This paper has used linear congruential generator
for generating initial pad and then genetic algorithm is used to improve the randomness of the initial pad.
The source noise can be obtained algorithmically using, for example, a congruential generator
, or physically, using a semiconductor noise generator.
As it is usually implemented, the algorithm is known as a Prime Modulus Multiplicative Linear Congruential Generator
. It is better known as a Lehmer generator.
As a last resort, Ferrenberg substituted different random-number generators and, to his surprise, found that he came much closer to the correct answer by using a linear congruential generator
, which has known defects.
--param selects the appropriate parameters (e.g., the multiplier for a Linear Congruential Generator
or the lag for a Lagged Fibonacci Generator).
* The congruential generator
[x.sub.n] = 16807[x.sub.n]-1 mod [2.sup.31] - 1 is a good generator, but not a great generator.
"A good congruential generator
could be used to run the casinos in Las Vegas and Atlantic City and all the state lotteries with no one the wiser."
We have used a linear congruential generator
fish by Fishman and Moore , an explicit inversive congruential generator
[Eichenauer-Herrmann 1993], and a twisted GFSR generator (tt800 by Matsumoto and Kurita ); at last the infamous randu (again an LCG) as an example of a generator with bad lattice structure (see Park and Miller ).
Equation (1) defines a linear congruential generator
(LCG) in matrix form.
Wu  proposed a clever-looking way to select the parameters and implement a linear congruential generator
(LCG): take a Mersenne prime modulus m, i.e., a prime of the form m = [2.sup.e] - 1 (see Knuth  for more on Mersenne primes), and a multiplier of the form
The BMT uses sine and cosine functions--periodic functions that, when used in conjunction with a linear congruential generator
(LCG) such as the Lehmer generator, produces statistically correlated "random" numbers.
Although R250 passed a number of statistical tests, a recent experience [Selke 1993] showed that R250 gives wrong results for a clustered Monte Carlo simulation, while the multiplicative congruential generator