This paper demonstrates the use of the multi-objective grey wolf algorithm to optimize a discrete Raman amplifier (DRA) in a P2O5-doped optical fiber. Specifically, the multi-objective grey wolf algorithm is combined with the DRA to carry out a process that seeks to maximize the gain and minimize the ripple. The P2O5-doped optical fiber employed in this study has a Raman gain coefficient spectrum with multiple peaks with different frequency shifts. This allows them to be combined in more complex ways than optical fibers with a single peak in the Raman gain spectrum. Consequently, the gain curve produced with this fiber has the potential to be more adjustable even when fewer pumps are used. Thus, this paper explores this fact to perform, to the best of our knowledge, the first specialized optimization process reported in the scientific literature of a wideband discrete Raman amplifier in a P2O5-doped optical fiber. With a different gain profile of this fiber compared to those of traditional standard optical fibers, it was possible to design a wideband DRA, going from 1530 nm to 1675 nm, covering C+L+U bands, maintaining a ripple of up to 8 dB with a net gain of 14 dB using only 3 pumps. Moreover, this work demonstrates for the first time, through a comparative analysis, that the multi-objective grey wolf algorithm performs better than the standard and well-known non-dominated sorting genetic optimization algorithm to optimize a DRA in a P2O5-doped optical fiber. The proposed DRA is a feasible, low-cost, and simple alternative for building fiber amplifiers for future high-bandwidth and wideband wavelength division multiplexing (WDM) communication systems, network infrastructures such as data centers, undersea cables, 5G and beyond, and cutting-edge research applications.