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The relay coordination problem is of dire importance as it is critical to isolate the faulty portion in a timely way and thus ensure electrical network security and reliability. Meanwhile a relay protection optimization problem is highly constraint and complicated problem to be addressed. To fulfill this purpose, Harris Hawk Optimization (HHO) is adapted to solve the optimization problem for Directional Over-current Relays (DOCRs) and numerical relays. As it is inspired by the intelligent and collegial chasing and preying behavior of hawks for capturing the prey, it shows quite an impressive result for finding the global optimum values. Two decision variables; Time Dial Settings (TDS) and Plug Settings (PS) are chosen as the decision variables for minimization of overall operating time of relays. The proposed algorithm is implemented on three IEEE test systems. In comparison to other state-of-the-art nature inspired and traditional algorithms, the results demonstrate the superiority of HHO. [ABSTRACT FROM AUTHOR]