This paper considers the problem of searching for good multiple recursive generators (MRGs) with long period and good lattice structure. We propose a new algorithm that embeds both the tabu list of tabu search and the mutation of genetic algorithm into the simulated annealing (SA) method. Taguchi method is used to find the optimal heuristic parameters in the SA such that the effectiveness of the SA can be further improved. The proposed algorithm is compared with forward/backward method, and its effectiveness is numerically confirmed by the experiments we perform on the reduced third-order MRGs.