To overcome the disadvantages of traditional genetic algorithms, which easily fall to local optima, this paper proposes a hybrid genetic algorithm based on information entropy and game theory. First, a calculation of the species diversity of the initial population is conducted according to the information entropy by combining parallel genetic algorithms, including using the standard genetic algorithm (SGA), partial genetic algorithm (PGA) and syncretic hybrid genetic algorithm based on both SGA and PGA for evolutionary operations. Furthermore, with parallel nodes, complete-information game operations are implemented to achieve an optimum for the entire population based on the values of both the information entropy and the fitness of each subgroup population. Additionally, the Rosenbrock, Rastrigin and Schaffer functions are introduced to analyse the performance of different algorithms. The results show that compared with traditional genetic algorithms, the proposed algorithm performs better, with higher optimization ability, solution accuracy, and stability and a superior convergence rate.

An iterative method for identifying generalized diagonally dominant matrices\break (GDDMs, or H-matrices) was given in [B. Li et al., Linear Algebra Appl., 271 (1998), pp. 179--190], where the method is divergent when the matrix is not a GDDM. In this paper, we present an improved version. The new method is always convergent and needs fewer iterations than the earlier one. Some interesting features of the new method are presented. Spectral radii of nonnegative matrices with a constant diagonal entry also can be computed by our method.