A Review of Genetic Algorithm Approaches for Wildfire Spread Prediction Calibration
Abstract
:1. Introduction
 A literature review focused on wildfire spread prediction calibration using GAs is performed. The GA was chosen as a technique for the calibration due to its predominance in research works that used EAs to calibrate the wildfire spread prediction model;
 Based on the presented literature review, in a didactic way, wildfire spread calibration using genetic algorithm is described, in which a specific GA framework for Rothermel model calibration is presented. Moreover, the parameters to be calibrated are discussed, namely the surfaceareatovolume ratio ($\sigma $), fuel bed depth ($\delta $), fuel moisture (${M}_{f}$), and midflame wind speed (U);
 The actual feasibility of using GAs for the calibration of the Rothermel model for wildfire spread prediction is explored/studied on 37 real datasets.
2. Literature Review of Wildfire Spread Prediction Calibration
 Acceptance
 The article uses the Rothermel model or a Rothermel modelbased simulator for fire propagation prediction/simulation;
 The article uses evolutionary algorithms for Rothermel model calibration;
 The article focuses on improving the prediction results or its execution time.
 Rejection
 The article’s method for fire propagation prediction is not based on the Rothermel model;
 The article implements calibration techniques other than evolutionary algorithms.
2.1. Rothermel Model
2.2. The Need for a Fire Spread Model Calibration
2.3. Wildfire Spread Calibration Literature Overview
2.4. Wildfire Spread Calibration Literature Using Genetic Algorithms
2.5. Calibration through Parallel Computing
2.6. Literature Review Summary
3. Wildfire Spread Calibration Using Genetic Algorithm
3.1. Genetic Algorithms Overview
Algorithm 1 General genetic algorithm steps. 

3.2. Calibration Methodology Using Genetic Algorithms
 (1)
 the fact that the first three parameters are related to fuel characteristics, which in simulations are approximated using fuel models. Fuel models assume constant and uniform fuel characteristics inside a cell, which is a fair approximation for small cell sizes, a large variety of fuel models and accurate fitting of the model to the existing fuels. However, available fuel maps can suffer from low resolution (large cell sizes), low variety of models (the most commonly used standard NFFL fuel models [42] includes only 13 different fuel models) and low accuracy, therefore increasing the probability of fuel models failing to accurately depict the average characteristics of existing fuels.
 (2)
 Furthermore, the fire dynamics are known to induce local changes in the fuel characteristics, as well as wind speed and direction, in the close vicinity of the fire front [43,44,45] (fuel moisture drastically decreases while wind speed increases). To some extent, such changes are intrinsic to the semiempirical Rothermel model. However, local variations in such parameters should be expected.
 (3)
 The selection operator is the tournament selection [47], which consists of randomly selecting a certain number of individuals of the current population, creating a tournament. The winner of the tournament is the individual with the best fitness and it is selected to be a parent for the next generation. This process is repeated a second time, and a pair of parent individuals is obtained.
 The crossover operator is the single point crossover technique [47]. It is executed on the parent pair by cutting the two chromosomes at corresponding points and exchanging the sections after the cuts. This generates a new offspring pair.
 The mutation operator is the uniform operator [48]. This operator consists of altering the value of a random gene in the offspring by a uniform random value which fits the gene’s respective search space, at a given probability of mutation $mu{t}_{prob}$, a parameter defined at the beginning of the GA implementation.
 The elitism is applied to the whole new population, i.e., a small percentage of the best individuals ($elitism$) of the previous generation replaces random individuals in the new population [48].
Algorithm 2 Genetic algorithm for wildfire spread calibration. 

4. Results
 ${\sigma}^{n}\in [43,80]\phantom{\rule{0.166667em}{0ex}}\left[\mathrm{cm}{}^{1}\right]$;
 $\delta \in [0.25,1.2]\phantom{\rule{0.166667em}{0ex}}\left[\mathrm{m}\right]$;
 ${M}_{f}\in [0.8\times {M}_{f}^{\prime},1.2\times {M}_{f}^{\prime}]\phantom{\rule{0.166667em}{0ex}}[\%]$;
 $U\in [0.75\times {U}^{\prime},1.25\times {U}^{\prime}]\phantom{\rule{0.166667em}{0ex}}[\mathrm{m}/\mathrm{s}]$.
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Parameter  Description 

