A Review of Genetic Algorithm Approaches for Wildfire Spread Prediction Calibration

  Citation: 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 Academic Editor: Ioannis G. Tsoulos Received: 16 December 2021 Accepted: 13 January 2022 Published: 19 January 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). mathematics Review A Review of Genetic Algorithm Approaches for Wildfire Spread Prediction Calibration Jorge Pereira 1, Jérôme Mendes 1,* , Jorge S. S. Júnior 1, Carlos Viegas 2and João Ruivo Paulo 1 1Department of Electrical and Computer Engineering, Institute of Systems and Robotics, University of Coimbra, Pólo II, 3030-290 Coimbra, Portugal; [email protected] (J.P.); [email protected] (J.S.S.J.); [email protected] (J.R.P.) 2Association for the Development of Industrial Aerodynamics, University of Coimbra, 3030-289 Coimbra, Portugal; [email protected] *Correspondence: [email protected] Abstract: Wildfires are complex natural events that cause significant environmental and property damage, as well as human losses, every year throughout the world. In order to aid in their management and mitigate their impact, efforts have been directed towards developing decision support systems that can predict wildfire propagation. Most of the available tools for wildfire spread prediction are based on the Rothermel model that, apart from being relatively complex and computing demanding, depends on several input parameters concerning the local fuels, wind or topography, which are difficult to obtain with a minimum resolution and degree of accuracy. These factors are leading causes for the deviations between the predicted fire propagation and the real fire propagation. In this sense, this paper conducts a literature review on optimization methodologies for wildfire spread prediction based on the use of evolutionary algorithms for input parameter set calibration. In the present literature review, it was observed that the current literature on wildfire spread prediction calibration is mostly focused on methodologies based on genetic algorithms (GAs). Inline with this trend, this paper presents an application of genetic algorithms for the calibration of a set of the Rothermel model’s input parameters, namely: surface-area-to-volume ratio, fuel bed depth, fuel moisture, and midflame wind speed. The GA was validated on 37 real datasets obtained through experimental prescribed fires in controlled conditions. Keywords: wildfire; wildfire spread prediction; calibration; genetic algorithm; evolutionary algorithms 1. Introduction Wildfires are one of nature’s most dangerous hazards and, in the last few years, their impact has been increasing significantly, as reported by the European Commission’s 20th issue of the annual wildfire report [ 1 – 3 ]. This report, from 2019, shows a total burned area of 789,730 (ha) registered for 40 countries from Europe, the Middle East, and North Africa. This number is nearly four times larger than the records for the previous year (2018). Wildfires can impact ecosystems by destroying natural habitats, resources, and wildlife. Furthermore, they cause significant damage to society, being responsible for numerous fatalities, accidents, injuries, health problems, and the destruction of human infrastructures. These damages bear a significant economic impact, not only due to the fire damage but also the large investments in prevention, preparedness, fire suppression and recovery efforts [ 4 ]. It is essential to direct efforts towards understanding the behavior of wildfires and improving their management. In this sense, knowledge of how wildfires propagate is critical, allowing the prediction of where the fire will be and taking the appropriate measures to mitigate its impact. Theoretical, empirical and semiempirical models have been developed to predict the wildfire behavior [ 5 ]. The semiempirical Rothermel model [ 6 ] is the most widely used model for wildfire spread prediction [ 5 ], particularly in Mediterranean European countries [ 7 ], being the core of some of the most cited fire simulators such as FARSITE [ 8 ] Mathematics 2022,10, 300. https://doi.org/10.3390/math10030300 https://www.mdpi.com/journal/mathematics Mathematics 2022,10, 300 2 of 19 and FIRESTATION [ 9 ]. The Rothermel model uses several input parameters related to the available forest fuels, such as trees, grass or bushes (surface-area-to-volume ratio, height and moisture content), the terrain configuration (slope), and atmospheric conditions (wind speed and direction). The quality of the fire spread prediction depends on the quality of the propagation model, and on the accuracy of the input parameters [ 10 ]. The present work focuses on the latter cause of uncertainty in wildfire spread predictions. As a matter of fact, while some variables remain constant throughout the whole fire event or can be obtained with a high degree of accuracy (e.g., terrain slope), other variables may change due to fire and cannot be obtained with enough temporal or spatial resolution (e.g., fuel characteristics and wind