Hole making is an important phase in composite machining as structural applications of composites require assemblage. To do so, abrasive waterjet machining (AWM) is recommended by several fabricators and researchers. The quality of the holes produced in composites severely affects the durability of assembled structures. Hence, exploring this aspect is important. In this context, the current study investigates the influence of the AWM variables on GFRP composites. Here, cutting speed (V_c), and abrasive flow rate (Q_ab) are selected as input variables whereas the output attributes are the material removal rate (MRR), surface roughness (R_a), roundness (R_o), and cylindricity (C_y). Initially, mathematical models (objective functions) are derived using statistics of nonlinear regression for correlating the aforementioned variables and output attributes. In the next phase, the study utilizes recently developed Rao algorithms i.e. Rao 1, Rao 2, and Rao 3 to determine the ideal machining condition as V_c = 100 cm/min, and Q_ab = 300 gm/min. The results were also compared with the JAYA and TLBO approaches in order to show the effectiveness of the proposed methodology and it was observed that exploration of Rao 1, Rao 2, and Rao 3 algorithms appears more fruitful in terms of computational time and effort.