# Evacuation Shelter Decision Method Considering Non-Cooperative Evacuee Behavior to Support the Disaster Weak

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## Abstract

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## 1. Introduction

- First, we focus on the issues of the disaster weak and critical support for their quick evacuation. To support the disaster weak, our strategy not only gives priority to them but also tries to avoid burdening them further due to evacuees’ selfish behaviors. To achieve this, we extend the procedure of limiting the assignment number of each shelter to the method by Umeki et al. [7], and the disaster weak are also given priority in the shelter decision procedure.
- Second, we further propose a unique method for assigning evacuees to shelters. We conduct simulations of evacuation behavior to estimate how the disaster weak will be affected when evacuees ignore evacuation instructions. The estimation determines how to assign evacuees to shelters. We estimate which shelters get crowded and how many evacuees will be rejected in advance. Based on the estimation result, we set the maximum number of evacuees to assign to each shelter.
- Finally, we evaluate our methods using multi-agent system simulations for the scenario of evacuation of 30,000 visitors for Gion Festival to show the effectiveness of the proposed methods. As a result, our methods can reduce the average evacuation time of the disaster weak and evacuate more of the disaster weak in a shorter time compared with the existing methods when the number of evacuees who are non-cooperative is less than the expected number.

## 2. Related Work

#### 2.1. Studies for Disaster Events

#### 2.2. Studies on People with Disabilities in Disaster Situations

#### 2.3. Our Approach

## 3. Preliminary Work

#### 3.1. Outline and Prerequisite

#### 3.2. Method by Solving Combinatorial Optimization Problem

#### 3.3. Problems with COP Involving Disaster Weak

## 4. Proposed Methods

#### 4.1. Outline

#### 4.2. Fixed-Rate Reduction Method (FRM)

#### 4.3. Simulation-Based Reduction Method (SRM)

**Step_1: Detecting which shelters will be crowded by simulation**

- The number of evacuees who will arrive at shelter i.
- The number of evacuees who will be refused by shelters.

**Step_2: Setting the number of evacuees to assign**

**Step_3: Combinatorial optimization problem method with priority for disaster weak**

## 5. Performance Evaluations

#### 5.1. Evaluation Environments

- OS: CentOS 7
- Memory: 125.7 GiB
- CPU: Intel Core i7-6850K CPU @ 3.60 GHz × 12

#### 5.2. Parameters

#### 5.2.1. Walking Speed

#### 5.2.2. Initial Locations

- Group 1: 4000 evacuees start from Area 1.
- Group 2: 8000 evacuees start from Area 2.
- Group 3: 4000 evacuees start from Area 3.
- Group 4: 4000 evacuees start from Area 4.
- Group 5: 10,000 evacuees start from random points on the map.

#### 5.2.3. Shelter Capacity

#### 5.2.4. Evacuees Behavior

#### 5.3. Comparison Methods

#### 5.3.1. Nearest-Shelter Selection Method

#### 5.3.2. COP

#### 5.3.3. FRM

#### 5.3.4. SRM

#### 5.4. Results

#### 5.4.1. Average Evacuation Time

#### 5.4.2. Total Evacuation Rate

## 6. Discussion

## 7. Conclusions

- Giving priority to the disaster weak can make healthy people take longer time for evacuation. When some healthy people are non-cooperative with evacuation instructions, the disaster weak can be turned away by shelters. Thus, it is important to assume non-cooperative evacuees’ behavior for strategies that attempt to ease burdens on the disaster weak.
- FRM with a margin rate, which sets the assignment number at the same percentage for all shelters, can reduce the evacuation time of the disaster weak compared to the method that only gives priority to them. However, if the value of the margin rate is too high, FRM is not able to decide the destinations of evacuees.
- SRM, which estimates how congestion in disaster areas occurs by simulations, sets the assignment number for shelters based on estimation instead of limiting the assignment numbers for all shelters uniformly like FRM. Compared to FRM, SRM can evacuate more of the disaster weak earlier.
- SRM can reduce the average evacuation time of the disaster weak and evacuate more of the disaster weak compared to COP when the number of non-cooperative evacuees is less than the assumed number.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 10.**Total Evacuation Rate of disaster weak (when percentage of non-cooperative healthy people is 60 and 80%).

