## 5 Conclusions  
In this paper, optimization of both load shedding and PEMFCS size in a commercial aircraft was investigated. The proposed multi-objective optimization was cast as MIQP. A model to better prioritize system's loads was presented, then its effect on the optimum size of the fuel cell was studied and compared with the simple priority method. The proposed model also takes into account the cost of interruption, EENS and load criticality. The main results of the numerical analysis are as follows:  
1. With the proposed two-objective optimization model, it is possible to establish a tradeoff between choosing the size of the fuel cell (in terms of weight and consumption of hydrogen) and load shedding in the critical modes. The output of the proposed two-objective problem is to provide a series of solutions that help the user to select the appropriate fuel cell size. The optimal solution is to reduce hydrogen consumption and load shedding during emergency condition simultaneously;
2. Prioritizing loads will definitely affect the size of the fuel cell as a source of emergency power unit. By choosing a suitable model to prioritize the loads in critical situations, the optimal fuel cell size can be selected. With the proposed priority model an optimum size of fuel cell which uses lower hydrogen and reduces the load shedding is achieved;
3. Paying more attention to the cost of hydrogen consumption rather than the cost of load shedding leads to better solutions. Because for \(\beta=0.6\) or \(\beta=0.7\), the more appropriate solutions are achieved;
4. The amount of battery capacity has a significant impact on the optimal solutions. Without considering the weight limits of the ESS, the load shedding during emergency situations will be reduced with the increase in its capacity;
5. Using the transformations performed in Section 3.1, the optimization model is solved with CPLEX, which makes it possible to efficiently and quickly solve the problem. The execution time of the model in GAMS was 0.114 s.
6. In future research, the degradation of ESS and PEMFCS will be considered in this model.  
All the authors conceived the idea, developed the method, and conducted the experiment. [PERSON] contributed to the formulation of methodology and experiments. [PERSON] contributed to the data analysis and performance analysis. [PERSON] contributed to the overview of the proposed approach and decision analysis. [PERSON] and [PERSON] contributed to the algorithm design and data sources. All authors read and approved the final manuscript.  
This research was funded by the National Natural Science Foundation of China [61811530332, 61811540410], the Open Research Fund of Hunan Provincial Key Laboratory of Intelligent Processing of Big Data on Transportation [2015 TP1005], the Changsha Science and Technology Planning [KQI703018, KQI706064], the Research Foundation of Education Bureau of Hunan Province [17A007, 16A008], Changsha Industrial Science and Technology Commissioner [2017-7].  
We are grateful to our anonymous referees for their useful comments and suggestions. The authors also thank [PERSON], [PERSON], [PERSON] and [PERSON] for their useful advice during this work. [PERSON] is the corresponding author.  
The authors declare no conflict of interest.