Proceedings of the ASME 2009 Dynamic Systems and Control Conference DSCC2009 October 12-14, 2009, Hollywood, California, USA

DSCC2009-2707

GENERATION OF OPTIMAL FIRE–LINE FOR FIGHTING WILDLAND FIRES USING GENETIC ALGORITHMS Baisravan HomChaudhuri*, Sheng Zhao*, Kelly Cohen**, Manish Kumar* Department of Mechanical Engineering*, Department of Aerospace Engineering** University of Cincinnati Cincinnati, Ohio [email protected]

ABSTRACT Every year all over the world, wildfires do extensive damages to the human lives, properties and natural resources. National Interagency Fire Center data provides a detailed description of the severe damages caused by the wildfires every year. Forest Fire Decision Support Systems (FFDSS) have been developed all over the world during the last thirty years with the purpose of fire detection, fire behavior prediction, and risk assessment. But optimized wildland fire containment strategies are largely lacking in these FFDSS. In this paper, decision making strategies have been formulated for wildland fire suppression so that the total burned area and hence the damage is minimized. This goal is achieved by the application of optimization tools such as the Genetic Algorithms (GA). For a given number of resources, the GA will determine their best utilization strategy so that the total area burnt is minimized. For generating optimal strategies for resource utilization, the Genetic Algorithm uses an advanced fire propagation model that predicts the propagation of wildland fires under given environmental conditions and topography. The fire-fighting strategy considered in this paper is fireline generation. Using the Genetic Algorithm, the optimal fireline is built that minimizes the area of land burned. GA also provides the proper locations of the attacking crews so that the fireline is built before the fire escapes. Using these intelligent decision making strategies, the damage caused due to a forest fire can be minimized significantly.

provided by the National Interagency Fire Center [1]. Forest Fire Decision Support Systems (FFDSS) have been developed during the last thirty years which provide valuable information on forest fire behavior, fire detection, and risk assessment. Examples of FFDSS include LANIK [2], Spatial Fire Management System (SFMS) of Canada [3], and FOMFIS [4] and DEDICS [5] of Europe. Each of these systems has its own merits and demerits. LANIK includes an initial attack simulation model that predicts the impact of ground and aerial resources. SFMS incorporates a full implementation of the Canadian Forest Fire Danger Rating System, providing assessments of fire ignition and growth potential and predicted fire behavior. FOMFIS is aimed at the definition, design, and implementation of a computer based system giving support to the process of planning activities and resource distribution for the preventive operations carried out by the forest fire fighting services. The DEDICS system emphasizes more on detection, situation awareness, database management, and communication which can support decision making and management. However, these decision support systems largely lack the optimization and intelligent capabilities that can be used for effective decision making and allocation of resources in a dynamic and uncertain environment that characterizes a complex wildfire. FARSITE [12] is a fire propagation model widely used by the USDI National Park Service, USDA Forest Service, and other federal and state land management agencies to simulate the spread of wildfires, and it automatically computes wildfire growth and behavior for long time periods under heterogeneous conditions of terrain, fuels, and weather. It incorporates the existing models for surface fire, crown fire, spotting, post-frontal combustion, and fire acceleration into a 2-dimensional fire growth model. FARSITE uses spatial information on topography and fuels along with

INTRODUCTION Almost every year, more than tens of thousands of square kilometers of area is burned and valuable properties and lives destroyed due to forest fires. In the last couple of years, the damage has increased significantly as reflected from the data

