# Simulation Optimization of Search and Rescue in Disaster Relief Based on Distributed Auction Mechanism

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Description of Multi-Agent Model

#### 2.1. Victims

#### 2.2. Rescue Teams

## 3. Auction-Based Cooperative Rescue Plan

#### 3.1. Auctioneers

#### 3.2. Bidders

#### 3.2.1. The Utility Function of Bidders

#### 3.2.2. The Cost of Bidders

#### 3.2.3. The Bidding Strategy of Bidders

#### 3.3. The Adjustment in Task Allocation

## 4. Simulation Results

#### 4.1. Experimental Settings

_{a}to evaluation level ${v}_{b}$, denoted as ${r}_{ab}$, is calculated through semi-trapezoid distribution function. For example, the membership degree of buried depth to ${v}_{1}$ is calculated by Equation (10).

#### 4.2. Results

#### 4.3. Verification and Validation

## 5. Analytical Evaluation

#### 5.1. Robustness Analysis

#### 5.2. Sensitivity Analysis

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 4.**The deterioration rate of survival probabilities of victims with different injury severity.

**Figure 8.**Robustness analysis of cooperative rescue plan. (

**a**) Effect of search radius on rescue efficiency; (

**b**) Effect of cooperation scope on rescue efficiency.

**Figure 9.**Sensitivity analysis of cooperative rescue plan. (

**a**) Relation between the time limit for rescuing one site and rescue efficiency; (

**b**) Relation between the maximum turning angle and rescue efficiency.

Notation | Definition |
---|---|

$N=\{1,\text{}2,\text{}\dots ,\text{}n\}$ | The set of buried site, where $i\in N$ denotes a buried site |

$M=\{1,\text{}2,\text{}\dots ,\text{}m\}$ | The set of rescue teams, where $j\in M$ denotes a rescue team |

${T}_{i}$ | The task of rescuing buried site $i$, where $\text{}i\in N$ |

${A}_{i}$ | The auctioneer who publishes task ${T}_{i}$, where $i\in N$ |

${B}_{j}$ | The team $j$ who received auction message, i.e., the bidder, where $j\in M$ |

${u}_{i}$ | The utility for a bidder who completes task ${T}_{i}$, where $i\in N$ |

${g}_{ij}$ | The net utility for bidder ${B}_{j}$ who completes task ${T}_{i}$, which equals ${u}_{i}-{c}_{ij}$ |

${c}_{ij}$ | The cost of ${B}_{j}$ participating in task ${T}_{i}$, where $i\in N$ and $j\in M$ |

${c}_{ij}^{\prime}$ | The opportunity cost of ${B}_{j}$ participating in task ${T}_{i}$, where $i\in N$ and $j\in M$ |

${t}_{need}$ | The time limit for completing rescue operations in each buried site |

${n}_{i}$ | The number of teams required to complete task ${T}_{i}$, which is related to ${t}_{need}$ |

${d}_{ij}$ | The distance between task ${T}_{i}$ and ${B}_{j}$, where $i\in N$ and $j\in M$ |

${t}_{ij}$ | The time ${B}_{j}$ spent in rescue operation of task ${T}_{i}$, where $i\in N$ and $j\in M$ |

${y}_{j}$ | The number of buried sites within the scope of cooperation |

${l}_{j}$ | The number of available rescue teams within the scope of cooperation |

$\lambda $ | The coefficient of bid price, $\lambda \in (0,\text{}1)$ |

${p}_{ij}$ | The bid on task ${T}_{i}$, which is made by ${B}_{j}$ |

Injury Severity | Scenarios | ||
---|---|---|---|

Fatal (%) | Serious (%) | Normal (%) | |

Death | 40 | 30 | 20 |

Heavy injury | 30 | 25 | 20 |

Slight injury | 10 | 15 | 20 |

No injury | 20 | 30 | 40 |

Urgent | Less Urgent | Normal | |
---|---|---|---|

Buried depth | 150 | 120 | 90 |

Number of victims | 3 | 2 | 1 |

Total injury severity | 9 | 5 | 1 |

${\overline{\mathit{p}}}_{\mathit{r}\mathit{s}}$ (%) | ${\overline{\mathit{p}}}_{\mathit{r}}$ (%) | ${\overline{\mathit{t}}}_{\mathit{a}}$ (min) | ||
---|---|---|---|---|

Fatal | Cooperation | 56.40 | 64.62 | 512.2 |

No-cooperation | 48.96 | 57.22 | 653.2 | |

t test | 7.44 *** | 7.40 *** | −141.0 *** | |

Serious | Cooperation | 68.17 | 75.11 | 587.0 |

No-cooperation | 62.37 | 69.04 | 703.6 | |

t test | 5.80 *** | 6.07 *** | −116.6 *** | |

Normal | Cooperation | 76.26 | 82.15 | 624.1 |

No-cooperation | 71.30 | 78.01 | 749.0 | |

t test | 4.96 *** | 4.14 *** | −124.9 *** |

${\mathit{p}}_{\mathit{r}\mathit{s}}$ | ${\mathit{p}}_{\mathit{r}}$ | ${\mathit{t}}_{\mathit{a}}$ | ||
---|---|---|---|---|

Fatal | Cooperation | 7.5%, [0.7%, 16.2%] | 6.9%, [0.5%, 14.9%] | 8.7%, [0.8%, 20.3%] |

No-cooperation | 10.3%, [0.8%, 23.9%] | 9.4%, [0.3%, 24.4%] | 8.6%, [0.9%, 20.5%] | |

Serious | Cooperation | 5.8%, [0.8%, 13.8%] | 5.6%, [0.6%, 14.4%] | 8.2%, [0.7%, 20.7%] |

No-cooperation | 6.6%, [0.2%, 16.1%] | 5.9%, [0.5%, 15.2%] | 6.8%, [0.4%, 17.1%] | |

Normal | Cooperation | 4.4%, [0.2%, 10.7%] | 3.4%, [0.2%, 8.5%] | 6.5%, [0.8%, 17.0%] |

No-cooperation | 4.6%, [0.4%, 12.5%] | 4.7%, [0.4%, 12.1%] | 6.1%, [0.5%, 15.1%] |

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**MDPI and ACS Style**

Tang, J.; Zhu, K.; Guo, H.; Liao, C.; Zhang, S. Simulation Optimization of Search and Rescue in Disaster Relief Based on Distributed Auction Mechanism. *Algorithms* **2017**, *10*, 125.
https://doi.org/10.3390/a10040125

**AMA Style**

Tang J, Zhu K, Guo H, Liao C, Zhang S. Simulation Optimization of Search and Rescue in Disaster Relief Based on Distributed Auction Mechanism. *Algorithms*. 2017; 10(4):125.
https://doi.org/10.3390/a10040125

**Chicago/Turabian Style**

Tang, Jian, Kejun Zhu, Haixiang Guo, Can Liao, and Shuwen Zhang. 2017. "Simulation Optimization of Search and Rescue in Disaster Relief Based on Distributed Auction Mechanism" *Algorithms* 10, no. 4: 125.
https://doi.org/10.3390/a10040125