Editing Random optimization (section)

== Algorithm ==
{{See also|Simulated annealing}}
Let <math>f: \mathbb{R}^{n} \rarr \mathbb{R}</math> be the fitness or cost function which must be minimized. Let <math>x \isin \mathbb{R}^{n}</math> designate a position or candidate solution in the search-space. The basic RO algorithm can then be described as:

* Initialize '''x''' with a random position in the search-space.
* Until a termination criterion is met (e.g. number of iterations performed, or adequate fitness reached), repeat the following:
** Sample a new position '''y''' by adding a [[normal distribution|normally distributed]] random vector to the current position '''x'''
** If (''f''('''y''')&nbsp;<&nbsp;''f''('''x''')) then move to the new position by setting '''x'''&nbsp;=&nbsp;'''y'''
* Now '''x''' holds the best-found position.

This algorithm corresponds to a (1+1) [[evolution strategy]] with constant step-size.