# Optimal Evacuation Route Planning of Urban Personnel at Different Risk Levels of Flood Disasters Based on the Improved 3D Dijkstra’s Algorithm

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## Abstract

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## 1. Introduction

## 2. Research Areas and Methods

#### 2.1. Research Area

^{2}and an average annual population of more than 67,000 [33]. Shanmei Reservoir is located on the north side of Meishan Town, with a straight-line distance of 6.8 km. Because the area is close to the Taiwan Strait, it is prone to typhoon weather. For example, during the typhoon in June 1985, the total accumulated rainfall in the upstream of the Shanmei Reservoir reached 234 mm, the maximum peak flow reached 1287 m

^{3}/s, and the total accumulated flood discharge from the reservoir was 143 million m

^{3}. During the typhoon in mid-August of the same year, the total accumulated rainfall in the upstream of the reservoir was 145.8 mm, the maximum flood peak flow reached 1427 m

^{3}/s, and the total flood discharge from the reservoir was 950,000 m

^{3}during the typhoon. In mid-August 2002, the reservoir was affected by the severe tropical storm “Beimian” [34], and the accumulated flood discharge exceeded 116 million m

^{3}. Based on the above background and according to the flood data provided by the Meishan Town government, there are three flood risk grades: once-in-20-year, once-in-50-year, and once-in-100-year. ArcGIS software was used to calculate the different inundated areas in Meishan Town. The flood inundation area was obtained from Meishan Town government, and we verified it with HEC-RAS software, the inundation area is reliable, factors affecting flood scale include flood volume, data accuracy and topographic. The research site and inundated area map is shown in Figure 1.

#### 2.2. Route Planning Parameter Setting

#### 2.3. Lasso Regression Model

#### 2.4. Shelter Selection

#### 2.5. 3D Dijkstra’s Algorithm

#### 2.6. Improved 3D Dijkstra’s Algorithm Steps

#### 2.7. Workflow of Optimal Evacuation Route Planning

## 3. Results

#### 3.1. Road Node Statistics

#### 3.2. Locations of Available Shelter

#### 3.3. Pedestrian Speed Analysis

#### 3.4. The Optimal Shelter

#### 3.5. Improved 3D Dijkstra’s Algorithm

#### 3.6. Shelter Coverage

#### 3.7. Model Application and Software

## 4. Discussion

#### 4.1. Optimal Shelter Location

#### 4.2. Time Optimization Effect

#### 4.3. Comparison between Ours and Other Methods

#### 4.4. The Effect of Age on Evacuation Speed

#### 4.5. Limitation and Outlook

## 5. Conclusions

- (1)
- The improved 3D Dijkstra’s algorithm proposed in this study has a great potential in optimizing evacuation route selection, reducing evacuation time, and alleviating congestion. Experiments show that when the evacuation starting point of the inundated area is farther from the shelter, the evacuation efficiency will be improved after the optimized algorithm is used.
- (2)
- The method also can analyze the location of the existing shelters and propose a new reference for the selection of shelters. The study finds that when Guozhuan Middle School and Guoguang Middle School are selected for the establishment of shelters, and the evacuation time of pedestrians is the shortest, compared with the existing shelter, the evacuation time can be significantly reduced.
- (3)
- Through the proposal of this optimization method, an algorithm of the industrial application level is developed, which shortens the evacuation time of the crowd. It also provides scientific advice for the related work of road repair and government disaster prevention.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Research site and the urban inundated area under flood: (