Shelter 0 (Capacity: One Person) | Shelter 1 (Capacity: Two People) | Shelter 2 (Capacity: Two People) | |
---|---|---|---|

Evacuee_1 | 5 min | 35 min | 35 min |

Evacuee_2 | 30 min | 10 min | 20 min |

Evacuee_3 | 25 min | 20 min | 15 min |

Evacuee_4 | 15 min | 20 min | 25 min |

Evacuee_5 | 40 min | 30 min | 25 min |

Shelter 0 (Capacity: One Person) | Shelter 1 (Capacity: Two People) | Shelter 2 (Capacity: Two People) |
---|---|---|

5 min (Evacuee_1) | 10 min (Evacuee_2) | 15 min (Evacuee_3) |

15 min (Evacuee_4) | 20 min (Evacuee_4) | 20 min (Evacuee_2) |

25 min (Evacuee_3) | 20 min (Evacuee_3) | 25 min (Evacuee_5) |

30 min (Evacuee_2) | 30 min (Evacuee_5) | 35 min (Evacuee_1) |

40 min (Evacuee_5) | 35 min (Evacuee_1) | 40 min (Evacuee_4) |

Shelter 0 (Capacity: One Person) | Shelter 1 (Capacity: Two People) | Shelter 2 (Capacity: Two People) | |
---|---|---|---|

Evacuee_1 (Healthy People) | 5 min | 20 min | 30 min |

Evacuee_2 (Healthy People) | 15 min | 10 min | 30 min |

Evacuee_3 (Healthy People) | 25 min | 15 min | 25 min |

Evacuee_4 (Disaster Weak) | 60 min | 65 min | 85 min |

Evacuee_5 (Disaster Weak) | 70 min | 50 min | 90 min |

Shelter 0 (Capacity: One Person) | Shelter 1 (Capacity: Two People) | Shelter 2 (Capacity: Two People) |
---|---|---|

5 min [Evacuee_1 (Healthy)] | 10 min [Evacuee_2 (Healthy)] | 25 min [Evacuee_3 (Healthy)] |

15 min [Evacuee_2 (Healthy)] | 15 min [Evacuee_3 (Healthy)] | 30 min [Evacuee_1 (Healthy)] |

25 min [Evacuee_3 (Healthy)] | 20 min [Evacuee_1 (Healthy)] | 30 min [Evacuee_2 (Healthy)] |

60 min [Evacuee_4 (Weak)] | 50 min [Evacuee_5 (Weak)] | 85 min [Evacuee_4 (Weak)] |

70 min [Evacuee_5 (Weak)] | 65 min [Evacuee_4 (Weak)] | 90 min [Evacuee_5 (Weak)] |

Variables | Definitions |
---|---|

${C}_{i}$ | Capacity of Shelter i |

${A}_{i}$ | Maximum number of evacuees to assign to Shelter i (${A}_{i}$ ≥ 0) |

${m}_{i}$ | Decreased number of evacuees to assign to Shelter i |

${f}_{i}$ | Number of healthy people whose destination in the simulation
conducted in Step_1 of SRM is not the nearest shelter, which is shelter i |

r | Margin rate for shelters (0 ≤ r < 1) |

E | The number of all evacuees. |

s | The number of all shelters. |

Shelter 0 (One Person) | Shelter 1 (Two People) | Shelter 2 (Two People) |
---|---|---|

60 min [Evacuee_4 (Weak)] | 50 min [Evacuee_5 (Weak)] | 85 min [Evacuee_4 (Weak)] |

70 min [Evacuee_5 (Weak)] | 65 min [Evacuee_4 (Weak)] | 90 min [Evacuee_5 (Weak)] |

5 min [Evacuee_1 (Healthy)] | 10 min [Evacuee_2 (Healthy)] | 25 min [Evacuee_3 (Healthy)] |

15 min [Evacuee_2 (Healthy)] | 15 min [Evacuee_3 (Healthy)] | 30 min [Evacuee_1 (Healthy)] |

25 min [Evacuee_3 (Healthy)] | 20 min [Evacuee_1 (Healthy)] | 30 min [Evacuee_2 (Healthy)] |

Parameters | Values | |
---|---|---|

Map Size | 2.5 km × 2.5 km | |

Number of Evacuation Shelter | 32 shelters | |

Number of Evacuees | Healthy People | 30,000 people |

Disaster Weak | 6000 people | |

Standard Walking Speed | Healthy People | 1.0–1.5 m/s |

Disaster Weak | 0.4–0.7 m/s | |

Margin Rate | 0.2, 0.4, 0.6, 0.8 |

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**MDPI and ACS Style**

Tanaka, T.; Matsuda, Y.; Fujimoto, M.; Suwa, H.; Yasumoto, K.
Evacuation Shelter Decision Method Considering Non-Cooperative Evacuee Behavior to Support the Disaster Weak. *Sustainability* **2021**, *13*, 5106.
https://doi.org/10.3390/su13095106

**AMA Style**

Tanaka T, Matsuda Y, Fujimoto M, Suwa H, Yasumoto K.
Evacuation Shelter Decision Method Considering Non-Cooperative Evacuee Behavior to Support the Disaster Weak. *Sustainability*. 2021; 13(9):5106.
https://doi.org/10.3390/su13095106

**Chicago/Turabian Style**

Tanaka, Tomoki, Yuki Matsuda, Manato Fujimoto, Hirohiko Suwa, and Keiichi Yasumoto.
2021. "Evacuation Shelter Decision Method Considering Non-Cooperative Evacuee Behavior to Support the Disaster Weak" *Sustainability* 13, no. 9: 5106.
https://doi.org/10.3390/su13095106