speed/direction). This uncertainty in the input parameters results in considerable deviations between the predicted and the real fire spread. In order to improve the fire spread simulations/predictions, it is essential to deal with this uncertainty in the Rothermel model input parameters. In an effort to find the accurate input parameters values for the wildfire prediction, some methodologies based on Evolutionary Algorithms (EAs) have been proposed to calibrate the Rothermel model [ 11 ]. EAs, such as genetic algorithms (GA), ant colony optimization (ACO), and particle swarm optimization (PSO), have proven their effectiveness for optimization/calibration problems [12–14]. In this paper, we present a review of genetic algorithm approaches for wildfire spread prediction calibration. The main contributions of the paper are: • 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 surface-area-to-volume ratio ( σ ), fuel bed depth ( δ ), fuel moisture (Mf), 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. The results show a significant error reduction in the wildfire spread prediction, i.e., from 95% to 10%. This paper is organized as follows. Section 2contains a description of the Rothermel model, as well as an insight into the current state of the art regarding methods of wildfire spread prediction using genetic algorithms. In Section 3, GAs are revised, and the method used in this paper to calibrate the Rothermel model is presented. In Section 4, the results of the proposed calibration are presented and analyzed. Finally, Section 5presents the final conclusions. 2. Literature Review of Wildfire Spread Prediction Calibration Genetic algorithms are the most adopted technique for calibration of the Rothermel model’s input parameters. Due to the importance of this subject for wildfire spread prediction, and due to the number of latest developments in this particular field, a literature review of the most relevant work in this area is fundamental. The search process for the presented literature review was performed by using the Science Direct and IEEE Xplore databases and defining the following search keywords: (“fire spread” OR “fire prediction” OR “fire rate of spread” OR “Rothermel model”) AND (“genetic algorithm” OR “evolutionary algorithm” OR “calibration” OR “tuning”). The years considered for the search were from 2000 until 2021. Additionally, the references of the selected papers were also analyzed and served as a source for finding new papers. The literature review rationale for article selection was based on the following criteria: • Acceptance 1. The article uses the Rothermel model or a Rothermel model-based simulator for fire propagation prediction/simulation; Mathematics 2022,10, 300 3 of 19 2. The article uses evolutionary algorithms for Rothermel model calibration; 3. The article focuses on improving the prediction results or its execution time. • Rejection 1. The article’s method for fire propagation prediction is not based on the Rothermel model; 2. The article implements calibration techniques other than evolutionary algorithms. Based on this process, 15 papers were obtained. 2.1. Rothermel Model The Rothermel model, proposed in [ 6 ], estimates a Rate Of Spread R of a fire front, given by R=IRξ(1+φw+φs) ρbεQig , (1) which is measured in units of distance per unit of time ( [m/s] or [ft/min] ), and it represents the linear velocity of a fire, in a given direction and set of conditions. The equations of the associated factors in (1)IR(ρp,σ,δ,w0,ST,h,Mx,Mf,Se),ξ(σ,ρp,w0,δ),φw(ρp,w0,δ,σ,U), φs(ρp , w0 , δ , tanφ) , ρb(w0 , δ) , ε(σ) , and Qig(Mf) depend on several input parameters and are given by: IR=Γ0wnhηMηS(2) Γ0=Γ0 maxβ βop A expA1− − β βop  (3) A=133σ−0.7913 (4) β=ρb ρp(5) ρb=w0 δ(6) Γ0 max =σ1.5 (495 +0.0594σ1.5)(7) βop =3.348σ−0.8189 (8) wn=w0(1−ST)(9) ηM=1− −2.59rM+5.11(rM)2− −3.52(rM)3(10) rM=Mf Mx (max =1.0)(11) ηS=0.174S−0.19 e(max =1.0)(12) ξ=exp[(0.792 +0.681σ0.5)(β+0.1)] (192 +0.2595σ)(13) φw=CUBβ βop −E (14) C=7.47exp(−0.133σ0.55)(15) B=0.02526σ0.54 (16) E=0.715exp(−3.59 ×10−4σ)(17) φS=5.275β−0.3(tanφ)2(18) ε=exp−138 σ(19) Qig =250 +1116Mf(20) where the description of the respective parameters is presented in Table 1. Mathematics 2022,10, 300 4 of 19 Table 1. Identification of the parameters in Equations (2)–(20) [6,15]. Parameter Description IRReaction intensity (Btu/ft2min) Γ0Optimum reaction velocity (min−1) βPacking ratio ρbOven-dry bulk density (lb/ft3) Γ0 max Maximum reaction velocity (min−1) βop Optimum packing ratio wnNet fuel load (lb/ft2) ηMMoisture damping coefficient ηSMineral damping coefficient ξPropagating flux ratio φwWind factor φSSlope factor εEffective heating number Qig Heat of preignition (Btu/lb) The input parameters of the Rothermel model (1) can be separated into three categories: fuel properties, topography and wind properties. The fuel properties are heat content ( h ), mineral content ( ST (total) and Se (effective)), oven-dry particle density ( ρp ), oven-dry fuel load ( w0 ), surface-area-to-volume ratio ( σ ), fuel bed depth ( δ ), dead fuel moisture of extinction ( Mx ) and fuel moisture ( Mf ). Topography is represented by slope steepness (tan φ ), and wind properties correspond to the midflame wind speed ( U ). A deeper insight into the Rothermel model can be seen in [6,15]. 