This work presents an analysis of L-band Erbium-Doped Fiber Amplifier (EDFA) performance under various pumping configurations. We employed an artificial neural network and a multi-objective optimization algorithm to find the amplifier Pareto front for gain and noise figure. To achieve this, we utilized a recurrent neural network (RNN), trained with experimentally acquired data, jointly with the Multi-Objective Water Cycle Algorithm (MOWCA). Results demonstrate the feasibility of achieving reasonable gains (up to 22 dB) with low noise figures (around 4 dB) across various pumping configurations. Furthermore, we observed a potential gain increment of up to 3.5 dB without significant noise figure degradation when employing bi-directional pumping compared with forward pumping. These insights may contribute to the design of more efficient L-band EDFAs.