This paper introduces an adaptive artificial intelligence (AI)-based home energy management system (HEMS) to mitigate the discomfort of customers and reduce operational costs. A techno-economic smart HEMS is proposed for home microgrid management, employing two control approaches. The initial approach involves employing an FPGA as a central control unit due to its high-speed processing capabilities and efficient handling of rapid changes within desired limits. The other approach aims to optimize the performance of the microgrid and obtain an optimal operating plan for home microgrids by integrating power limitations using a developed coordinated strategy. A multi-objective optimization problem is formulated that involves the coordinated operation of backup sources. The study utilizes the African Vultures Optimization Algorithm (AVOA) and compares it with newly introduced algorithms, with a specific emphasis on three techno-economic objectives. The simulation and experimental results indicate that the AI-embedded FPGA-based HEMS not only enhances performance and extends Battery Energy Storage Systems (BESSs) life but also reduces peak times resulting from random electric vehicle charging. Through comparative analysis, the superiority of the AVOA is evident, attaining the lowest operating cost of 1308.85$ by the end of the day, reflecting a 3.77% reduction in operating costs compared to the previous study.