Response surface methodology (RSM) is one of the most effective tools for optimizing processes, and it has been used in conjunction with the Analysis of Variance (ANOVA) test to establish the effect of input factors on output factors. However, when this methodology is used in mineral flotation, its polynomial model usually performs poorly. An alternative is to use artificial neural networks (ANNs) in such situations. Within this context, the ANOVA test is not the best option for these model types; moreover, it requires statistical assumptions that are difficult to satisfy in flotation. This work proposes replacing the polynomial model of the RSM with ANNs and the Sobol methods to determine the influential input factors instead of the ANOVA test. This proposal is applied to two porphyry copper ores with a high content of pyrite, clay, and dilution media. In addition, this study shows how other computational intelligence techniques, such as swarm intelligence, can be incorporated into this type of problem to improve the learning process of ANNs. The results gave an adjustment of over 0.98 for R2 using ANNs, in comparison to values of around 0.5 when the polynomial model of RSM was utilized. On the other hand, the application of Global Sensitivity Analysis (GSA) identified the aeration rate and P80 size as the most influential variables in copper recovery under the conditions studied. Additionally, we identified significant interactions that affect the recovery of copper, with the interactions between the aeration rate, frother concentration, and P80 size being the most important.