*3.1. Case Study*

In order to establish the e ffectiveness of the proposed solution method, a case study calculated on an extra-urban railway line is presented. The NPV of the system is evaluated in 3 cases:


The PSO algorithm is coded in MATLAB ™ (MATLAB 2019b (v9.7), The MathWorks, Inc., Natick, MA, USA) in the "Global Optimization Toolbox" library and was run by entering the following parameters:


### 3.1.1. Topological Characteristics of Railway Line

Figure 5 shows the line: on the x-axis there is the kilometric progressive, while on the y-axis there is the height above sea level. The green line shows the planimetric profile of the railway line, which has a length of 75.1 km. Railway stations are highlighted with red circles while the electric substations along the route are highlighted with blue circles.

**Figure 5.** Characteristics of the railway line.

Between the arrival and departure stations there are three intermediate stations, as shown in the Table 3. As can be seen from Figure 5, there are two tunnels on the line, highlighted with gray rectangles, whose characteristics are shown in Table 4.




**Table 4.** Tunnels' position.

### Finally, Figure 6 shows the slopes of the line.

**Figure 6.** Slope of line.
