Genetic algorithms can be used to obtain good linear congruential generators

Abstract

Linear Congruential Generators (LCGs) are one model of pseudorandom number generators used in a great number of applications. They strongly depend on, and are completely characterized by, some critical parameters. The selection of good parameters to define a LCG is a difficult task mainly done, nowadays, by consulting tabulated values [10] or by trial and error. In this work, the authors present a method based on genetic algorithms that can automatically solve the problem of finding good parameters for a LCG. They also show that the selection of an evaluation function for the generated solutions is critical to the problem and how a seemingly good function such as entropy could lead to poor results. Finally, other fitness functions are proposed and one of them is shown to produce very good results. Some other possibilities and variations that may produce fine linear congruential generators are also mentioned.