The effective functioning and regulation of power systems crucially rely on the coordination of distance and directional overcurrent relays. Accurate fault detection and successful clearing sequences require support for each relay and the maintenance of the coordination time interval (CTI) between major distance relays, directional overcurrent relay support, and other relay zones. Efficiently initiating relays while adhering to complex coordination limitations poses a challenging task that demands innovative solutions. This study addresses the intricate problem of relay coordination by employing heuristic methods, specifically genetic algorithms (GA) and biogeography-based optimization (BBO), in both a 9-bus and 39-bus system. The primary objective is to determine the most efficient time setting factor (TSM) that minimizes the duration of relay operation. Additionally, the intelligent features of the overcurrent relay are carefully chosen to enhance the research's results. The integration of edge computing capabilities plays a significant role in advancing this coordination method. By incorporating advanced algorithms and communication technologies at the edge, the prompt activation of relays becomes possible, thereby meeting coordination demands. This study explores the combination of edge-based servers with genetic algorithms (GA) and biogeography-based optimization (BBO) techniques to enhance relay coordination. The findings indicate a notable enhancement compared to conventional approaches. However, comparative research suggests that BBO's performance is similar to GA, without a distinct advantage in achieving higher outcomes.