2.2. The Need for a Fire Spread Model Calibration Figure 1presents a general illustration for wildfire spread prediction, which consists in feeding a fire simulator with a set of input parameters that aim to represent the initial real fire conditions, at t0 . The result of the fire simulator, i.e., the simulated wildfire perimeter, at t1 , should match the propagation of the real wildfire, i.e., the real wildfire perimeter [ 16 ]. However, the input parameters are related to the environmental conditions, e.g., fuel, weather, and terrain characteristics as described in Section 2.1, and obtaining them becomes a difficult task in order to provide an accurate prediction. Time Real fire ignition Real wildfire perimeter Real fire data Simulated wildfire perimeter Fire simulator Input parameters Figure 1. Illustration of fire spread prediction using only one set of non-calibrated input parameters. Adapted from [17]. In more detail, some input parameters can be directly measured, such as terrain slope, which can also be obtained based on previous topographical information. However, other parameters, such as fuel-specific parameters, require detailed knowledge about the local vegetation, which might not be available. Some input parameters, such as fuel moisture, are calculated using models based on meteorological data [18], while wind field maps are Mathematics 2022,10, 300 5 of 19 estimated based on point observations from the available meteorological stations closer to the fire location. These estimations introduce a great amount of error in the prediction. In terms of behavior change, characteristics such as the terrain slope and the type of vegetation in a certain region are constant in time and space, while others, such as wind speed and direction, have very sudden variations during the wildfire [ 10 ]. Therefore, finding a set of input parameters that produces accurate results solely based on previous knowledge about the wildfire location and weather conditions is a challenging task. Due to the uncertainty and the consequent inaccuracy in wildfire spread simulation, there is a need to calibrate the input parameters. 2.3. Wildfire Spread Calibration Literature Overview The Rothermel model is the most used and recognized fire spread prediction model, serving as the base for several fire simulators (FARSITE [ 8 ] and FIRESTATION [ 9 ]). Research works that deal with Rothermel model calibration and wildfire spread prediction mostly use genetic algorithms. Initially, works such as [ 19 , 20 ] have proved the performance of genetic algorithms by comparing them against other optimization techniques and with implementation in a parallel two-stage prediction framework. More recently, other works such as [ 17 , 21 ] aim to improve the calibration by merging the algorithms with other tools that complement their performance, such as the Statistical System for Forest Fire Management ( S2F2M ) and WildFire Analyst (WFA) (a component of the Tecnosylva Incident Management software suite designed to directly support multi-agency wild-fire incident management). Given that the quality of genetic algorithms was proven early, works evolved into directing efforts to improve their performance. One of the areas explored to improve the performance of genetic algorithms is parallel computing. Several works used parallel implementations of genetic algorithms to reduce calibration time. In general, these strategies consisted of implementing a simulator’s intrinsic functions in parallel and allocating more processing cores to individuals (elements of a population that represent one possible solution for the problem) with longer predicted execution times. In the following sections, the main works dealing with this topic are provided, providing a perspective of the philosophy currently being pursued in this research field. 2.4. Wildfire Spread Calibration Literature Using Genetic Algorithms Genetic algorithms have been used to find the set of input parameters that better adjusts the wildfire spread model predictions to the real observations. In other words, optimizing the model using a framework for wildfire spread prediction tuning. The authors in [ 20 ] introduced a framework, illustrated in Figure 2, that consists of two stages: a calibration stage and a prediction stage. After the ignition, the calibration stage starts, at t0 . Sets of Rothermel’s input parameters are generated (using an optimization approach). Each set of input parameters is evaluated, at instant of time t1 , by comparing the simulator prediction with the real observed fire data for that time instance. The optimal set of input parameters is the one that minimizes the deviation between the predicted and the real fire perimeter. This process is repeated several times or until a certain solution criterion