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.