# Cluster-Based Relocation of Stations for Efficient Forest Fire Management in the Province of Valencia (Spain)

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Land Mapping

#### 2.2. Management of Fire Data

#### 2.3. Data Clustering Algorithms

#### 2.3.1. Partition-Based Clustering: k-Means

#### 2.3.2. Density-Based Spatial Clustering: DBSCAN

#### 2.4. Floyd–Warshall Algorithm

## 3. Proposed Approach

- Location information about existing forest fire stations. This information was obtained from public records published by the Valencian Agency for Safety and Emergency Response.
- Historical data about forest fires in the Valencia province. This information was also obtained from public records, more specifically from the integrated forest fire management system developed by the fire prevention service of the GVA.
- Distances between all pairs of adjacent municipalities measured in travel time. This information was collected from publicly available online map applications. In particular, Google Maps has been used.

#### 3.1. Fire Station Relocation

#### 3.2. Shortest Path Calculation

## 4. Results

#### 4.1. Time to Reach a Fire

#### 4.2. Optimized Location of Forest Fire Stations

#### 4.3. Optimized Forest Fire Station Planning

#### 4.4. Discussion of Results

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Small part of the province divided as the matrix $\mathbf{P}$ would do. The numbers at the bottom indicate the column numbers and those on the right the row numbers. Painted in red, there is the road linking two villages: Ayora and Teresa de Cofrentes.

**Figure 6.**Evolution of time saved with respect to having one cluster less for different numbers of clusters.

**Figure 7.**In the left image, the real stations (red Xs) are compared with those calculated by k-means (blue Xs), and in the right image, the same comparison is made with the results of running DBSCAN (green Xs).

**Figure 8.**Small part of the province divided as the matrix $\mathbf{P}$ would do. The numbers at the bottom imply the column numbers and those on the left border the row numbers. The red Xs are placed where the current forest fire stations are, and the blue Xs represent the same stations in their optimized locations.

**Table 1.**Average and weighted times to reach a fire obtained with k-means and DBSCAN for different numbers of clusters between 20 and 30. Missing values for DBSCAN indicate that any optimized distribution was found with said number of clusters. Results with 26 clusters are highlighted in bold font to be compared with the existing distribution of stations (nowadays ${t}_{avg}$ = 12${}^{\prime}$37${}^{\prime}$${}^{\prime}$ and ${t}_{w}$ = 10${}^{\prime}$05${}^{\prime}$${}^{\prime}$).

Distribution | Time | Number of Fire Stations | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | ||

k-means | ${t}_{avg}$ | 11${}^{\prime}$22${}^{\prime}$${}^{\prime}$ | 11${}^{\prime}$10${}^{\prime}$${}^{\prime}$ | 11${}^{\prime}$02${}^{\prime}$${}^{\prime}$ | 10${}^{\prime}$43${}^{\prime}$${}^{\prime}$ | 10${}^{\prime}$42${}^{\prime}$${}^{\prime}$ | 10${}^{\prime}$25${}^{\prime}$${}^{\prime}$ | 10${}^{\prime}$17${}^{\prime}$${}^{\prime}$ | 10${}^{\prime}$11${}^{\prime}$${}^{\prime}$ | 9${}^{\prime}$55${}^{\prime}$${}^{\prime}$ | 9${}^{\prime}$52${}^{\prime}$${}^{\prime}$ | 9${}^{\prime}$47${}^{\prime}$${}^{\prime}$ |

${t}_{w}$ | 9${}^{\prime}$33${}^{\prime}$${}^{\prime}$ | 9${}^{\prime}$19${}^{\prime}$${}^{\prime}$ | 9${}^{\prime}$11${}^{\prime}$${}^{\prime}$ | 8${}^{\prime}$48${}^{\prime}$${}^{\prime}$ | 8${}^{\prime}$47${}^{\prime}$${}^{\prime}$ | 8${}^{\prime}$29${}^{\prime}$${}^{\prime}$ | 8${}^{\prime}$18${}^{\prime}$${}^{\prime}$ | 8${}^{\prime}$08${}^{\prime}$${}^{\prime}$ | 7${}^{\prime}$58${}^{\prime}$${}^{\prime}$ | 7${}^{\prime}$53${}^{\prime}$${}^{\prime}$ | 7${}^{\prime}$49${}^{\prime}$${}^{\prime}$ | |

DBSCAN | ${t}_{avg}$ | 20${}^{\prime}$44${}^{\prime}$${}^{\prime}$ | - | 20${}^{\prime}$08${}^{\prime}$${}^{\prime}$ | 19${}^{\prime}$52${}^{\prime}$${}^{\prime}$ | 19${}^{\prime}$30${}^{\prime}$${}^{\prime}$ | 19${}^{\prime}$26${}^{\prime}$${}^{\prime}$ | 19${}^{\prime}$21${}^{\prime}$${}^{\prime}$ | 19${}^{\prime}$12${}^{\prime}$${}^{\prime}$ | 19${}^{\prime}$07${}^{\prime}$${}^{\prime}$ | - | - |