is reached. In the prediction stage, assuming that environmental conditions remain constant, the resulting optimal set of parameters from the calibration stage is used as input for the fire simulator to predict the fire spread at every instant of time ti ( i∈N ). Here, the prediction stage is similar to the classical method/framework ( Figure 1 ), except that now a tuned set of input parameters is used. Mathematics 2022,10, 300 6 of 19 Time Real fire ignition Real wildfire perimeter Real fire data Input parameters Simulated wildfire perimeter Feedback Best set of parameters Real wildfire perimeter Simulated wildfire perimeter Fire simulator Fire simulator Figure 2. Two-stage method for fire spread prediction, adapted from [17]. During the calibration stage, the goal is to find an optimal solution for the input parameters. In a generic way, the optimization problem can be defined as: x∗=arg min x∈S F(x), (21) where F(x) represents the function to be minimized (by an optimization algorithm, such as GA), x represents the input parameters vector, S is the respective search space, and x∗ represents the input parameters that minimize F(x) . A usual function to be optimized in wildfire spread calibration is the difference between the real wildfire rate of spread (measured from the real-time wildfire data) and the predicted rate of spread (obtained by the Rothermel model), or the difference between the real and the predicted burned area. The goal is to find the set of input parameters x of (21) that most accurately predicts the real fire propagation. The majority of the works from the current state of the art on wildfire spread prediction are based on the previously presented Two-Stage framework (Figure 2). Early works, such as [ 19 , 20 ], have proposed evolutionary algorithms as techniques that could be used to find an optimal set of input parameters for a fire simulator. Genetic algorithms are included in the group of evolutionary algorithms and they are the dominant optimization technique for input parameter calibration. In [ 20 ], following the presentation of the two-stage framework, a sensitivity analysis was carried out in order to evaluate how the individual variation of each Rothermel input parameter across its range of possible values affects the model output: the bigger the sensitivity of one parameter, the more it affects the model’s output. Based on the sensitivity results, an experimental study was conducted to confirm that calibrating parameters with larger sensitivities and fixing the others reduces the GA’s search space and accelerates the optimization time. The results showed that, after 1000 generations, the scenarios in which only 6 input parameters were calibrated achieved an improvement in the objective function (XOR area between the real and simulated burned areas) of approximately 33.3% (one third) in relation to the scenario in which 10 input parameters were calibrated. This reduction also matches the reduction in GA’s search space from one scenario to the other. In [ 19 ], the genetic algorithm’s performance is tested against three other algorithms: Random Search, Tabu Search and Simulated Annealing. The tests were carried out by comparing the simulated fire line based on the sets of parameters generated by the algorithms against a fire line obtained by setting known values for all the inputs and running the ISStest simulator for 45 min. Each algorithm was executed 10 times up to 1000 iterations. The fire lines were compared using the Hausdorff distance H (22), which measures the degree of mismatch between two sets of points F1 and F2 , representing the fire line simulated based on the optimized parameters and the fire line generated with known input parameters for comparison. H(22) is given by H(F1,F2) = max(h(F1,F2),h(F2,F1)), (22) Mathematics 2022,10, 300 7 of 19 where h(F1 , F2) and h(F2 , F1) represents the Hausdorff distance between two sets of points F1 and F2 at a specific point in F2 and F1 , respectively (see [ 19 ] for more details). The results show that simulated annealing, tabu search and genetic algorithms presented similar results after the 500th generation. In [ 16 ], a dynamic data-driven genetic algorithm was proposed to tune the fire simulator’s input parameters based on the real fire behavior. The simulator used was fireLib and, through reverse engineering, it was possible to obtain equations for wind values (wind speed and direction). These equations are fed with terrain slope with the position ( x , y ) of the fire front with the maximum rate of spread. The obtained wind speed and direction values were used to steer the search for an optimal input parameter set carried out by the genetic algorithm. Afterwards, in [ 22 ], the same research group proposed a new calibration steering method as an improvement to the previous strategy. Since this was highly dependent on the underlying simulator, the new approach consisted of generating a database with fire evolution information from both real and simulated (synthetic) fires. For the calibration stage, a