Protection coordination is the process of determining the primary protective device that is responsible for clearing the fault as quickly as possible. For each fault location, taking into account in the event that any of these devices fail, each should be backup by another protective device. The coordination of these overcurrent relays is a very tedious process, thus, automating the relay settings with the desired coordination time interval is necessary. This paper introduces a new problem formulation and presents the justification using mathematical proof and computer simulation. The objective function to be minimize is defined as the sum of the time dial settings of all the relays. The inequality constraints guarantee the coordination margin for each primary/backup relay pair having a fault very close to the primary relay. Using this formulation, the size of the optimization problem is significantly reduced. However, in this study, coordination of directional overcurrent relays solved using genetic algorithm, the test system is IEEE 14-bus bar and a meshed system with DGs. Three case studies has been considered, case 1 with no DG (reference case), case 2 with presents of four DGs and last case is worst case scenario. The results of this study are vital to the determination of the best coordination settings of overcurrent relays by minimizing the operation time. The z-test and percent difference are used to determine the significant difference of case studies and compared to the reference case.