It is widely known that particle swarm optimization (PSO) has some drawbacks, especially it loses diversity easily. In order to solve this problem, some improved PSOs were proposed which update velocity according to diversity. However, some important information about particles is still not sufficiently utilized such as fitness values. As a gradient descent method, backpropagation (BP) algorithm is often used to train artificial neural networks (ANNs), but it is apt to converge to local minima. To improve global search ability, it was combined with improved PSOs to form new hybrid algorithms like IARPSOs-BP. In this paper, we introduced two algorithms based on IARPSOs and they are combined with BP to train ANNs. In the new algorithms, particles were classified according to fitness values, and different categories have different flight strategies. The experiment results of three benchmark functions and four benchmark classifications prove the proposed algorithms have a better performance than IARPSOs.