In designing a power system, efficacious synchronization of directional over-current relays (DOCRs) plays a pivotal role in guaranteeing the system's stability and ensuring continuous power flow, even in the event of disturbance. However, attaining this optimized strategy pertains to the persistence of solving extremely constrained and nonlinear optimized complications. The main intention is to formulate an optimized coordination strategy to optimize the overall operational time (OT) of DOCRs. This involves featuring optimized values of decision variables, specifically the relay plug settings (PS) and time dial settings (TDS). The designed formulation for DOCRs is employed on various IEEE bus networks like the 8, 9, and 15 bus systems. Comparative evaluation of obtained results is accomplished with numerous algorithms that showcase the competency of the GAMS-driven optimization strategy. The results depict that there is an improvement of 1.8-23 % in the total operational time of relays depending upon the test system under consideration.