Much attention has been paid to optimizing smart grids (SGs) and microgrids (MGs) protection schemes. The SGs' operation in different operating modes (especially gridconnected and islanded conditions) and various system configurations (such as the outage of each of the distribution generations) adversely influence the protection system. The adaptive protection schemes using different setting groups are suitable and reliable solutions to achieve a fast protective system. However, the literature shows a research gap in developing optimized adaptive protection schemes, focusing on constraint reduction, besides the optimal selection of time-current characteristics for direction overcurrent relays (DOCRs) and high-set relays (HSRs). This research aims to fill such a research gap. The power system analyses, such as power flow and short circuit studies, are done in DIgSI-LENT, and the genetic algorithm (GA) is used to find the optimum solutions. Test results of the IEEE 38-bus distribution system illustrate the advantages of this study compared to existing ones. The comparative test results emphasize that 31.78% and 21.62% decrement in time of the protective scheme in different topologies for the distribution networks of the IEEE 38-bus and IEEE 14-bus test systems could be achievable by simultaneously optimizing relay characteristics and HSRs compared to existing approaches.