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International Journal of Wildland Fire International Journal of Wildland Fire Society
Journal of the International Association of Wildland Fire
RESEARCH ARTICLE (Open Access)

Fireline path optimisation in a heterogeneous forest landscape

Xu Yang A * , Emanuel Melachrinoudis A , Peter Kubat A and James MacGregor Smith B
+ Author Affiliations
- Author Affiliations

A Department of Mechanical and Industrial Engineering, Northeastern University, Boston, MA 02115, USA.

B Department of Mechanical and Industrial Engineering, University of Massachusetts, Amherst, MA 01003, USA.

* Correspondence to: yang.xu1@northeastern.edu

International Journal of Wildland Fire 31(11) 1068-1079 https://doi.org/10.1071/WF22037
Submitted: 29 March 2022  Accepted: 13 September 2022   Published: 10 October 2022

© 2022 The Author(s) (or their employer(s)). Published by CSIRO Publishing on behalf of IAWF. This is an open access article distributed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND)

Abstract

Background: When fighting high-intensity wildfire, firefighters may construct a defensive fireline (fuel break) away from the raging front. The path of the fireline is the key to successful fire containment. However, the study of fireline path optimisation in the literature is limited.

Aims: We aim to find the optimal path for firefighting crews to encircle and contain a growing fire in the minimum time while keeping firefighters safe.

Methods: The model considers the realistic topographic factors that affect fire behaviour and fireline production rates. The forest landscape is partitioned into small homogeneous polygons according to their burning characteristics and modelled as a complex topological network using Delaunay triangulation. An algorithm is developed to find the fireline path for firefighting crews, traversing ‘safe’ edges of a dynamic network to meet at the earliest time at which the fireline path is completed.

Key results: Various experiments were conducted leading to insights on how the algorithm can be utilised to develop more effective firefighting strategies.

Conclusions: The proposed algorithm provides an efficient way to generate the optimal fireline path.

Implications: Future work could include the stochastic and dynamic factors in the system by considering probabilistic fire propagation and fireline construction rates.

Keywords: algorithm, Delaunay triangulation network, fireline optimisation, forest fire, geographic information system (GIS), heterogeneous landscape, network optimisation, operations research in natural resources, optimal fireline path, optimal meeting path, wildfire, wildfire containment.


References

Albini FA, Korovin GN, Gorovaya EH (1978) ‘Mathematical analysis of forest fire suppression.’ Research Paper INT-RP-207. (USDA Forest Service, Intermountain Forest and Range Experiment Station)

Andrews PL (1986) ‘Behave: fire behavior prediction and fuel modeling system.’ Intermountain Research Station Technical Report. (USDA Forest Service: Ogden, UT)

Andrews PL (2009) ‘BehavePlus fire modeling system, version 5.0.’ Rocky Mountain Research Station Research Paper RMRS-RP-4. (USDA Forest Service: Ogden, UT)

Andrews PL (2018) ‘The Rothermel surface fire spread model and associated developments: a comprehensive explanation.’ Rocky Mountain Research Station Research Paper RMRS-GTR-371. (USDA Forest Service: Ogden, UT)

Beighley M (1995) Beyond the safety zone: Creating a margin of safety. Fire Management 55, 21–24.

Belval EJ, Wei Y, Bevers M (2015) A mixed integer program to model spatial wildfire behavior and suppression placement decisions. Canadian Journal of Forest Research 45, 384–393.
A mixed integer program to model spatial wildfire behavior and suppression placement decisions.Crossref | GoogleScholarGoogle Scholar |

Butler BW (2014) Wildland firefighter safety zones: a review of past science and summary of future needs. International Journal of Wildland Fire 23, 295–308.
Wildland firefighter safety zones: a review of past science and summary of future needs.Crossref | GoogleScholarGoogle Scholar |

Butler BW, Cohen JD (1998) Firefighter safety zones: a theoretical model based on radiative heating. International Journal of Wildland Fire 8, 73–77.
Firefighter safety zones: a theoretical model based on radiative heating.Crossref | GoogleScholarGoogle Scholar |

Calkin DE, Gebert KM, Jones JG, Neilson RP (2005) Forest service large fire area burned and suppression expenditure trends, 1970–2002. Journal of Forestry 103, 179–183.
Forest service large fire area burned and suppression expenditure trends, 1970–2002.Crossref | GoogleScholarGoogle Scholar |

Campbell MJ, Dennison PE, Butler BW (2017) Safe separation distance score: a new metric for evaluating wildland firefighter safety zones using lidar. International Journal of Geographical Information Science 31, 1448–1466.
Safe separation distance score: a new metric for evaluating wildland firefighter safety zones using lidar.Crossref | GoogleScholarGoogle Scholar |

Campbell MJ, Page WG, Dennison PE, Butler BW (2019) Escape route index: a spatially explicit measure of wildland firefighter egress capacity. Fire 2, 40
Escape route index: a spatially explicit measure of wildland firefighter egress capacity.Crossref | GoogleScholarGoogle Scholar |

