The design of fin structures and the formulation of heat conductivity enhancers have always been critical factors influencing the performance of latent heat storage devices. However, achieving the optimal parameters of fin structures and the fraction of heat conductivity enhancers when adjusting multiple parameters simultaneously remains a time-consuming and labor-intensive task. In this paper, a combination of machine learning methods and computational fluid dynamics (CFD) was employed to optimize the parameters of fin structures and the mass fraction of expanded graphite with minor computational resources and time costs, thereby obtaining a set of Pareto optimal latent heat storage (LHS) devices that simultaneously considers energy storage power and energy storage capacity. The combination essentially is a surrogate assistant multi-objective evolutionary optimization algorithm, which utilizes batch recommendation strategies to recommend multiple high-quality candidate solutions that achieve a balance between two conflicting optimization objectives in CFD simulations. This method significantly reduces the number of model iterations and saves the time and computational resources required for multi-objective optimization. The results showed that the proposed algorithm only required 80 cases of CFD calculations to obtain two well-fitted Gaussian process models, leading to a 91 % improvement in computational efficiency. According to the recommendations from the algorithm, the LHS device with 78 fins of 2.0 mm thickness and 20 % mass fraction of expanded graphite could achieve the optimal trade-off of energy storage power and energy storage capacity. Compared to the prototype, the energy storage power and total energy storage capacity increased by 46.7 % and 22.1 %, respectively. The method proposed in this study can provide guidance for the optimal configuration design of LHS devices.