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.