Campbell MJ, Dennison PE, Thompson MP, Butler BW (2022) Assessing potential safety zone suitability using a new online mapping tool. Fire 5, 5
Assessing potential safety zone suitability using a new online mapping tool.Crossref | GoogleScholarGoogle Scholar |

Clark KH, Patterson WA (2003) Fire management plan for Montague plain wildlife management area. Department of Natural Resources Conservation Technical Report. (University of Massachusetts: Amherst, MA)

Dijkstra EW (1959) A note on two problems in connexion with graphs Numerische Mathematik 1, 269–271.
A note on two problems in connexion with graphsCrossref | GoogleScholarGoogle Scholar |

Donovan GH, Rideout DB (2003) An Integer programming model to optimize resource allocation for wildfire containment. Forest Science 49, 331–335.
An Integer programming model to optimize resource allocation for wildfire containment.Crossref | GoogleScholarGoogle Scholar |

Duff TJ, Tolhurst KG (2015) Operational wildfire suppression modelling: a review evaluating development, state of the art and future directions. International Journal of Wildland Fire 24, 735–748.
Operational wildfire suppression modelling: a review evaluating development, state of the art and future directions.Crossref | GoogleScholarGoogle Scholar |

Fernandes PM, Pacheco AP, Almeida R, Claro J (2016) The role of fire-suppression force in limiting the spread of extremely large forest fires in Portugal. European Journal of Forest Research 135, 253–262.
The role of fire-suppression force in limiting the spread of extremely large forest fires in Portugal.Crossref | GoogleScholarGoogle Scholar |

Finney MA (2006) An overview of FlamMap fire modeling capabilities. In ‘Fuels management – how to measure success: conference proceedings’. (Eds LA Patricia, WB Bret) Proceedings RMRS-P-41, 213–220. (USDA Forest Service, Rocky Mountain Research Station: Fort Collins, CO)

Fried JS, Fried BD (1996) Simulating wildfire containment with realistic tactics. Forest Science 42, 267–281.
Simulating wildfire containment with realistic tactics.Crossref | GoogleScholarGoogle Scholar |

Fried JS, Fried BD (2010) A foundation for initial attack simulation: the Fried and Fried fire containment model. Fire Management Today 70, 44–47.

Hajian M, Melachrinoudis E, Kubat P (2016) Modeling wildfire propagation with the stochastic shortest path: a fast simulation approach. Environmental Modelling & Software 82, 73–88.
Modeling wildfire propagation with the stochastic shortest path: a fast simulation approach.Crossref | GoogleScholarGoogle Scholar |

Hof J, Omi PN, Bevers M, Laven RD (2000) A timing-oriented approach to spatial allocation of fire management effort. Forest Science 46, 442–451.
A timing-oriented approach to spatial allocation of fire management effort.Crossref | GoogleScholarGoogle Scholar |

HomChaudhuri B, Kumar M (2010) Optimal fireline generation for wildfire fighting in uncertain and heterogeneous environment. In ‘Proceedings of the 2010 American control conference’. pp. 5638–5643. (IEEE)
| Crossref |

Hu X, Ntaimo L (2009) Integrated simulation and optimization for wildfire containment. ACM Transactions on Modeling and Computer Simulation 19, 1–29.
Integrated simulation and optimization for wildfire containment.Crossref | GoogleScholarGoogle Scholar |

Hu X, Sun Y (2007) Agent-based modeling and simulation of wildland fire suppression. In ‘2007 Winter Simulation Conference proceedings’, Washington, DC. (IEEE)
| Crossref |

Jewell WS (1963) Forest fire problems—a progress report. Operations Research 11, 678–692.
Forest fire problems—a progress report.Crossref | GoogleScholarGoogle Scholar |

Kennard M (2022) How do you fight a wildfire? Available at https://wildlandfirejobs.com/how-do-you-fight-a-wildfire/ [Verified 20 July 2022]

Lee Y, Fried JS, Albers HJ, Haight RG (2012) Deploying initial attack resources for wildfire suppression: Spatial coordination, budget constraints, and capacity constraints. Canadian Journal of Forest Research 43, 56–65.
Deploying initial attack resources for wildfire suppression: Spatial coordination, budget constraints, and capacity constraints.Crossref | GoogleScholarGoogle Scholar |

Mees RM (1985) ‘Simulating initial attack with two fire containment models.’ Report P-7. (USDA Forest Service, Pacific Southwest Forest and Range Experiment Station)

Minas JP, Hearne JW, Handmer JW (2012) A review of operations research methods applicable to wildfire management. International Journal of Wildland Fire 21, 189–196.
A review of operations research methods applicable to wildfire management.Crossref | GoogleScholarGoogle Scholar |

Moreira A, Santos MY (2007) Concave hull: a k-nearest neighbors approach for the computation of the region occupied by a set of points. In ‘Proceedings of the Second International Conference on Computer Graphics Theory and Applications’ Volume 2. (Eds J Braz, P-P Vazquez, JM Pereira) pp. 61–68.
| Crossref |

