The manufacturing quality generated by the magnetic abrasive finishing (MAF) of brass depends of some critical process variables. Therefore, in this survey were investigated the optimization of this process taking into account the material removal rate and surface characteristics using a hybrid nature inspired algorithm (particle swarm optimization (PSO) coupled with firefly algorithm (FA)). In the initial step, the design matrix was generated using the Taguchi L16 orthogonal array, thereafter, obtaining the experimental protocol for developing the MAF process. The regression analysis was confronted with the analysis of variance (ANOVA) simulations to facilitate determination of the percentage contribution of each input parameters. The influence of individual and combined process parameters investigated via standard PSO, FA, and hybrid HPSO-FA were used for mono and bi-objective constrained optimization. This innovative way of processing the brass plate revealed that machining time was the most dominant parameter which contributed maximum towards variation in response variables determined.