# Improved Particle Swarm Path Planning Algorithm with Multi-Factor Coupling in Forest Fire Spread Scenarios

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Spatial Modeling of Forest Fire Spread

#### 2.2. State Space of Firefighting Rescue Configuration Modeling

#### 2.3. Time-Varying Search Space Modeling

#### 2.4. Vertical Partitioning and Simplification of Time-Varying Search Space

#### 2.5. Improved Particle Swarm Optimization Search

_{i}(i = 1, 2, …,k) is each mass center passed by the target planning path, $S\left({q}_{i},{q}_{i+1}\right)$, is the path length function from mass center ${q}_{i}$ to mass center ${q}_{i+1}$, and $\tilde{V}\left({q}_{i},{q}_{i+1}\right)$ is the velocity adjustment function determined by different slope magnitudes. The values of the speed adjustment function are detailed in Table 1. $M\left({q}_{i},{q}_{i+1}\right)$ is the judgment function of whether the path falls into the preference region, and $m$ is the corresponding preference coefficient. Thus, it is known that the preference coefficient for dangerous terrain areas is relatively low, whereas the preference coefficient for flat and safe areas is relatively high. $\alpha $ and $\beta $ are cost adjustment weights, which can be taken as 1. $g\left({q}_{1},{q}_{2},\dots ,{q}_{k}\right)$ is the adaptation degree of the target planning path.

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The overall design of the improved particle swarm optimization algorithm for path planning.

**Figure 2.**Four general cases of vertical sectioning: (

**a**) can be extended upward and downward; (

**b**) can only be extended upward; (

**c**) can only be extended downward; (

**d**) cannot be extended.

**Figure 4.**Vertical dissection process: (

**a**) topology of the dissected route; (

**b**) initial solution of the path.

**Figure 5.**Schematic diagram of forest fire path planning based on improved particle swarm optimization (Case 1, N = 100).

**Figure 6.**Comparison of path planning effects between the original PSO and improved PSO (Case 1, N = 100): (

**a**) average slope of path; (

**b**) maximum fitness value of path.

**Figure 7.**The variation in features under different particle dimensions and quantities. (

**a**) The variations in total path length under different particle numbers. (

**b**) The variations in average slope under different particle numbers. (

**c**) The variation in total path length under different particle dimensions. (

**d**) The variation in average slope under different particle dimensions.

Slope (°) | Average Walking Speed (Steps/minute) | Average Walking Speed (km/h) | |
---|---|---|---|

Uphill | Downhill | ||

0~3 | 120 | 5.0 | 5.0 |

3~5 | 100 | 4.0 | 4.5 |

5~10 | 90 | 3.5 | 4.5 |

10~15 | 80 | 3.0 | 4.0 |

15~20 | 60~70 | 2.5 | 3.5 |

20~25 | 50~60 | 2.0 | 3.0 |

25~30 | 40~50 | 1.5 | 2.5 |

Properties | Description | Value |
---|---|---|

Raster Interpretation | Geometric nature of the raster | ‘cells’ |

XIntrinsicLimits | Raster limits in intrinsic x coordinates | [0.5, 3612.5] |

YIntrinsicLimits | Raster limits in intrinsic y coordinates | [0.5, 3612.5] |

CellExtentInLatitude | Extent in latitude of individual cells | 2.7778 × 10^{−4} |

CellExtentInLongitude | Extent in longitude of individual cells | 2.7778 × 10^{−4} |

LatitudeLimits | Latitude limits of the geographic quadrangle bounding the georeferenced raster | [22.645233, 23.576067] |

LongitudeLimits | Longitude limits of the geographic quadrangle bounding the georeferenced raster | [112.384655, 113.387988] |

RasterSize | Number of rows and columns of the raster or image associated with the referencing object | [3351, 3612] |

AngleUnit | Unit of measurement used for angle-valued properties | ‘degree’ |

ColumnsStartFrom | Edge from which column indexing starts | ‘north’ |

RowsStartFrom | Edge from which row indexing starts | ‘west’ |

Coordinate System Type | Geographic coordinate reference system | ‘geographic’ |

Case | Start Point | Target Point | $\mathit{N}$ | $\mathit{D}$ | ${\mathit{w}}_{\mathit{m}\mathit{i}\mathit{n}}$ | $\left[{\mathit{c}}_{1}{}_{\mathit{m}\mathit{i}\mathit{n}},{\mathit{c}}_{2}{}_{\mathit{m}\mathit{i}\mathit{n}}\right]$ | Stage |
---|---|---|---|---|---|---|---|

1 | 22°43′0.08″ N 112°36′32.79″ E | 22°43′34.86″ N 112°37′14.88″ E | 100 | 10 | 0.4 | [0.4, 0.4] | 1, 2, 3, 4, 5, 6 |

200 | |||||||

300 | |||||||

2 | 22°43′0.08″ N 112°36′32.79″ E | 22°43′34.86″ N 112°37′14.88″ E | 200 | 5 | 0.4 | [0.4, 0.4] | 1, 2, 3, 4, 5, 6 |

10 | |||||||

15 | |||||||

3 | 22°43′0.08″ N 112°36′32.79″ E | 22°43′34.86″ N 112°37′14.88″ E | 200 | 10 | 0.4 | [0.4, 0.4] | 1, 2, 3, 4, 5, 6 |

[0.8, 0.8] | |||||||

[0.12, 0.12] |

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## Share and Cite

**MDPI and ACS Style**

Lin, K.; Zhang, L.; Huang, L.; Feng, Z.; Chen, T.
Improved Particle Swarm Path Planning Algorithm with Multi-Factor Coupling in Forest Fire Spread Scenarios. *Fire* **2023**, *6*, 202.
https://doi.org/10.3390/fire6050202

**AMA Style**

Lin K, Zhang L, Huang L, Feng Z, Chen T.
Improved Particle Swarm Path Planning Algorithm with Multi-Factor Coupling in Forest Fire Spread Scenarios. *Fire*. 2023; 6(5):202.
https://doi.org/10.3390/fire6050202

**Chicago/Turabian Style**

Lin, Kaiyi, Lifan Zhang, Lida Huang, Zhili Feng, and Tao Chen.
2023. "Improved Particle Swarm Path Planning Algorithm with Multi-Factor Coupling in Forest Fire Spread Scenarios" *Fire* 6, no. 5: 202.
https://doi.org/10.3390/fire6050202