In this paper, we present a new evolutionary technique to train three general neural networks. Based on family competition principles and adaptive rules, the proposed approach integrates decreasing-based mutations and self-adaptive mutations to collaborate with each other. Different mutations act as global and local strategies respectively to balance the trade-off between solution quality and convergence speed. Our algorithm is then applied to three different task domains: Boolean functions, regular language recognition, and artificial ant problems. Experimental results indicate that the proposed algorithm is very competitive with comparable evolutionary algorithms. We also discuss the search power of our proposed approach.