In this work, we suggest that the poorer results obtained with particle swarm optimization (PSO) in some previous studies should be attributed to the cross-validation scheme commonly employed to improve generalization of PSO-trained neural network river forecasting (NNRF) models. Cross-validation entails splitting the training dataset into two, and accepting particle position updates only if fitness improvements are concurrently measured on both subsets. The NNRF calibration process thus becomes a multi-objective (MO) optimization problem which is still addressed as a single-objective one. In our opinion, PSO cross-validated training should be carried out under an MO optimization framework instead. Therefore, in this work, we introduce a novel MO variant of the swarm optimization algorithm to train NNRF models for the prediction of future streamflow discharges in the Shenandoah River watershed, Virginia (USA). The case study comprises over 9,000 observations of both streamflow and rainfall observations, spanning a period of almost 25 years. The newly introduced MO fully informed particle swarm (MOFIPS) optimization algorithm is found to provide better performing models with respect to those developed using the standard PSO, as well as advanced gradient-based optimization techniques. These findings encourage the use of an MO approach to NNRF cross-validated training with swarm optimization.