Searching for good multiple recursive random number generators via a genetic algorithm

In designing ideal multiple recursive random number (RN) generators (MRGs), the best set of multipliers, in terms of the lattice structure of the RNs produced, is sought. As the order of the MRG increases, the number of possible sets of multipliers to be examined grows exponentially. This paper proposes a genetic algorithm for designing good MRGs. The set of multipliers associated with the MRG is encoded as a binary string. Via the operations of reproduction, crossover, and mutation, new sets of multipliers are generated. The spectral values of the MRGs are calculated to guide the search process. As an illustration, the proposed algorithm is employed to find good sets of multipliers for MRGs of orders three and four. The results are better than those derived from other studies. To conclude, this paper not only finds better MRGs of orders three and four, but also develops an algorithm for designing MRGs of higher orders.