The hybrid energy storage microgrid consists of multiple energy storage technologies, including battery energy storage systems, supercapacitors, compressed air energy storage, and hydrogen energy storage, among others. This multi-energy storage system enables efficient conversion, storage, and utilization of electrical and thermal energy through collaborative operation and mutual supplementation, thereby enhancing the energy supply reliability and economic viability of the overall energy system. In this paper, we propose a novel genetic algorithm-based optimal economic dispatch strategy for hybrid energy storage microgrids. The objective is to minimize the operational cost of the microgrid while satisfying the energy demand and various operational constraints. The proposed genetic algorithm considers the dynamic characteristics and constraints of different energy storage technologies, allowing for an optimized allocation of power and energy among the storage systems.