# Optimal Emergency Evacuation Route Planning Model Based on Fire Prediction Data

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## Abstract

**:**

## 1. Introduction

## 2. Automatic Avoidance Route Planning Method in Fire Areas

#### 2.1. Model Overview

#### 2.2. Dynamic Optimization for Rapid Evasion of Fire Areas

Algorithm 1: Evacuation route dynamic optimization algorithm pseudo code. |

- (1)
- start from a vertex V0 in graph G and visit V0 first;
- (2)
- visit all the vertices V1, V2, … that are adjacent to V0;
- (3)
- visit all vertices adjacent to V1, V2, … that have not been visited before;
- (4)
- follow that order, until all vertices have been visited.

## 3. The Inner Construction of the Cruise Ship Model

#### 3.1. Cruise Ship Model Networking

#### 3.2. Fire Dynamics Modeling

#### 3.3. Evacuation Simulation

## 4. Analysis of Simulation Results

#### 4.1. The Shortest Evacuation Routes under Three Fire Conditions

#### 4.2. Rapidity of the Dynamic Optimization Algorithm

#### 4.3. Model Validation

## 5. Discussion and Limitations

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**The layouts of the model with Anylogic: (

**a**) first deck layout of cruise ship; (

**b**) second deck layout of cruise ship.

**Figure 7.**(

**a**) CO volume fraction changing with time; (

**b**) temperature changing with time; (

**c**) visibility changing with time.

**Figure 8.**(

**a**) Temperature cloud at 200 s; (

**b**) CO volume fraction cloud at 200 s; (

**c**) smoke visibility cloud at 200 s.

**Figure 10.**The results of dynamically optimizing the route (

**a**) node S3 was simulated with fire; (

**b**) node T7 was simulated with sudden fire.

**Figure 11.**(

**a**) Number of nodes in the setwith fire nodes; (

**b**) computation time comparison between the algorithm and evacuation route dynamic optimization algorithm for optimized routes.

**Figure 14.**Heat map of the number of people in case of sudden fire at node T1 (

**a**) a priori route strategy; (

**b**) shortest evacuation time strategy.

**Figure 15.**(

**a**) The variation of the number of people in each roadway section under the shortest evacuation route strategy; (

**b**) the variation of the number of people in each roadway section under the shortest evacuation time route strategy.

Sex | Age | Height (m) | Weight (kg) | Speed (m/s) |
---|---|---|---|---|

Male | 20–30 | 1.7 | 60 | 1.5 |

Female | 20–30 | 1.6 | 52 | 1.35 |

Male | 30–40 | 1.7 | 60 | 1.35 |

Female | 30–40 | 1.6 | 52 | 1.22 |

Male | 40–50 | 1.69 | 60.5 | 1.22 |

Female | 40–50 | 1.59 | 52.5 | 1.1 |

Male | 50–60 | 1.68 | 61 | 1.1 |

Female | 50–60 | 1.58 | 53 | 1 |

Roads Number | Adjacent Joints | Length (m) | Unit Area Capacity | Roads Number | Adjacent Joints | Length (m) | Unit Area Capacity |
---|---|---|---|---|---|---|---|