dynamic data-driven genetic algorithm (DDDGA) was proposed to define the best wind direction and wind speed values, by searching the database of previous fires that were similar in terms of rate of spread, slope and fuel model to the real observed fire spread, and using wind values from those fires to steer the genetic algorithm’s search. The authors in [ 17 ] introduced a system called SAPIFE (Spanish acronym for Adaptive System for Fire Prediction Based in Statistical-Evolutive Strategies) which is based on the two-stage fire spread prediction framework with a genetic algorithm implemented during the calibration stage. However, in SAPIFE, the genetic algorithm is coupled with another method called the Statistical System for Forest Fire Management ( S2F2M ) [ 23 ]. This new method receives a certain population from the GA and analyzes almost all possible input parameter combinations from all individuals in the population. From this analysis, S2F2M evaluates the probability of each map cell to be burned or not and generates a probabilistic map. Then, based on these probabilities, the number of possible scenarios (parameter combinations between different individuals) is reduced, decreasing the calibration time required. In [ 24 ], the two methods introduced in [ 16 , 22 ] were compared. The method introduced in [ 16 ] is named as the “analytical method” and, as was described above, is based on the inversion of a fire simulator. The method introduced in [ 22 ] is named as the “computational method” and relies on a database with information from past fires. Both of these methods use ongoing fire propagation data to obtain wind speed and direction values and use them to steer the genetic algorithm’s search. Two sets of tests were carried out: first, the two-stage framework was tested against the classical wildfire spread prediction method, which uses a single set of input parameters introduced in the fire simulator. This test used data from past fires and confirmed that the two-stage framework with a genetic algorithm provides better results than the classical prediction without input parameter calibration. Then, the second set of tests compared the use of a simple non-guided genetic algorithm against genetic algorithms with different configurations of the proposed steering strategies. The guided genetic algorithm with the computational and analytical methods obtained similar results and improved prediction quality over the non-guided genetic algorithm. The work developed by [ 10 ] is also based on the two-stage prediction framework with a genetic algorithm and introduces an approach for reducing the prediction errors caused by the variability of wind parameters (wind speed and direction). During the calibration stage, wind parameters are not calibrated; instead, real wind measurements from the fire location are taken in periodic sub-intervals. These measurements are used as inputs for the fire simulator in the recurring simulations. Afterwards, during the prediction stage, a numerical weather prediction (NWP) model [ 25 ] is used to periodically estimate the wind parameters between sub-intervals of the prediction stage. The estimated wind parameters are introduced in the simulator and are updated at each sub-interval. The prediction result is obtained using the real wind measurements and the calibrated parameters, which are moisture contents and vegetation features. The test results showed that, when the wind Mathematics 2022,10, 300 8 of 19 conditions are stable, the basic two-stage framework with a genetic algorithm provides satisfactory results, in comparison with the new method of using measured and estimated wind values (prediction error of 0.4 vs. 0.29, respectively). However, when the wind conditions are more dynamic, the results obtained by the introduced method are significantly better compared to the basic two-stage framework with a genetic algorithm (prediction error of 0.19 vs. 0.58 m, respectively). In [ 26 ], a calibration of the fuel models within the Rothermel’s fire spread prediction model was carried out through the use of genetic algorithms. The GA’s individuals consisted of the following Rothermel fuel parameters: oven-dry fuel load ( w0 ), surface-areato-volume ratio ( σ ), fuel bed depth ( δ ), fuel moisture of extinction ( Mx ), and heat content ( h ). Two tests were performed to evaluate the proposed GA method. The first test consisted of using GAs for the fuel model calibration method, with the support of two works [ 27 , 28 ] (grass and shrub fuels, respectively) that provided datasets of observed rate of spread R and other input parameters’ data (fuel moisture, wind speed and slope steepness). The GA was performed with 9999 maximum iterations, 100 individuals, mutation probability and elitism factor equal to 0.1 and 0.05, respectively, and the fuel input parameters calibrated based on the parameter ranges given by the papers. Each individual was evaluated using the Root Mean Square Error (RMSE) between the observed and predicted rate of spread R . The second test