**a**) inundated area under once-in-20-year, (

**b**) inundated area under once-in-50-year, (

**c**) inundated area under once-in-100-year.

**Figure 2.**(

**a**) Example of a time graph; the weight of an edge represents the true evacuation time. (

**b**) Time storage matrix, the numbers in the figure are the time from the node ${V}_{i}$ to node ${V}_{j}$.

**Figure 7.**(

**a**) Optimized route for the nine evacuation starting points under the once-in-20-year flood. (

**b**) Evacuation time saved and improvement effect.

**Figure 8.**(

**a**) Optimized route for the nine evacuation starting points under the once-in-50-year flood. (

**b**) Evacuation time saved and improvement effect.

**Figure 9.**(

**a**) Optimized route for the nine evacuation starting points under the once-in-100-year flood. (

**b**) Evacuation time saved and improvement effect.

$1\to 5$ | Time | $5\to 1$ | Time |
---|---|---|---|

$1\to 3\to 2\to 5$ | 7 | $5\to 2\to 3\to 1$ | 10 |

$1\to 3\to 5$ | 3 | $5\to 3\to 1$ | 4 |

$1\to 4\to 3\to 5$ | 18 | $5\to 3\to 4\to 1$ | 17 |

$1\to 4\to 3\to 2\to 5$ | 21 | $5\to 2\to 3\to 4\to 1$ | 23 |

Shelters | Distance (m) | Once-in-20-Year Flood (s) | Once-in-50-Year Flood (s) | Once-in-100-Year Flood (s) |
---|---|---|---|---|

(1) Guozhuan Middle School | 858 | 2303.70 | 2359.65 | \ |

(2) Guoguang Middle School | 1339 | 2756.87 | 2736.74 | 2219.04 |

(3) Guoguang Second Middle School | 1540 | 2709.50 | 2784.83 | 2290.21 |

(4) Mingxin Village Shelter | 1904 | 3208.38 | 2760.39 | \ |

(5) Nan’an Lanyuan Middle School | 2490 | 3206.32 | 3098.07 | \ |

(6) Fengxi Primary School | 3560 | 3701.81 | 3011.77 | \ |

(7) Puzai Village Liutang Central Primary School | 3570 | 3534.10 | 3825.12 | \ |

(8) Shuikou Village Primary School | 4280 | 4788.12 | 4383.93 | 4263.94 |

(9) Xiaoziting Tourist Attraction | 4920 | 4904.57 | 4812.30 | 4698.14 |

**Table 3.**Average evacuation time spent by pedestrians walking to shelters and rate of improvement in time savings (once-in-50-year flood).

Shelters | 2D Time (s) | 3D Time (s) | Improvement Rate (%) | Saved Time (s) |
---|---|---|---|---|

(1) Guozhuan Middle School | 2397.87 | 2359.65 | 1.32 | 38.22 |

(2) Guoguang Middle School | 2782.16 | 2736.74 | 1.33 | 45.42 |

(3) Guoguang Second Middle School | 2823.67 | 2784.83 | 1.10 | 38.84 |

(4) Mingxin Village Shelter | 2806.81 | 2760.39 | 1.54 | 46.43 |

(5) Nan’an Lanyuan Middle School | 3141.97 | 3098.07 | 1.14 | 43.90 |

(6) Fengxi Primary School | 3101.05 | 3011.77 | 1.85 | 89.28 |

(7) Puzai Village Liutang Central Primary School | 3927.26 | 3825.12 | 2.07 | 102.14 |

(8) Shuikou Village Primary School | 4535.11 | 4383.93 | 2.49 | 151.18 |

(9) Xiaoziting Tourist Attraction | 5145.40 | 4812.30 | 5.80 | 333.10 |

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**MDPI and ACS Style**

Zhu, Y.; Li, H.; Wang, Z.; Li, Q.; Dou, Z.; Xie, W.; Zhang, Z.; Wang, R.; Nie, W.
Optimal Evacuation Route Planning of Urban Personnel at Different Risk Levels of Flood Disasters Based on the Improved 3D Dijkstra’s Algorithm. *Sustainability* **2022**, *14*, 10250.
https://doi.org/10.3390/su141610250

**AMA Style**

Zhu Y, Li H, Wang Z, Li Q, Dou Z, Xie W, Zhang Z, Wang R, Nie W.
Optimal Evacuation Route Planning of Urban Personnel at Different Risk Levels of Flood Disasters Based on the Improved 3D Dijkstra’s Algorithm. *Sustainability*. 2022; 14(16):10250.
https://doi.org/10.3390/su141610250

**Chicago/Turabian Style**

Zhu, Yang, Hong Li, Zhenhao Wang, Qihang Li, Zhan Dou, Wei Xie, Zhongrong Zhang, Renjie Wang, and Wen Nie.
2022. "Optimal Evacuation Route Planning of Urban Personnel at Different Risk Levels of Flood Disasters Based on the Improved 3D Dijkstra’s Algorithm" *Sustainability* 14, no. 16: 10250.
https://doi.org/10.3390/su141610250