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weather and wind data, and has been shown to accurately predict the propagation of fire. In real life wildfire fighting scenarios, a limited number of resources are available and the goal is to use those resources in the best possible manner so that the total damage due to the forest fire is minimized. The damage due to a forest fire may be quantified in terms of the damage done to the properties and the cost of resources used to fight the fire. One of the strategies to fight a wildfire is to construct a "fireline" around the wildfire. A fireline, which looks a lot like a trail or small road, is a strip of land cleared of flammable materials like plants and shrubs. Hand crews build a fireline by clearing vegetation with tools such as shovels, "Pulaskis," and chainsaws. When the firefront reaches the fireline it is contained due to the lack of additional flammable materials. Optimum resource utilization and allocation is an important part of forest fire fighting. Over the time, researchers have come up with fire fighting strategies to minimize the damage due to wildland fire such as in [10] and [11]. Researchers in [10] have used the Genetic Algorithm to construct the best combination of available resources and their working area and duration of work to minimize the forest fire containment time. The paper [11] has put forward a general framework for the formalization of problems relevant to forest fire emergency management through real time resource assignment. In this paper, the Genetic Algorithm (GA) is used to generate the optimum fireline that minimizes the damage due to forest fire and provide the location of the firefighting crews on the landscape from which fire suppression should start so that the fire doesn’t escape and the burnt area is minimized at the same time. Using such resource allocation strategy, the total damage for wildland fire can be reduced considerably. In this paper, a simulation-optimization technique (showed in Fig. 1.) is used to evaluate the different parameters to be optimized by the Genetic Algorithm. In the proposed simulation-optimization technique, the forest fire is allowed to progress in simulation with the help of fire propagation models when the fireline is built concurrently. A population of solutions that have different parameters representing different strategies of the firefighting crews are generated by the Genetic Algorithm and their performance is evaluated when the fire is propagated for a certain time. This information is sent back to the GA where it is used to evaluate the performance index for a particular solution in the population. At the end of each simulation, the performance index is evaluated and is stored as an individual solution of the Genetic Algorithm. The performance index, which represents the goodness of a solution, may be chosen to be the total damaged area or a combination of burned area and the total cost of fire fighting. After a number of generations, the optimal solution is provided by the GA which minimizes the performance index. Fig. 1 shows the model of simulationoptimization technique.

FIGURE 1. SIMULATION-OPTIMIZATION USING THE GENETIC ALGORITHM

FIRE PROPAGATION MODEL Assuming a uniform fuel distribution, uniform landscape and weather, and constant wind direction, forest fire propagation can be modeled using Richard’s mathematical model [6]. This model uses the Huygens principle of wave propagation, where each point on the firefront is considered to be a new source of fire generation. The fire propagation is shown in Fig. 2.

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FIGURE 2. ENVELOP MODEL OF FIRE PROPAGATION

This model is called the Envelope Model of fire propagation. The fire-fronts are considered to be elliptical in shape under uniform conditions. Each point on the current firefront acts as an independent source of fire and generates elliptical fire-front. Each of these points on the current firefront moves to the next fire-front that is modeled by the Envelope Model. Equations governing the Envelop Model are provided below: Xt  Yt 

a 2 cos ( xs sin   y s cos )  b 2 sin  ( x cos  y s sin  ) b 2 ( xs cos  y s sin  ) 2  a 2 ( x s sin   y s cos ) 2

 c sin 

 a 2 sin  ( xs sin   y s cos )  b 2 cos ( x cos  y s sin  ) b 2 ( xs cos  y s sin  ) 2  a 2 ( x s sin   y s cos ) 2

( 1)

 c cos

Here “ X t ” and “ Yt ” are the rate differentials and the angle θ is the wind direction. “xs ” and “ys” are the orientation

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The processes involved in the generation of new populations mainly consist of operations such as Reproduction, Crossover and Mutation. The steps involved in GA for simulationoptimization is as follows: Step 1: Initialize a population-string of individuals (candidate solutions) Step 2: Use simulation models to evaluate the fitness of each individual Step 3: Carry out the genetic operations (See Figure 3) viz. reproduction (selection of sub-population for next generation), crossover (swapping of corresponding parts of strings at a random point for two individuals selected on the basis of their fitness), and mutation (randomly changing the value of strings at randomly selected position of the string). Step 4: Test for termination criterion. GA operates by finding a solution that minimizes a performance index. A performance index is the measure of goodness or effectiveness of a solution. In this case, performance index is the combination of factors representing area burned and resources used.

of the vertex on the on the fire front in the terms of component differentials. The location of the new fire-front is available by multiplying the rate differentials with the step time. PROBLEM FORMULATION The aim of this paper is to develop an optimization scheme for determining decision making strategies for containment of a wildland fire. The fire containment technique considered in this paper is by fireline construction. The optimization problem is to determine a fireline that will minimize the total burned area. Considering a known rate of fireline production of the firefighting crews, the optimal fireline is the one that minimizes the damaged area. This paper evaluates two different fireline building strategies. Strategy 1: Under homogeneous topology and weather conditions, the fire-front forms an elliptical curve. Hence, an optimal fireline can be approximated to be elliptical in shape which will be big enough just to envelope the fire when complete. Any fireline larger than the optimal fireline would result in larger burned and hence damaged area. On the other hand, a smaller elliptical fireline will result in escape of the fire, i.e. the fire-front will the cross the fireline before it is been completed by the firefighting crews. Strategy 2: The total burned area can be reduced if a number of polynomial curves are used as the fireline rather than a single elliptical curve. A more effective solution is to find the locations of a given number of firefighting crews on the landscape along with the parameter of the curves representing the fireline that they would build. Such method promises better and efficient results, since the forest fire growth rate in all directions are not equal even under homogenous conditions. Intelligent resource allocation techniques are needed to be used to solve this problem which is required by the Forest Fire Decision Support Systems.