consisted of implementing the GA for calibrating a fuel model for a type of vegetation (Calluna heath). Nine prescribed fire experiments were carried out in dry Calluna heathland vegetation and R , fire weather (1 h fuels moisture, live woody fuel moisture and wind speed) and terrain data (ignition line length, fire plot size and slope) were recorded from each experiment. From the nine fire experiments, four were considered for GA calibration and five were considered for validation. The calibration experiments data were used to run the GA and calibrate the fuel parameters, similarly to the first test. Then, predicted rate of spread R values were calculated using different fuel models: GA calibrated fuel parameters, the Standard Fuel Model which provided the smaller RMSE when comparing predicted vs. observed R , a custom fuel model for Calluna vegetation and a “custom fuel model parameterized with modal values from fuels inventoried in each fire experiment”. An additional prediction of the rate of spread R was obtained by a Rothermel model reformulation implemented in the Fuel Characteristics Classification System (FCCS) [ 29 ]. For the validation experiments data, the calibrated GA fuel parameters resulted in the lowest RMSE between predicted and observed rate of spread R, in comparison to the alternative models. The study in [ 21 ] presents a dynamic data-driven genetic algorithm and introduces a new approach for predicting fire propagation based on Wildfire Analyst (WFA) [ 30 ]. The paper describes the two-stage prediction framework with a genetic algorithm, where the fire propagation is simulated using the FARSITE fire simulator [ 8 ], and the fitness function corresponds to the symmetric difference between predicted and burned areas obtained by: Difference =UnionCells − −IntersectionCells RealCells − −Init Cells , (23) where UnionCells represents the sum of the number of cells that were burned in the predicted area and the real area, IntersectionCells is the number of cells burned simultaneously in the predicted area and the real area, RealCells is the final number of cells burned in the real area, and InitCells is the starting number of cells burned in the real fire area. The newly introduced approach uses WildFire Analyst (WFA) and seeks the best R (Rate of Spread) adjustment factors, minimizing the error between simulated fire and the real fire data. Both the FARSITE fire simulator and Wildfire Analyst use the Rothermel model. Afterwards, the two-stage framework with the genetic algorithm and Wildfire Analyst are coupled together by overlapping their predicted fire spread maps. In order to test the two-stage framework and Wildfire Analyst, experiments were carried out with data from a real fire that occurred in Cardona, Catalonia, Spain in 2005. The results show that both methods adapt to drastic changes in the fire characteristics. Mathematics 2022,10, 300 9 of 19 In [ 31 ], the two-stage framework was considered to reduce input parameter uncertainty and predict fire spread. However, when the wildfire is large, wind cannot be considered uniform throughout the whole wildfire area. So, this work introduced a wind field model (WindNinja), being represented by a cell map, to account for this variation. In essence, during the calibration phase, the obtained meteorological wind parameters are used to calculate the wind field for each scenario generated by the genetic algorithm. Then, having each individual’s wind field, the corresponding fire propagation map is calculated and the error function is evaluated. Finally, in [ 32 ], a statistical study was carried out to characterize the genetic algorithm in the calibration phase of the two-stage prediction method. The characterization refers to estimating which GA parameter configuration results in a better calibration within the imposed time restrictions. A statistical study was conducted based on the results of a genetic algorithm calibration on a simulated five-hour fire obtained using FARSITE as the fire spread simulator. The results from this study were maximum adjustment errors which have different degrees of guarantee depending on the number of generations that the GA iterates. These results are important in understanding the compromise between the algorithm’s execution time (number of generations) and the adjustment error, which is larger when the algorithm iterates fewer generations. 