## 3 Results and Discussion
### Multi-Objective Evaluation Procedure  
The last step in this study is the multi-objective optimization of the unit by using energy and economic criteria. As it was found in the previous section, the use of the SPP as  
Figure 27: Simple payback period for different collecting areas and collector types for Kastoria. Figure 26: Simple payback period for different collecting areas and collector types for Thessaloniki. the sole criterion is not able to lead to energy-efficient designs, and, thus, the combination of the (SPP) and of the (F) is examined through a multi-objective optimization analysis. The objective is to determine the overall optimum choice which combines both low SPP and high F. The described methodology of Section 2.5 is applied, and the goal is to determine the design point with the minimum dimensionless geometric distance from the ideal one, for every city separately. This procedure is a proper one in order to evaluate both criteria in a respective way without taking into account the absolute values of every criterion. Figures 28-31 depict the multi-objective optimization procedures for the cities of Heraklion, Athens, Thessaloniki, and Kastoria, respectively. In every figure, all the design points (combinations of different collectors and collecting areas) are depicted, and the optimum point is the one with the minimum dimensionless distance from the respective ideal one. For all the cities, the optimum collector type is the advanced FPC. This conclusion comes in accordance with the results from the economic optimization according to the LCC minimization criterion. So, there is an accordance in the quality conclusions for the collector type. The last step is to indicate the global optimum designs according to the multi-objective optimization analysis. Table 8 gives these optimum designs; one for every location. For Athens, Thessaloniki, and Kastoria the optimum collecting area is found at 25 m\({}^{2}\), while for Heraklion, the optimum area is 20 m\({}^{2}\). The higher solar potential in Heraklion makes possible the proper operation with a bit lower collecting area. More specifically, for Heraklion, the 20 m\({}^{2}\) of collectors have to be placed with a 40\({}^{\circ}\) tilt angle which leads to 78.59% solar coverage, 13,731 \(\upepsilon\) LCC, and 1.87 years SPP. For Athens, the 25 m\({}^{2}\) of collectors have to be placed with a 45\({}^{\circ}\) tilt angle which leads to 80.25% solar coverage, 15,257 \(\upepsilon\) LCC, and 2.03 years SPP. For Thessaloniki, the 25 m\({}^{2}\) of collectors have to be placed with a 45\({}^{\circ}\) tilt angle which leads to 72.22% solar coverage, 20,257 \(\upepsilon\) LCC, and 2.08 years SPP. For Kastoria, the 25 m\({}^{2}\) of collectors have to be placed with a 45\({}^{\circ}\) tilt angle which leads to 78.67% solar coverage, 22,193 \(\upepsilon\) LCC, and 1.99 years SPP. Figure 28: Multi-objective optimization for the Heraklion city—Zone A.  
Figure 30: Multi-objective optimization for the Thessaloniki city—Zone C.  
Figure 29: Multi-objective optimization for the Athens city—Zone B. The simple environmental analysis shows the CO\({}_{2}\) avoidance due to the use of solar energy for the optimum scenarios of the multi-objective optimization procedure. According to the Greek energy mix, the specific CO\({}_{2}\) emissions are 0.487 kg CO\({}_{2}\)/kWh [36], so this value is used for the calculations in Table 8. It is obvious that there are significant CO\({}_{2}\) avoidance values that indicate the high environmental character of the solar thermal systems. More specifically, the yearly CO\({}_{2}\) avoidance is 5854 kg CO\({}_{2}\)/year for Heraklion, 6762 kg CO\({}_{2}\)/year for Athens, 6573 kg CO\({}_{2}\)/year for Thessaloniki, and 6896 kg CO\({}_{2}\)/year for Kastoria. It is useful to say that the present work indicates relatively low SPP for about two years which are very promising values. These low SPP are lower than other reported in the literature for Greece which was around five years [20; 24].