The problem of coordinating directional overcurrent relay is one of the most important in electrical power system planning and operation. In this paper, a new objective function, based on genetic algorithms of Chu–Beasley, to carry out an optimal coordination of directional overcurrent relay is presented. The characteristics of the genetic algorithms of Chu–Beasley and some modifications, having taken into account inherent constraints to the problem, were used in order to properly solve the problem. A case study including 11 nodes and 22 directional relays was conducted to validate the performance of the proposed technique. Finally, a methodology to obtain a directional overcurrent relay coordination is proposed, including an expert (human) criterion. Detailed results are presented and discussed. © 2018 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.