Traditional design methods for thermal energy storage systems (TES) with phase change material (PCM) are mostly based on worst-case scenario, which causes too large size of main components. Current optimal design methods for these systems mainly focus on single optimization objective, which only satisfies the unilateral requirement. A multi-objective optimal design method for these systems is urgently needed, and therefore this paper remedies this knowledge gap. The response surface methodology is adopted to develop the surrogated models of the optimization objectives to improve the computational efficiency. Then, the non-dominated sorting genetic algorithm II is used to perform the double-objective and triple-objective optimization for acquiring the Pareto optimal solutions. Finally, the final decision-making methods that includes LINMAP and TOPSIS are adopted to identify the final optimal solutions. A case study of optimizing the design for an outdoor swimming pool (OSP) heating system with PCM storage tank, is conducted to illustrate the proposed approach. Eight final optimal solutions were identified, and the s_p of the system in these solutions was 1.05, 1.24, 1.04, 1.22, 1.06, 1.06, 1.07, and 0.88 years, respectively. Results indicate that the proposed approach is effective to conduct the multi-objective optimization for the OSP heating systems and guide the design optimization for the TES systems with PCM.

具有相变材料（PCM）的热能存储系统（TES）的传统设计方法主要基于最坏情况，这会导致主要组件尺寸过大。这些系统当前的最佳设计方法主要集中在单个优化目标上，仅满足单方面要求。这些系统迫切需要一种多目标优化设计方法，因此本文弥补了这一知识空白。采用响应面方法开发了优化目标的替代模型，以提高计算效率。然后，采用非支配排序遗传算法Ⅱ进行双目标和三目标优化，得到帕累托最优解。最后，采用包括LINMAP和TOPSIS在内的最终决策方法来确定最终的最佳解决方案。以优化带有PCM储水箱的室外游泳池（OSP）加热系统设计为例，以说明所提出的方法。确定了八个最终的最优解，并且在这些解决方案中，系统的s _p分别为1.05年，1.24、1.04、1.22、1.06、1.06、1.07和0.88年。结果表明，所提出的方法对于进行OSP加热系统的多目标优化是有效的，并且可以指导采用PCM的TES系统的设计优化。