In order to design a simple and efficient method to search for the optimal neural network architecture, we propose an improved whale optimization algorithm and its shallow neural architecture search's weights and thresholds optimization. This method first improves the traditional whale optimization algorithm by simulating the individual preference behavior of whale hunting and the nonlinear weight update mechanism of whale group position movement; Then, the improved whale optimization algorithm is used as a shallow BP neural network architecture search strategy, and a architecture based on the optimization method of weight threshold search for the optimal network architecture of the shallow BP neural network is constructed. The numerical experimental results show that the improved whale optimization algorithm not only has good optimization performance in solving complex functions with different dimensions, but also the optimal shallow BP neural network architecture searched by the improved whale optimization algorithm has better prediction accuracy and generalization performance in regression tasks.