FIGURE 3. GENETIC ALGORITHM OPERATIONS

The different parameters of the fireline can be optimized by the Genetic Algorithm according to the assigned performance index. The optimum fireline that minimizes the total damage of the forest fire can then be established from the evaluated parameters. Strategy 1: Since the wildland fire propagation under certain conditions can be assumed to be elliptical in shape, an elliptical fireline can be considered for the containment of forest fire. The equation of the elliptical fireline then can be represented by equation (2).

APPROACH To achieve the goal of this paper and satisfactorily solve the problem described above, Genetic Algorithm is used for optimization. A Genetic Algorithm (GA) is a search and optimization technique used in computing to find the exact or approximate solutions to an optimization and search problem. Genetic Algorithms are a particular class of evolutionary algorithms that use techniques inspired by evolutionary biology such as inheritance, mutation, selection, and crossover (also called recombination). The GA based search and optimization techniques have recently found increasing use in machine learning, robot motion planning, scheduling, pattern recognition, image sensing and many other engineering applications. The Genetic Algorithms are based on mechanics of natural selection and natural genetics [7-9]. They combine survival of the fittest among the candidate solutions with randomized, yet organized, information exchange to form search algorithms with capabilities of natural evolution. The GA starts with a random creation of a population of strings representing candidate solutions and thereafter generates successive populations of strings that improve over generations.

x  x c  a cos  cos   b sin  sin  y   y c  a cos  sin   b sin  cos 

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(2)

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ELLIPTICAL FIRELINE

equation for a crew moving from points xi , , yi to x j , y j is given by: for x going from xi to xj

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Phi

y  y i  a( x 2  x i )  b( x  x i )

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When the parameter a following equation:

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(5)

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The parameter “ b ” along with the grid locations (the grid x and y coordinates) of the fire fighting crew are used as the parameters of GA that are to be optimized. The GA, through its different generations of solution, can yield the required parameters that minimize the total burned and damaged area.

FIGURE 4. ELLIPTICAL FIRELINE

a and b are the semi-minor and semi-major axis respectively and  Here, xc , yc are the center of the elliptical fireline,

Genetic Algorithm generates a vector of solutions for the evaluation of the performance index. In the example considered in this paper, four teams of crews are considered to be allocated. Hence, the GA generates a solution that consists of the locations of the four crew teams, and the parameter ‘b’ of their respective fireline curves. Now, as the fireline is built from one point to another, some combinations of the four points will result in intersection of two filelines which is a practically wrong solution. Hence, concepts from the Travelling Salesman Problem (TSP) are used here to obtain the proper order of the points so that all the points are touched with no intersection of two or more firelines. TSP is a combinational optimization problem which determines the shortest possible tour that visits each city exactly once given a list of cities and their pair wise distances. In our case, a TSP algorithm can be used to obtain the proper sequence of the four points so that an intersection of lines is avoided.

is the parameter of the fireline that goes from 0 to 2π. The angle θ is the angle between the Y axis and semi-major axis i.e. the orientation of the elliptical fireline. In Fig. 4. the ellipse center is at (250,250) with zero (θ=0) angle between Y-axis and semimajor axis. The five parameters (a, b, θ, xc and yc) that completely defines an elliptical fireline are considered to be the parameters for the GA. The performance index of GA is set as the total burned area, i.e., the area within the elliptical fireline. The GA then updates its population of solutions based on the evaluated performance index of each solution to yield the global solution as shown in the next section. Strategy 2: As mentioned earlier, forest fire growth rate is not same in all directions. The rate of fire growth is highest in the direction of the head of the firefront (which coincides with the wind direction under other homogeneous conditions) and lowest in the tail direction. Hence, placing more resources near the head of the firefront, i.e., attacking more towards the head of the firefront, can yield better result and hence lesser burned area. In this strategy, the location (x and y coordinates in the landscape) of different fire fighting agents on the landscape is set as the parameters for optimum fireline generation along with the parameters of the polynomial curve that each crew will build. Here, we propose a grid based approach where the landscape is divided into a number of grids. Each fire fighting crew allocated in different grid locations are assumed to build the fireline in the shape of a quadratic function which is given by:

y  ax 2  bx  c

can be computed from the

( y j  y i )  b( x j  x i ) x j  xi

(4)

