The availability of sustainable, efficient electricity access is critical for rural communities as it can facilitate economic development and improve the quality of life for residents. Isolated microgrids can provide a solution for rural electrification, as they can generate electricity from local renewable energy sources and can operate independently from the central grid. Residential load scheduling is also an important aspect of energy management in isolated microgrids. However, effective management of the microgrid’s energy resources and load scheduling is essential for ensuring the reliability and cost-effectiveness of the system. To cope with the stochastic nature of RERs, the idea of an optimal energy management system (EMS) with a local energy transactive market (LETM) in an isolated multi-microgrid system is proposed in this work. Nature-inspired algorithms such as JAYA (Sanskrit word meaning victory) and teaching–learning based optimization algorithm (TLBO) can get stuck in local optima, thus reducing the effectiveness of EMS. For this purpose, a modified hybrid version of the JAYA and TLBO algorithm, namely, the modified JAYA learning-based optimization (MJLBO), is proposed in this work. The prosumers can sell their surplus power or buy power to meet their load demand from LETM enabling a higher load serving as compared to a single isolated microgrid with multi-objectives, resulting in a reduced electricity bill, increased revenue, peak-average ratio, and user discomfort. The proposed system is evaluated against three other algorithms TLBO, JAYA, and JAYA learning-based optimization (JLBO). The result of this work shows that MJLBO outperforms other algorithms in achieving the best numerical value for all objectives. The simulation results validate that MJLBO achieves a peak-to-average ratio (PAR) reduction of 65.38% while there is a PAR reduction of 51.4%, 52.53%, and 51.2% for TLBO, JLBO, and JAYA as compared to the unscheduled load.