${r}_{1}$ | S1,S8 | 16 | 7 | ${r}_{13}$ | T4,S5 | 29 | 5 |

${r}_{2}$ | S8,T2 | 18 | 9 | ${r}_{14}$ | S4,T5 | 29 | 7 |

${r}_{3}$ | S1,T1 | 19 | 9 | ${r}_{15}$ | S5,T5 | 29 | 5 |

${r}_{4}$ | S9,T2 | 8 | 9 | ${r}_{16}$ | T5,E2 | 8 | 7 |

${r}_{5}$ | T1,S9 | 8 | 9 | ${r}_{17}$ | T5,T6 | 19 | 8 |

${r}_{6}$ | T2,S3 | 18 | 6 | ${r}_{18}$ | T6,S6 | 23 | 6 |

${r}_{7}$ | T1,S2 | 18 | 6 | ${r}_{19}$ | T6,T7 | 14 | 6 |

${r}_{8}$ | S3,T3 | 18 | 6 | ${r}_{20}$ | T7,T8 | 16 | 5 |

${r}_{9}$ | S2,T4 | 18 | 6 | ${r}_{21}$ | T7,T9 | 15 | 6 |

${r}_{10}$ | T3,T4 | 15 | 6 | ${r}_{22}$ | S7,T9 | 17 | 5 |

${r}_{11}$ | T4,E1 | 13 | 7 | ${r}_{23}$ | S7,T8 | 15 | 6 |

${r}_{12}$ | T4,S4 | 29 | 7 | ${r}_{24}$ | S6,T8 | 16 | 6 |

Node | Static Evacuation Route | Static Evacuation Time |
---|---|---|

S1 | $\{S1,T1,S2,T4,E1\}$ | 68 s |

S2 | $\{S2,T4,E1\}$ | 31 s |

S3 | $\{S3,T3,T4,E1\}$ | 46 s |

S4 | $\{S4,T5,E2\}$ | 37 s |

S5 | $\{S5,T5,E2\}$ | 37 s |

S6 | $\{S6,T6,T5,E2\}$ | 50 s |

S7 | $\{S7,T8,T7,T6,T5,E2\}$ | 72 s |

S8 | $\{S8,T2,S3,T3,T4,E1\}$ | 82 s |

S9 | $\{S9,T1,S2,T4,E1\}$ | 57 s |

T1 | $\{T1,S2,T4,E1\}$ | 49 s |

T2 | $\{T1,S2,T4,E1\}$ | 64 s |

T3 | $\{T3,T4,E1\}$ | 28 s |

T4 | $\{T4,E1\}$ | 13 s |

T5 | $\{T5,E2\}$ | 8 s |

T6 | $\{T6,T5,E2\}$ | 27 s |

T7 | $\{T7,T6,T5,E2\}$ | 41 s |

T8 | $\{T8,T7,T6,T5,E2\}$ | 57 s |

T9 | $\{T9,T7,T6,T5,E2\}$ | 56 s |

CO Concentration | Human Body Reaction Symptoms |
---|---|

0.05 | The human body is not affected much after one hour of leakage |

0.1 | The human body feels uncomfortable after one hour of leakage |

0.5 | The human body faces threat of death after 20–30 min |

1 | Death after 1–2 min |

Ambient Temperature | Human Tolerance Time/min |
---|---|

50 | >60 |

70 | 60 |

100–130 | 15 |

200–250 | 5 |

Visibility | Effect on the Speed of Escapees |
---|---|

0–$0.6$ | Extremely high |

$0.6$–3 | Higher |

>3 | No effect |

**Table 7.**Time used for each node to change from a safe state to danger in case of sudden fire at T1.

Node i | ${\mathit{t}}_{\mathit{fire}-\mathit{i}}^{}$ | Node i | ${\mathit{t}}_{\mathit{fire}-\mathit{i}}^{}$ |
---|---|---|---|

S1 | 70 | T1 | 0 |

S2 | 46 | T2 | 73 |

S3 | 86 | T3 | 104 |

S4 | 112 | T4 | 89 |

S5 | 112 | T5 | None |

S6 | None | T6 | None |

S7 | None | T7 | None |

S8 | 74 | T8 | None |

S9 | 54 | T9 | None |

E1 | 118 | E2 | None |

Node | Dynamic Evacuation Route | Dynamic Evacuation Time |
---|---|---|

S1 | $\{S1,S8,T2,S3,T3,T4,E1\}$ | 98 s |

S2 | $\{S2,T4,E1\}$ | 31 s |

S3 | $\{S3,T3,T4,E1\}$ | 46 s |

S4 | $\{S4,T5,E2\}$ | 37 s |

S5 | $\{S5,T5,E2\}$ | 37 s |

S6 | $\{S6,T6,T5,E2\}$ | 50 s |

S7 | $\{S7,T8,T7,T6,T5,E2\}$ | 72 s |

S8 | $\{S8,S1,T1,S2,T4,E1\}$ | 82 s |

S9 | $\{S9,T2,S3,T3,T4,E1\}$ | 72 s |

T1 | $\{T2,S3,T3,T4,E1\}$ | 49 s |

T2 | $\{T1,S2,T4,E1\}$ | 64 s |

T3 | $\{T3,T4,E1\}$ | 28 s |

T4 | $\{T4,E1\}$ | 13 s |

T5 | $\{T5,E2\}$ | 8 s |

T6 | $\{T6,T5,E2\}$ | 27 s |

T7 | $\{T7,T6,T5,E2\}$ | 41 s |

T8 | $\{T8,T7,T6,T5,E2\}$ | 57 s |

T9 | $\{T9,T7,T6,T5,E2\}$ | 56 s |

Fire Area | Static Planning Route | Theoretical Shortest Evacuation Route |
---|---|---|

