeking, Rosenbrock Function, Steepest Descent