# Optimization of Heat Pump Systems in Buildings by Minimizing Costs and CO\({}_{2}\) Emissions
## 5 Discussion  
The results of this study indicate that the optimal heating systems for various types of buildings can be determined using a MINLP multi-objective optimization model. By minimizing the objective function of the problem analyzed, the lowest total costs of the selected heating systems were achieved. The optimization model simulations enabled the determination of the optimal number, type, and capacity of HPs and EHs needed to meet the heat demand for SH and DHW preparation. The results of the optimization include the optimal heating system components, their heating capacity in December, and the proportion of heat produced by HPs and EHs in the first year for each analyzed building. One of the key findings of this study is that in all cases analyzed, the optimal heat production and supply system includes air-to-water HPs as one of its components. Furthermore, for schools and a supermarket (buildings no. 9, 10, and 11), these HPs were combined with hybrid HPs. This implies that the use of air-to-water HPs is a cost-effective and energy-efficient solution for meeting the heating needs of various types of buildings. The use of hybrid HPs in certain buildings can also provide an additional source of energy and enhance the overall efficiency of the heating system. Additionally, EHs of various capacities were selected for all buildings to meet the peak heat demand. The results of the economic and financial analysis show that the optimal heating systems for the buildings are cost-effective, as they have positive NPV and IRR indicators. However, it is important to note that not all systems have positive NPV and IRR indicators, which can be due to the fact that different buildings have different characteristics, and this leads to different optimal systems. The results of this study align with previous research on the topic of heating systems for buildings, which has demonstrated the benefits of using HPs, particularly air-to-water HPs, for energy efficiency and environmental sustainability. Additionally, the findings of this study have practical implications for the design and operation of buildings, as they provide guidance on the selection of heating systems that can meet the heat demand while minimizing total costs. However, it is important to acknowledge that this case study has some limitations. One limitation is that the data used in the simulation were based on assumptions, which may not accurately represent the real-world situation. Additionally, the study only considered a 10-year period. Therefore, it would be beneficial to extend the analysis to a longer time horizon to observe how the optimal heating systems evolve over time. In terms of future research, there are several aspects that could be considered. First, it would be valuable to expand the scope of the study to consider other factors such as environmental sustainability and energy security. Additionally, the study could broaden its scope to include not only heating technologies but cooling technologies as well. This would provide a more complete picture of the energy demands and requirements of buildings and could lead to the development of more efficient and effective systems. Additionally, it would be useful to investigate the potential of using other RES such as solar or wind power in heating and cooling systems. This would not only enhance the overall cost-effectiveness and environmental impact of the systems but also would demonstrate the potential of using a mix of RES in the built environment. Another aspect that would be useful to consider is the use of HPs together with waste heat or water and their application in low-temperature heat networks. Finally, it would be important to apply the methodology of optimal system selection to a city block. By considering the heating and cooling demands of multiple buildings within a city block, the study can better understand the interconnections and synergies between buildings and help to optimize the energy systems at a neighborhood level.