$\left\{T1\right\}$ | $\begin{array}{c}\{S1,T1,S2,T4,E1\}\\ \{S9,T1,S2,T4,E1\}\end{array}$ | $\begin{array}{c}\{S1,S8,T2,S3,T3,T4,E1\}\\ \{S9,T2,S3,T3,T4,E1\}\end{array}$ |

$\left\{S3\right\}$ | $\begin{array}{c}\{T2,S3,T3,T4,E1\}\\ \{S8,T2,S3,T3,T4,E1\}\end{array}$ | $\begin{array}{c}\{T2,S9,T1,S2,T4,E1\}\\ \{S8,T2,S9,T1,S2,T4,E1\}\end{array}$ |

$\left\{T7\right\}$ | $\begin{array}{c}\{S4,T5,E2\}\\ \{S5,T5,E2\}\\ \{T9,T7,T6,T5,E2\}\\ \{S7,T9,T7,T6,T5,E2\}\\ \{T8,T7,T6,T5,E2\}\end{array}$ | $\begin{array}{c}\{S4,T4,E1\}\\ \{S5,T4,E1\}\\ \{T9,S7,T8,S6,T6,T5,E2\}\\ \{S7,T8,S6,T6,T5,E2\}\\ \{T8,S6,T6,T5,E2\}\end{array}$ |

Start-End | Method | Evacuation Path | Path Length |
---|---|---|---|

555-6 | $\begin{array}{c}Method1\phantom{\rule{2.0pt}{0ex}}\\ Method2\phantom{\rule{2.0pt}{0ex}}\\ Method3\phantom{\rule{2.0pt}{0ex}}\end{array}$ | $\begin{array}{c}\{555,564,\mathbf{37},587,113,210,653,30,334,503,51,289,1201,6\}\phantom{\rule{2.0pt}{0ex}}\\ \{555,631,801,979,668,580,432,218,6\}\phantom{\rule{2.0pt}{0ex}}\\ \{555,631,801,979,668,580,432,218,6\}\phantom{\rule{2.0pt}{0ex}}\end{array}$ | $\begin{array}{c}284\phantom{\rule{2.0pt}{0ex}}\\ 325\phantom{\rule{2.0pt}{0ex}}\\ 325\phantom{\rule{2.0pt}{0ex}}\end{array}$ |

555-666 | $\begin{array}{c}Method1\phantom{\rule{2.0pt}{0ex}}\\ Method2\phantom{\rule{2.0pt}{0ex}}\\ Method3\phantom{\rule{2.0pt}{0ex}}\end{array}$ | $\begin{array}{c}\{555,564,\mathbf{37},474,761,558,666\}\phantom{\rule{2.0pt}{0ex}}\\ \{555,564,372,607,895,938,197,666\}\phantom{\rule{2.0pt}{0ex}}\\ \{555,564,372,607,895,938,197,666\}\phantom{\rule{2.0pt}{0ex}}\end{array}$ | $\begin{array}{c}243\phantom{\rule{2.0pt}{0ex}}\\ 268\phantom{\rule{2.0pt}{0ex}}\\ 268\phantom{\rule{2.0pt}{0ex}}\end{array}$ |

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**MDPI and ACS Style**

Deng, K.; Zhang, Q.; Zhang, H.; Xiao, P.; Chen, J. Optimal Emergency Evacuation Route Planning Model Based on Fire Prediction Data. *Mathematics* **2022**, *10*, 3146.
https://doi.org/10.3390/math10173146

**AMA Style**

Deng K, Zhang Q, Zhang H, Xiao P, Chen J. Optimal Emergency Evacuation Route Planning Model Based on Fire Prediction Data. *Mathematics*. 2022; 10(17):3146.
https://doi.org/10.3390/math10173146

**Chicago/Turabian Style**

Deng, Kunxiang, Qingyong Zhang, Hang Zhang, Peng Xiao, and Jiahua Chen. 2022. "Optimal Emergency Evacuation Route Planning Model Based on Fire Prediction Data" *Mathematics* 10, no. 17: 3146.
https://doi.org/10.3390/math10173146