Display Omitted We solved the Directional Over Current Relays (DOCRs) optimal coordination problem.We used the Electromagnetic Field Optimization Algorithm (EFO).We improved the EFO algorithm for the optimal coordination of DOCRs.The proposed algorithm is better than other optimization algorithms. The optimal coordination of Directional Overcurrent Relays (DOCRs) is of paramount importance for power systems protection. The optimization model of this problem is non-linear and highly constrained. The main objective of this paper is to develop a modified version of the Electromagnetic Field Optimization (EFO) algorithm referred to as MEFO for the optimal coordination of DOCRs. The EFO is inspired by the behaviour of particles of electromagnets with different polarities where attractionrepulsion forces among these electromagnets lead particles toward global minima. It uses also the golden ratio. The proposed algorithm has been applied to three test systems including the 8-bus, the 9-bus and the 15-bus test systems. Furthermore, the results obtained using the proposed MEFO are compared with those obtained using the traditional EFO and a number of well-known algorithms. The obtained results show the effectiveness of the proposed MEFO to minimize the relay operating time for the optimal coordination of DOCRs.