${t}_{w}$ | 19${}^{\prime}$13${}^{\prime}$${}^{\prime}$ | - | 18${}^{\prime}$07${}^{\prime}$${}^{\prime}$ | 18${}^{\prime}$02${}^{\prime}$${}^{\prime}$ | 17${}^{\prime}$40${}^{\prime}$${}^{\prime}$ | 17${}^{\prime}$38${}^{\prime}$${}^{\prime}$ | 17${}^{\prime}$35${}^{\prime}$${}^{\prime}$ | 17${}^{\prime}$34${}^{\prime}$${}^{\prime}$ | 17${}^{\prime}$33${}^{\prime}$${}^{\prime}$ | - | - |

**Table 2.**Comparison of current fire station coordinates in the province with the centroid positions obtained through k-means.

Fire Station Name | Position in P $\left(\mathit{Row},\mathit{Column}\right)$ | ||
---|---|---|---|

Current | k-Means | Comparison | |

La Font de la Figuera | (53,18) | (49,22) | Too different |

Ontinyent | (52,26) | (52,27) | Almost equal |

Castelló de Rugat | (49,33) | (48,32) | Similar |

Ròtova | (47,37) | (47,39) | Similar |

Enguera | (46,23) | (45,24) | Similar |

Xàtiva | (45,29) | (46,30) | Similar |

Ayora | (43,12) | (42,12) | Almost equal |

Zarra | (41,11) | (41,28) | Too different |

Navarrés | (41,23) | (40,22) | Similar |

Alzira | (38,32) | (38,31) | Almost equal |

Cortes de Pallás | (35,15) | (36,12) | Too different |

Yátova | (29,19) | (41,36) | Too different |

Los Isidros | (28,4) | (26,2) | Similar |

Buñol | (28,20) | (28,21) | Almost equal |

Requena | (25,10) | (25,10) | Equal |

Villargordo del Cabriel | (24,0) | (33,27) | Too different |

La Vallesa | (23,29) | (24,29) | Almost equal |

Bétera | (21,30) | (21,26) | Too different |

Pedralba | (20,22) | (20,19) | Similar |

Gilet | (17,34) | (17,35) | Almost equal |

Calles | (16,14) | (15,19) | Too different |

Olocau | (16,28) | (16,29) | Almost equal |

Sinarcas | (15,6) | (27,33) | Too different |

Chelva | (15,13) | (14,12) | Similar |

Titaguas | (10,10) | (9,12) | Similar |

Ademuz | (2,4) | (2,4) | Equal |

**Table 3.**Average and weighted times for the current distribution, the k-means distribution with two different numbers of stations and the proposal. The number of fire stations for each distribution is shown in parentheses.

Distribution | Current (26) | k-Means (26) | k-Means (23) | Proposal (23) |
---|---|---|---|---|

${t}_{avg}$ | 12${}^{\prime}$37${}^{\prime}$${}^{\prime}$ | 10${}^{\prime}$17${}^{\prime}$${}^{\prime}$ | 10${}^{\prime}$43${}^{\prime}$${}^{\prime}$ | 10${}^{\prime}$46${}^{\prime}$${}^{\prime}$ |

${t}_{w}$ | 10${}^{\prime}$05${}^{\prime}$${}^{\prime}$ | 8${}^{\prime}$18${}^{\prime}$${}^{\prime}$ | 8${}^{\prime}$48${}^{\prime}$${}^{\prime}$ | 8${}^{\prime}$31${}^{\prime}$${}^{\prime}$ |

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**MDPI and ACS Style**

de Domingo, M.; Ortigosa, N.; Sevilla, J.; Roger, S.
Cluster-Based Relocation of Stations for Efficient Forest Fire Management in the Province of Valencia (Spain). *Sensors* **2021**, *21*, 797.
https://doi.org/10.3390/s21030797

**AMA Style**

de Domingo M, Ortigosa N, Sevilla J, Roger S.
Cluster-Based Relocation of Stations for Efficient Forest Fire Management in the Province of Valencia (Spain). *Sensors*. 2021; 21(3):797.
https://doi.org/10.3390/s21030797

**Chicago/Turabian Style**

de Domingo, Miguel, Nuria Ortigosa, Javier Sevilla, and Sandra Roger.
2021. "Cluster-Based Relocation of Stations for Efficient Forest Fire Management in the Province of Valencia (Spain)" *Sensors* 21, no. 3: 797.
https://doi.org/10.3390/s21030797