Numerous investigations have shown that artificial neural networks (ANNs) can be successful for correlating experimental data sets of macroscopic multiphase-flow characteristics, e.g., holdup, pressure drop, and interfacial mass transfer. The approach proved its worth especially when rigorous fluid mechanics treatment based on the solution of first-principle equations is not tractable. One perennial obstacle facing correlations is the choice of a low-dimensionality input vector containing the most expressive dimensionless independent variables allowing the best correlation of the dependent output variable. Because no clue is known in advance, one has recourse to a laborious, often inefficient, and nonsystematic trial-and-error procedure to identify from a broad reservoir of possible candidates, the most relevant combination of ANN input dimensionless variables. The combinatorial nature of the problem renders the determination of the best combination, especially for multiphase flows, computationally difficult because of the large scale of the search space of combinations. A methodology is devised in this work to cope with this computational complexity by illustrating the potential of genetic algorithms (GAs) to efficiently identify the elite ANN input combination required for the prediction of desired characteristics. The multiobjective function to be minimized is a composite criterion that includes ANN prediction errors on both learning and generalization data sets, as well as a penalty function that embeds phenomenological rules accounting for ANN model likelihood and adherence to behavior dictated by the process physics. The proof of concept of the integrated GA-ANN methodology was illustrated using a comprehensive database of experimental total liquid holdup for countercurrent gas-liquid flows in randomly packed towers for extracting the best liquid hold-up correlation.