# An Agent-Based Simulation of Deep Foundation Pit Emergency Evacuation Modeling in the Presence of Collapse Disaster

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## Abstract

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## 1. Introduction

- It provides an agent-based system that is specifically designed for a deep foundation pit evacuation simulation of a collapse disaster, and a novel collapse model and agent escape model is built.
- The system is built for customization, and provides the user with the ability to seek optimal exit distribution. A simulation-based optimization algorithm is applied to optimize the distribution, the particle swarm optimization (PSO), and generalized Voronoi diagram (GVD) algorithm is mixed in the simulation-based algorithm.

## 2. Related Work

## 3. Simulation Framework of DPE System

## 4. Mathematical Model for the DPE System

#### 4.1. Collapse Model

#### 4.2. Agent-Based Escape Model

- Initializing the grid potential energy field, gravitational constant, and repulsion constant η;
- For each tile, calculating the distance to the target point and the gravitational potential energy;
- Extracting the threats in a map, calculating the repulsion potential, and superimposing the force;
- Adding the attracting potential force and the repulsion potential force to obtain the total potential force and assign it to tile $squar{e}_{\left(i,j\right)}$;
- If it is the last tile, the algorithm comes to an end. If not, goes to step 2.

- Input process. Agents arrive at the server according to the time they move to the escape route, and the arrival times are independent of each other.
- Queuing rules. When the server is occupied, agents will wait in the queue, and the queue length is not limited. The service order follows the first-come, first-served rule. The waiting time of agents for the service is only related to the pit situation. While waiting for service, the impact of disaster is still calculated. When the disaster approaches, agents will give up the queue and reselect another escape exit.
- Service characteristic. There are multiple exits in the deep foundation pit, which can be regarded as a parallel connection of multiple servers. Due to the long distance between each server, an agent can select a server at any time. Therefore, each exit can be seen as a single-server model.

- Arrival. wait queue: $s=s+1$.
- Accept the service: wait queue: $s=s-1$, and the server status is set to False.
- Service completed: exit queue: $r=r+1$, the server status is set to True.
- Reselect the exit: wait queue: $s=s-1$.
- Escape success: exit queue: $r\text{}=\text{}r-1$.

## 5. Optimization Algorithm

#### 5.1. Particle Swarm Optimization Algorithm

#### 5.2. Adaptive Weighted Voronoi Diagram

## 6. Experiment

#### 6.1. Experimental Environment and Settings

#### 6.2. Experimental Results and Analysis

#### 6.2.1. Exit Distribution Optimization Experiment

#### 6.2.2. Agent–Exit Match Optimization Experiment

#### 6.2.3. Warning Time

#### 6.3. Discussion of Experimental Results

- X is the variables set $\left\{{X}_{1},{X}_{2},\cdots ,{X}_{n}\right\}$;
- D is the range set $\left\{{D}_{1},{D}_{2},\cdots ,{D}_{n}\right\}$;
- C is the constraint set $\left\{{C}_{1},{C}_{2},\cdots ,{C}_{n}\right\}$.

## 7. Conclusions and Future Work

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The framework of our prototype for an agent-based simulation for evacuation in deep foundation pits (DPE) system.

**Figure 20.**The escape rate under the constraint satisfaction problem (CSP) and simulation-based optimization (SBO).

Pit A | Pit B | Pit C | |
---|---|---|---|

Dimension | 100 m × 100 m × 10 m | 160 m × 160 m × 15 m | 200 m × 150 m × 20 m |

Vertex coordinates | (15, 50), (30, 15), (80, 15), (85, 70), (40, 90) | (0, 0), (160, 0), (160, 120), (85, 70), (0, 120) | (20, 40), (40, 20), (160, 20), (180, 40), (180, 120), (160, 140), (40, 140), (20, 120) |

Agent number | 50 | 100 | 100 |

Collapse probability | 15%, 35%, 20%, 10%, 20% | 35%, 10%, 25%, 30% | 5%, 30%, 5%, 10%, 0%, 20%, 15%, 15% |

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**MDPI and ACS Style**

Yang, W.; Hu, Y.; Hu, C.; Yang, M.
An Agent-Based Simulation of Deep Foundation Pit Emergency Evacuation Modeling in the Presence of Collapse Disaster. *Symmetry* **2018**, *10*, 581.
https://doi.org/10.3390/sym10110581

**AMA Style**

Yang W, Hu Y, Hu C, Yang M.
An Agent-Based Simulation of Deep Foundation Pit Emergency Evacuation Modeling in the Presence of Collapse Disaster. *Symmetry*. 2018; 10(11):581.
https://doi.org/10.3390/sym10110581

**Chicago/Turabian Style**

Yang, Weilong, Yue Hu, Cong Hu, and Mei Yang.
2018. "An Agent-Based Simulation of Deep Foundation Pit Emergency Evacuation Modeling in the Presence of Collapse Disaster" *Symmetry* 10, no. 11: 581.
https://doi.org/10.3390/sym10110581