# Modeling and Optimization of NO2 Stations in the Smart City of Barcelona
## 4 Methodology
### Optimal Location of Stations  
Lastly, a new placement of stations at strategic locations is proposed to improve the NO2 pollution index in Barcelona, and obtain a more representative average of NO2 concentrations across the city. This is supported by the analysis since it has been determined that the current 8 monitoring stations are insufficient, as they do not cover a large or representative area of the city. To determine the potential new locations, we rely on the report from the European Commission's Mobility Observatory, using the Eltis method [57], which recommends selecting 40 sensitive locations in the city distributed as follows: (i) 5 locations near highways, (ii)5 locations near ring roads, (iii) 10 locations near access roads to the city center, (iv) 10 locations near sensitive facilities (schools, hospitals, residences, etc. ), (v) 5 locations in low-income neighborhoods, and (vi) 5 locations in recreational areas (sports facilities, parks, museums, etc.). The points chosen for this study are shown in Appendix A, Table A1. These strategically selected points cover the entire metropolitan area and are added to the existing stations to form an expanded set of air quality monitoring stations (Figure 2). This approach allows for a more detailed understanding of NO2 concentrations in the city, facilitating the implementation of effective measures to improve air quality in critical areas and throughout Barcelona. These results will support future research and environmental management actions, contributing to more effective policies to reduce NO2 pollution and its adverse impacts. To optimize the placement of air quality monitoring stations in Barcelona, we consider the effective radius of each station, which varies according to traffic levels in the area [58]. We choose an average radius of 500 m due to the city's high traffic intensity. This approach also aims to maximize city area coverage, minimizing the overlap between stations to avoid redundant measurements and ensure no areas are left uncovered. However, the budget constrains the number of stations that can be installed, necessitating a balance between maximizing coverage and managing the costs of implementation and maintenance of the stations. This problem can be modeled as a Capacitated Dispersion Problem (CPD) [59], which aims to maximize the minimum distance between elements. Various approaches have been proposed in the literature to solve the CDP, but it is common to employ heuristics  
Figure 2: Initial situation of air quality stations (red) and sensitive points for the possible location of new stations (blue). and metaheuristics to solve large-scale instances in short computing times [60]. This study uses an adapted version of the approach proposed by [61], which has been proven to generate high-quality solutions within short computational times. Algorithm 1 outlines the main steps of our algorithm. ```
1:functionBR-CDP(\(I,\beta,t_{\text{max}},it_{\text{max}}\))
2:\(S\leftarrow\textsc{DestructiveHeuristic}(I)\)
3:\(S\leftarrow\textsc{LocalSearch}(S,it_{\text{max}})\)
4:whiletime\(<\)\(\varepsilon_{\text{max}}\)do
5:\(S_{\text{new}}\leftarrow\textsc{DestructiveHeuristic}(I,\beta)\)
6:\(S_{\text{new}}\leftarrow\textsc{LocalSearch}(S_{\text{new}},it_{\text{max}})\)
7:if\(f(S_{\text{new}})>f(S)\)then
8:\(S\gets S_{\text{new}}\)
9:endif
10:endwhile
11:return\(S\)
12:endfunction
```  
**Algorithm 1** Biased-randomized algorithm. The algorithm receives as input an instance comprising the stations and the distances between stations, denoted by \(I\), as well as the maximum execution time \(t_{max}\) and the maximum number of iterations without improvement \(it_{max}\). The algorithm generates a feasible initial solution \(S\) by applying a destructive heuristic followed by a local search operator. The destructive heuristic and local search procedures are presented next. At this point, this initial solution becomes the best-found solution so far.