This study aims to address optimization and operational challenges in multi-energy coupled microgrids to enhance system stability and reliability. After analyzing the requirements of such systems within comprehensive energy systems, an improved fireworks algorithm (IFWA) is proposed. This algorithm combines an adaptive resource allocation strategy with a community genetic strategy, automatically adjusting explosion range and spark quantity based on individual optimization status to meet actual needs. Additionally, a multi-objective optimization model considering active power network losses and static voltage is constructed, utilizing the shuffled frog-leaping algorithm (SFLA) to solve constrained multi-objective optimization problems. Through simulation experiments on a typical northern comprehensive energy system, conducted with a scheduling period of T = 24, the feasibility and superiority of IFWA-SFLA are validated. Results indicate that IFWA-SFLA performs well in optimizing microgrid stability, managing electrical energy flow effectively within the microgrid, and reducing voltage fluctuations. Furthermore, the circuit structure and control strategy of microgrid energy storage bidirectional inverters based on IFWA are discussed, along with relevant simulation results.