## 3 Results  
### Least-Cost-Path Analysis for the Test Area  
As mentioned in the methodology, the development of the method for generating heating networks on the basis of street networks happened in a few steps. The first one involved matching the path line to each point (centroid) representing a building. Figure 7 provides a close-up view of a part of the network's branches to reveal its real structure.  
In the next step, the path line, as seen in the Figure 7, was optimized in order to run the network while taking into account all the network endpoints. Hereby, a path line Version 1 was generated. Figure 8 depicts the outcome of the automated analysis steps in the test area.  
In order to prevent branching out to each of the buildings and obtain only a generalized network structure, it was necessary to select the edge buildings for analysis and repeat it. The result is shown in Figure 9 as path line Version 2.  
Figure 10 shows the final result of the proposed LCPA. The result is the generated district heating network for the small analyzed test area. The generated DH network begins from the starting point, which is the heat source, and follows each of the heat consumers along the available street network.  
Figure 6: Workflow of the Closest Facility method generated using ArcGIS Pro Model Builder.  
Figure 7: Selection of network branches for the test area.  
Figure 8: Simplified network for the test area: Version 1.  
Figure 9: Final network for the test area: Version 2.  
Looking at the heating network generated for the test area, we can observe that it was generated appropriately considering our assumptions. This means that we decided to plot the network according to street network, starting from the heat source as the starting point and following to each of the end points, which are the heat consumers. Another really important issue when generating the DH route is that it should not have closing spaces like, e.g., circle or rectangle spaces. The DH generated should map out the shape of a tree.  
Cost Distance Surface (CDS)  
As mentioned in the above, the methodology generated in the first step a Cost Distance Surface (CDS), which calculates the least accumulative cost distance for each cell from or to the least-cost source over a cost surface. In Figure 11, a CDS for the selected study area is shown.  
Figure 11: Cost Distance Surface (CDS) for the selected study area.  
Figure 10: Final heating network generated for the test area.  
The raster shown above illustrates effectively the cost distance from the heat source (starting point) for each considered cell within it, considering only the distance in [m] from the heat source to each cell of the street network.  
Generated Heating Network  
The next steps for generating the heating network on the basis of the CDS were described in detail and visualized using the example of the test area in the previous sections of this paper. The same method was also used for the selected study area. The outcome of it, which is the DH network, is shown in Figure 12.  
Analyzing Figure 12, there is one important weak point by generating heating pipes using the LCPA method. This is due to the fact that the method presented in this paper generates some redundant (duplicate) heating pipes routes. This is caused by the fact that the method considers only the distance between the heat source and end points (heat consumers) each time the heating pipe is generated.  
One example of the weak point is shown in Figure 13 in the black box, where two heating pipes were generated even though only one would be enough to connect all the heat consumers placed in this area. The other one could be removed, as done using red lines in the Figure 13.  
This weak point results from the fact that each time the heating pipe is generated, it takes into consideration the distance between the heat source and the end point of the heat consumers, and not the shortest distance between the target not connected end point and the end point almost connected in case there is a street network available.