Random search (RS) is a family of numerical optimization methods that do not require the gradient of the problem to be optimized, and RS can hence be used on functions that are not continuous or differentiable. Such optimization methods are also known as direct-search, derivative-free, or black-box methods.
Anderson in 1953 reviewed the progress of methods in finding maximum or minimum of problems using a series of guesses distributed with a certain order or pattern in the parameter searching space, e.g. a confounded design with exponentially distributed spacings/steps.[1] This search goes on sequentially on each parameter and refines iteratively on the best guesses from the last sequence. The pattern can be a grid (factorial) search of all parameters, a sequential search on each parameter, or a combination of both. The method was developed to screen the experimental conditions in chemical reactions by a number of scientists listed in Anderson's paper. A MATLAB code reproducing the sequential procedure for the general non-linear regression of an example mathematical model can be found here (JCFit @ GitHub).[2]
The name "random search" is attributed to Rastrigin[3] who made an early presentation of RS along with basic mathematical analysis. RS works by iteratively moving to better positions in the search space, which are sampled from a hypersphere surrounding the current position.
The algorithm described herein is a type of local random search, where every iteration is dependent on the prior iteration's candidate solution. There are alternative random search methods that sample from the entirety of the search space (for example pure random search or uniform global random search), but these are not described in this article.
Random search has been used in artificial neural network for hyper-parameter optimization.[4]
If good parts of the search space occupy 5% of the volume the chances of hitting a good configuration in search space is 5%. The probability of finding at least one good configuration is above 95% after trying out 60 configurations (, making use of the counterprobability).
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