The present  study is focussed on a comparative analysis of different meta-heuristic optimization approaches for directional overcurrent relay (DOCRs) coordination which has been discussed and presented in the literature. Further, to have a comparative analysis of the performance of the optimization methods discussed they have been tested on power system network of different sizes. To overcome such issues, this work proposed a simplex linear programming technique-based overcurrent relay method using general algebraic modelling system (GAMS). The execution of this work is done on the MATLAB 2018 a platform. Based on the obtained result the best meta-heuristic optimization method for mitigating the problem of relay coordination has been identified. Nevertheless, the operating time of the relay is high, so the fault is not corrected at a time. The developed model has been tested on test system of different sizes namely IEEE 9 bus and IEEE 14 bus system. The obtained values through series of simulation are compared with different methods for proving the proposed protection coordination scheme is more effective and efficient than others in terms of operating time and coordination time.