A revised forward and backward heuristic for two-term multiple recursive random number generators

This paper is concerned with designing a full period two-term kth-order multiple recursive generator (MRG) with the objective of maximizing the spectral value. A new heuristic that combines a forward and backward method with random and best-improving is presented. We adopt a statistical analysis to compare the performance of the new heuristic to the random search method for the full period two-term MRGs of orders three and four. We also perform a single longer experiment with maximum allowed CPU 604 800 s to compare the spectral value found using the new heuristic with the best of the previously published one. The results presented in this paper show that our method is indeed very effective with respect to the spectral value. Therefore, the new heuristic is a good way of obtaining an ideal two-term MRG of higher orders.