Random search

A simple, but very popular approach is the random search which centres a symmetric probability density function - most the normal distribution, about the current best location. The standard normal N(0, 1) distribution is a popular choice, although the uniform distribution U[-1, 1] is also common.

A variation of
the random search technique determines the maximum of the objective function by
analysing the distribution of z(**p**) in the bounded subregion. In this
variation, the random data are fitted to an asymptotic extreme value
distribution, and z(**p**) is estimated
with a confidence statement. Unfortunately, these techniques cannot determine
the location of z(**p**) , which can be
as important as the z(**p**) value
itself. Some techniques calculate the mean value and the standard deviation of
z(**p**) from the random data as they are collected. Assuming that z(**p**) is distributed normally in the
feasible region, the first trial, that yields a z-value two standard deviations
within the mean value, is taken as a near optimum solution.