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A routing prediction strategy via a pigeon-inspired optimization (PIO)-based neural network (NN) is designed for UAV swarm networks with highly dynamic topology. The proposed strategy can predict the performance of the neighboring nodes as the next hop. For more precise prediction and less computational complexity, the states of the UAV swarm motion and the network are considered as the prior information, and the PIO-based NN framework is established. Based on the system model, PIO is applied to find the optimal weight matrices of the NN-based routing prediction model. The matrix of the hop count index function is calculated using this prediction model. The proposed strategy can directly determine the next hop based on the prediction results or can be combined with other routing methods to maintain a balance between the stability and the shortest path. Numerical simulations are conducted to demonstrate the effectiveness of the proposed strategy.