${I}_{R}$  Reaction intensity (Btu/ft${}^{2}$ min) 
${\mathsf{\Gamma}}^{\prime}$  Optimum reaction velocity (min${}^{1}$) 
$\beta $  Packing ratio 
${\rho}_{b}$  Ovendry bulk density (lb/ft${}^{3}$) 
${\mathsf{\Gamma}}_{max}^{\prime}$  Maximum reaction velocity (min${}^{1}$) 
${\beta}_{op}$  Optimum packing ratio 
${w}_{n}$  Net fuel load (lb/ft${}^{2}$) 
${\eta}_{M}$  Moisture damping coefficient 
${\eta}_{S}$  Mineral damping coefficient 
$\xi $  Propagating flux ratio 
${\varphi}_{w}$  Wind factor 
${\varphi}_{S}$  Slope factor 
$\epsilon $  Effective heating number 
${Q}_{ig}$  Heat of preignition (Btu/lb) 
Ref.  Focus  Source of Datasets  Individuals  Gens.  Others 

[20]  Input parameter calibration. Introduction of twostage framework + input parameter sensitivity analysis  Simulation (ISStest)  1000  20  Fitness function is the XOR area (from ISStest) between real and simulated burned areas 
[19]  Input parameter calibration using GAs, simulated annealing, random search and tabu search  Simulation (ISStest)  1000    Fitness function is the Hausdorff distance 
[16]  Input parameter calibration  Simulation and 1 prescribed fire (Portugal)  50  5  — 
[22]  Input parameter calibration. Twostage framework with GA and guided search by past fires database  Real map $110\times 110$ m^{2}. fireLib simulation and 1 prescribed fire (Portugal)  Parallel: 512 Dynamic: 50   5  — 
[17]  Input parameter calibration. Statistical integration to reduce search space  Real fire (California)  500  5  $elitism=0.04$, $cros{s}_{prob}=0.2$, $mu{t}_{prob}=0.01$, Fitness function is symmetric difference (23) 
[24]  Input parameter calibration. Twostage framework with GA and comparison of the methods from [16,22]  1 simulated fire map using fireLib and 1 prescribed fire (Portugal)  Simulated: 50 Real: 500  5 5  Real fire case: $0.2\le mu{t}_{prob}\le 0.4$, Fitness function is cellbycell comparison of real and simulated fire maps 
[10]  Input parameter calibration considering the rapid variation of wind speed and direction  Simulation (FARSITE)  50  10  Tests were performed 15 times 
[26]  Rothermel fuel models calibration  1st test (GAopt.): [27,28]; 2nd test (Custom fuel model calibration): [38,39]  100 for both  Max. 9999  $mu{t}_{prob}=0.1$, $elitism=0.05$. Fitness function is RMSE of observed vs. experimental rate of spread R 
[21]  Input parameter calibration. Twostage framework with GA and WildFire Analyst  Real fire (Spain)      Fitness function is the symmetric difference (23) 
[31]  Input parameter calibration, considering the spatial variation of wind in large fires  Real fire (Spain)  6  10  Tests were performed 15 times 
[32]  Statistical study of genetic algorithms as the optimization algorithm in the twostage framework  Simulation (FARSITE)  100  5  Tests were performed 50 times. $mu{t}_{prob}=0.1$, $elitism=0.1$ 
[34]  Reduction of calibration time by parallel implementation  Simulation (FARSITE) based on a real terrain map (Spain)  25; 25; 100  10  Fitness function is the symmetric difference (23) 
[36]  Reduction of calibration time by parallel implementation  Simulation (FARSITE) based on a real terrain map (Spain)  25  10  Tests were performed 50 times. Fitness function is the symmetric difference (23) 
[37]  Reduction of calibration time by parallel implementation  Real fire (Spain)  –  10  $\#elitism=10$, $cros{s}_{prob}=0.7$, $mu{t}_{prob}=0.3$. Tests were performed 10 times. Fitness function is the symmetric difference (23) 
[33]  Reduction of calibration time by early terminating individuals based on prediction error in parallel implementation  Real fire (Spain)  100  10  $cros{s}_{prob}=0.7$, $mu{t}_{prob}=0.3$, Fitness function is a weighted version of the symmetric difference (24) 
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Pereira, J.; Mendes, J.; Júnior, J.S.S.; Viegas, C.; Paulo, J.R. A Review of Genetic Algorithm Approaches for Wildfire Spread Prediction Calibration. Mathematics 2022, 10, 300. https://doi.org/10.3390/math10030300
Pereira J, Mendes J, Júnior JSS, Viegas C, Paulo JR. A Review of Genetic Algorithm Approaches for Wildfire Spread Prediction Calibration. Mathematics. 2022; 10(3):300. https://doi.org/10.3390/math10030300
Chicago/Turabian StylePereira, Jorge, Jérôme Mendes, Jorge S. S. Júnior, Carlos Viegas, and João Ruivo Paulo. 2022. "A Review of Genetic Algorithm Approaches for Wildfire Spread Prediction Calibration" Mathematics 10, no. 3: 300. https://doi.org/10.3390/math10030300