The precise estimation of a pressure drop in vertical multiphase flowing oil wells plays a crucial role in designing robust production facilities and evaluating optimum production plans. A significant amount of research has been conducted on determining a pressure drop via calculating the bottom hole pressure (BHP); these different methods as well as numerical, analytical, semi-analytical, and empirical correlations can be used for doing this task. Unfortunately, most of those correlations are unable to provide reasonable precision when calculating BHP and, consequently, improvements are still required. To predict BHP in vertical wells, several hybrids of meta-heuristic optimization methods and a bio-inspired connectionist approach, i.e., artificial neural network (ANN), are employed. The main goal of these optimization algorithms is to optimize the parameters of the ANN models, i.e., weights and biases, to improve their performance. Based on the obtained outputs and various robustness indexes, a hybrid genetic algorithm and particle swarm optimization (HGAPSO) is highly precise and has a maximum of 10 % error compared to measured pressure data. The results of this work reveal the capability of those hybrid connectionist models for predicting the BHP of multi-phase flow in vertical wells; these results demonstrate the promising use of connectionist methods in commercial production software in the near future.