2.5. Calibration through Parallel Computing Throughout Section 2.4, several works regarding fire spread prediction using genetic algorithms were described. Despite their focus being on improving prediction accuracy, some works have proposed/adapted a Master/Worker paradigm (Figure 3) in order to reduce the calibration and prediction times. Master Generated population Genetic algorithm ... Fire Simulator Worker 1 Error calculation Fire Simulator Worker 2 Error calculation Fire Simulator Worker N Error calculation Figure 3. Genetic algorithm using the Master/Worker paradigm, adapted from [33]. GAs, as with any evolutionary algorithm, require the execution of a set of individual simulations through several iterations, which can be very time-consuming, and given the urgency and need for accuracy associated with wildfire spread prediction in real-time, it is important to reduce the execution time of the calibration phase while maintaining appropriate accuracy. One way to achieve this is through the parallel implementation of the fire spread simulator used for the GA individuals’ simulation. The authors in [ 34 ] presented a technique based on the parallelization of both the GA (used in the two-stage fire prediction framework) and the FARSITE fire simulator. For the first experiments, with fire simulations of 20 s, the results showed an improvement in GA execution time for reaching the same error (15%) when using more cores per individual. Mathematics 2022,10, 300 16 of 19 is 0.9510 (95%). With GA calibration, the mean error is 0.0603 (6.03%). This shows the importance of input parameters calibration, as seen in the literature. 0 20 40 60 80 100 Generations, g 0.0 0.5 1.0 RFinal Error (a) 2 4 6 8 10 12 14 16 18 20 Generations, g 0.0 0.5 1.0 RFinal Error (b) Figure 5. Evolution of the 30-run average of the best fitness values for every calibrated dataset. ( a ) Evolution of the 30-run average of the best fitness values for 100 generations. ( b ) Evolution of the 30-run average of the best fitness values for 20 generations. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Dataset 0.0 0.5 1.0 Relative Error Non-calibrated Rothermel GA-calibrated Figure 6. Relative error between the predicted and observed rate of spread R for non calibrated vs. calibrated input parameters. 5. Conclusions Due to the physical complexity of wildfires, their prediction models require the definition of several input parameters. However, some of them are very difficult to obtain accurately or, due to their nature, present significant variations over a short period of time, due to weather or fire-driven dynamics (e.g., fuel and wind properties). Therefore, the use of optimization methodologies—specifically, genetic algorithms—to calibrate the model and to overcome input parameter uncertainty has shown to be a valid strategy to obtain accurate prediction results. This strategy will pave the way to improved fire spread simulators, capable of adapting to the particular and constantly evolving conditions of Mathematics 2022,10, 300 17 of 19 each location, producing vital data for the decision makers and potentially mitigating the impact of wildfires. In this work, a literature review of research works on fire spread prediction using genetic algorithms was presented, showing that genetic algorithms are the most wellaccepted methodology for this application, being well-suited techniques for Rothermel model calibration. More recently, some works focused on coupling genetic algorithms with other methods to improve the prediction quality. However, due to the nature of genetic algorithms and the complexity of the model, the calibration process can be very computationally demanding. Therefore, other works also explore the possibility of reducing genetic algorithms’ execution time by using parallel computing and core-allocation techniques. Furthermore, in this work, a calibration of the Rothermel model using a genetic algorithm implementation was carried out on real datasets. The calibration was performed on four input parameters: σ (surface-area-to-volume ratio), δ (fuel bed depth), Mf (fuel moisture) and U (midflame wind speed). The results of the fire spread prediction using the calibrated model were compared to the fire spread prediction without calibration. The results showed that calibration improves prediction quality by 93.66%. As future work, based on the literature review, we intend to extend the prediction to the domain of a two-dimensional grid in order to improve the model’s applicability to real fire situations, where cells represent a squared area of the terrain through which fire propagates. This will result in the prediction of real fire behavior in the form of a map of burned cells over time. Furthermore, the parallel implementation of a genetic algorithm for the calibration of the two-dimensional Rothermel model based on the two-stage framework should be considered, which is validated by the review performed in this paper. Lastly, the framework should be tested and applied on data obtained through prescribed fires. Author Contributions: Conceptualization, methodology, formal analysis: J.P. and J.M.; writing— original draft preparation: J.P., software, J.P. and J.S.S.J.; validation, writing—review and editing, J.M., C.V. and J.R.P. All authors have read and agreed to the published version of the manuscript. Funding: This research was carried out under the project IMFire–Intelligent Management of Wildfires, ref. PCIF/SSI/0151/2018, and was fully funded by national funds through the Ministry of Science, Technology and Higher Education. Conflicts of Interest: The authors declare no conflict of interest. References 1. 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