National Interagency Fire Center (2021) Federal firefighting costs (suppression only). Available at https://www.nifc.gov/fire-information/statistics/suppression-costs [Verified 20 July 2022]

National Wildfire Coordinating Group (1996) Wildland fire suppression tactics reference guide. Available at https://www.coloradofirecamp.com/suppression-tactics/how-to-attack.html [Verified 28 September 2022]​

National Wildfire Coordinating Group (2014) Incident Response Pocket Guide. Available at https://www.nwcg.gov/sites/default/files/publications/pms461.pdf [Verified 20 July 2022]

Ntaimo L, Hu X, Sun Y (2008) DEVS-FIRE: Towards an Integrated Simulation Environment for Surface Wildfire Spread and Containment Simulations 84, 137–155.
DEVS-FIRE: Towards an Integrated Simulation Environment for Surface Wildfire Spread and ContainmentCrossref | GoogleScholarGoogle Scholar |

Ntaimo L, Gallego Arrubla JA, Stripling C, Young J, Spencer T (2012) A stochastic programming standard response model for wildfire initial attack planning. Canadian Journal of Forest Research 42, 987–1001.
A stochastic programming standard response model for wildfire initial attack planning.Crossref | GoogleScholarGoogle Scholar |

O’Connor CD, Calkin DE, Thompson MP (2017) An empirical machine learning method for predicting potential fire control locations for pre-fire planning and operational fire management. International Journal of Wildland fire 26, 587–597.
An empirical machine learning method for predicting potential fire control locations for pre-fire planning and operational fire management.Crossref | GoogleScholarGoogle Scholar |

Page WG, Butler BW (2017) An empirically based approach to defining wildland firefighter safety and survival zone separation distances. International Journal of Wildland Fire 26, 655–667.
An empirically based approach to defining wildland firefighter safety and survival zone separation distances.Crossref | GoogleScholarGoogle Scholar |

Plucinski MP (2019) Contain and control: wildfire suppression effectiveness at incidents and across landscapes. Current Forestry Reports 5, 20–40.
Contain and control: wildfire suppression effectiveness at incidents and across landscapes.Crossref | GoogleScholarGoogle Scholar |

Rothermel RC (1972) ‘A mathematical model for predicting fire spread in wildland fuels.’ USDA Forest Service, Intermountain Forest and Range Experiment Station, Research Paper INT-RP-115. (Ogden, UT).

Stepanov A, Smith JM (2012) Modeling wildfire propagation with Delaunay triangulation and shortest path algorithms. European Journal of Operational Research 218, 775–788.
Modeling wildfire propagation with Delaunay triangulation and shortest path algorithms.Crossref | GoogleScholarGoogle Scholar |

Venn TJ, Calkin DE (2011) Accommodating non-market values in evaluation of wildfire management in the United States: Challenges and opportunities. International Journal of Wildland Fire 20, 327–339.
Accommodating non-market values in evaluation of wildfire management in the United States: Challenges and opportunities.Crossref | GoogleScholarGoogle Scholar |

Wei Y, Rideout DB, Hall TB (2011) Toward efficient management of large fires: a mixed integer programming model and two iterative approaches. Forest Science 57, 435–447.
Toward efficient management of large fires: a mixed integer programming model and two iterative approaches.Crossref | GoogleScholarGoogle Scholar |

Wei Y, Thompson MP, Haas JR, Dillon GK, O’Connor CD (2018) Spatial optimization of operationally relevant large fire confine and point protection strategies: Model development and test cases. Canadian Journal of Forest Research 48, 480–493.
Spatial optimization of operationally relevant large fire confine and point protection strategies: Model development and test cases.Crossref | GoogleScholarGoogle Scholar |

Wei Y, Thompson MP, Belval E, Gannon B, Calkin DE, O’Connor CD (2021) Comparing contingency fire containment strategies using simulated random scenarios. Natural Resource Modeling 34, 2295
Comparing contingency fire containment strategies using simulated random scenarios.Crossref | GoogleScholarGoogle Scholar |

Williams J (2013) Exploring the onset of high-impact mega-fires through a forest land management prism. Forest Ecology and Management 294, 4–10.
Exploring the onset of high-impact mega-fires through a forest land management prism.Crossref | GoogleScholarGoogle Scholar |

Xu Z, Jacobsen HA (2010) Processing proximity relations in road networks. In ‘Proceedings of the ACM SIGMOD international conference on management of data’, Indianapolis, Indiana, USA. pp. 243–254. (Association for Computing Machinery)
| Crossref |

Yan D, Zhao Z, Ng W (2015) Efficient processing of optimal meeting point queries in Euclidean space and road networks. Knowledge and Information Systems 42, 319–351.
Efficient processing of optimal meeting point queries in Euclidean space and road networks.Crossref | GoogleScholarGoogle Scholar |

Zambon MJO, de Rezende PJ, de Souza CC (2018) Finding exact solutions for the geometric firefighter problem in practice. Computers & Operations Research 97, 72–83.
Finding exact solutions for the geometric firefighter problem in practice.Crossref | GoogleScholarGoogle Scholar |