## 5 Conclusions  
This study proposed a new algorithm called SSO-DE, which combined a differential evolution (DE) algorithm as the local search strategy with simplified swarm optimization (SSO) to solve the optimization problem of CCHP combined with renewable energy. In addition, this study used the TOPSIS method to convert the original multi-objective optimization problem, including minimizing the operation cost, minimizing the carbon emissions, and maximizing the energy utilization rate, into a single-objective optimization problem to reduce the calculation steps and increase the efficiency of the solution. Moreover, this work studied the CCHP based on Xikou village, Lieyu township, Kinmen county, Taiwan as an experimental case to realize the CCHP-combined-with-microgrid system of renewable energy and help to solve the problem that most of the research on CCHP is limited to construction such as hotels and hospitals. The experimental results obtained by the proposed SSO-DE were compared with POS-DE, iSSO-DE, and ABC-DE, and the numerical results are as follows:  
1. For the spring (autumn) experimental data set, SSO-DE performed the best in terms of best fitness value, average fitness value, and average running time.
2. For the summer experimental data, SSO-DE performed the best in terms of average running time. ABC-DE had the best performance and SSO-DE had the second-best  
Figure 12: Box and whisker diagram for winter. *: Outliers.  
performance in terms of best fitness value, worst fitness value, and average fitness value.
3. For the winter experimental data, SSO-DE performed the best in terms of best fitness value, worst fitness value, average fitness value, and average running time.
4. The results of the [PERSON] test showed that the proposed SSO-DE had the best comprehensive performance among all experimental modules including spring (autumn), summer, and winter. In addition, SSO-DE had the lowest running time in all experiments.
5. The results of [PERSON]'s test (post-hoc test) showed that there was no significant difference between the other three algorithms with SSO-DE. The reason for this result should be that the fitness value performance of SSO-DE in the summer experiment is slightly inferior to that of ABC-DE and the standard deviation performance of SSO-DE is not as stable as that of PSO-DE.  
However, in the three data sets, the running time of SSO-DE was much shorter than other compared algorithms, and [PERSON]'s test in the previous paragraph also confirmed that the comprehensive performance of SSO-DE is the best.  
Conceptualization, W.-C.Y., W.Z., Y.-F.P. and C.-L.H.; methodology, W.-C.Y., W.Z., Y.-F.P. and C.-L.H.; software, W.-C.Y., W.Z., Y.-F.P. and C.-L.H.; validation, W.-C.Y., W.Z. and Y.-F.P.; formal analysis, W.-C.Y., W.Z., Y.-F.P. and C.-L.H.; investigation, W.-C.Y., W.Z. and Y.-F.P.; resources, W.-C.Y., W.Z. and Y.-F.P.; data curation, W.-C.Y., W.Z. and Y.-F.P.; writing--original draft preparation, W.-C.Y., W.Z., Y.-F.P. and C.-L.H.; writing--review and editing, W.-C.Y., W.Z., Y.-F.P. and C.-L.H.; visualization, W.-C.Y. and W.Z.; supervision, W.-C.Y.; project administration, W.-C.Y.; funding acquisition, W.Z. All authors have read and agreed to the published version of the manuscript.  
This research was supported in part by National Natural Science Foundation of China (Grant No. 621060482), Research and Development Projects in Key Areas of Guangdong Province (Grant No. 2021B0101410002) and National Science and Technology Council, R.O.C (MOST 107-2221-E-007-07-07-MY3, MOST 110-2221-E-007-107-MY3, MOST 109-2221-E-424-002 and MOST 110-2511-H-130-002).  
We wish to thank the anonymous editor and the referees for their constructive comments and recommendations, which significantly improved this paper. This article was once submitted to arXiv as a temporary submission that was just for reference and did not provide the copyright.  
The authors