FIGURE 5. CORRECT TRAVELLING ORDER

Both the figures (Fig. 5 and Fig. 6) show the location of the firefighting crews (1, 2, 3 and 4) generated by Genetic Algorithm. Fig. 6 shows the incorrect travelling order with a sequence 1-2-3-4-1 where one firefighting crew from position “1” move to position “2”, second crew moves from position “3” to “4” and so on. As a result there is intersection between the

(3)

Each crew moves from its own starting location to the starting location of the next crew. This guarantees an overall closed curve formation for fire containment. Hence, the fireline

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generated firelines, as shown in the Fig. 6, which is an impractical solution. Fig. 5 shows the correct order, 1-3-2-4-1, after applying the travelling salesman problem and negates the possibility of intersection of generated firelines.

production rate. Using simulation-optimization technique, the firefront coordinates after time t = 4 units are supplied to the Genetic Algorithm. From the solutions generated by the GA, the time required to build the fireline is evaluated and this time of fireline building is returned back to the firefront propagation program. The firefront is again simulated till the extra time for fireline building and the performance index is evaluated according to the ability of the fireline to contain the fire and the total burned area. For this simulation, 300 generations and a population size of 301 are used. The mutation probability is generally considered low and has been considered to be 0.0077 and the cross over probability of 0.77 has been considered (generally more than 0.5). In this problem, Steady State GA is used with a steady state population size of 31. In Steady State Genetic Algorithm, a percentage (user defined) of the population, selected based on its fitness value, is retained into the next generation. This subset of the population goes though regular selection for mating purposes but is not altered going into the next generation. This GA variant saves time while evaluating objective functions that require a large amount of computation time, and string lengths that require a large number of members in the population.

FIGURE 6. INCORRECT TRAVELLING ORDER

SIMULATION RESULTS/DISCUSSION Strategy 1: In this strategy, the forest fire is contained with the help of an elliptical fireline. As mentioned earlier, following the Richard’s mathematical model the fire-fronts are assumed to be elliptical in nature under homogenous conditions. Forest fire is simulated first till time t = 4 units. Fig. 7 shows the fire propagation under homogenous conditions with a constant wind direction of 20°. This angle is the angle between the Y-axis and the semi-major axis.

In Fig. 8 the optimal fireline is marked with red. It is the best possible solution because any elliptical fireline bigger than the proposed fireline will result in more burned area, when any smaller fireline will result in escape of the fire. In this simulation, 4 firefighting crews are used with a combined ability of generating 120 unit length of fireline at each time step.

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FIGURE 7. FIRE PROPAGATION WITH 20° WIND DIRECTION AT DIFFERENT TIME STEPS

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FIGURE 8. OPTIMAL FIRELINE GENERATION

The problem now is to find the optimal elliptical fireline that will minimize the burned area and make sure that the fire doesn’t escape i.e. fireline building is complete before the firefront reaches the fireline. As stated earlier, the parameters to be optimized by the GA are: the semi minor and semi major axis, orientation and center of the elliptical fireline i.e., a, b, θ, xc and yc (Fig 4). It is assumed that the fireline building starts at t = 4 time units. The time required by the firefighting agents to build the fireline can be calculated from their known fireline

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considered low and is taken as 0.0077 and the crossover probability of 0.77 is considered. Steady State GA is used with a steady state population size of 31. The optimal resource locations are shown in Fig.10.

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FIGURE 9 PERFORMANCE INDEX VS NUMBER OF GENERATIONS FOR STRATEGY 1

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FIGURE 10. FIRE SUPPRESSION CREW INITIAL LOCATIONS AND INITIAL FIREFRONT

Fig. 9 shows a plot of the best performance index of population in a generation as the number of generations increase in the GA. It is seen that the performance index decreases and finally converges to the optimal solution.

In Fig. 10, the blue dots on the landscape denote the fire crew locations when the red grids denote the firefront. It is seen from the figure above, that even though the rate of fireline generation is equal for all the 4 resources, optimal solution locates the resources closer to the head of the fire where the fire propagation rate is maximum. Fig. 11 shows the evolution of best performance index value in different generations and its convergence to the optimal value.

Strategy 2: To improve the fire containment strategy, the elliptical fireline is replaced by a number of different quadratic equations. This provides more flexibility to the shape of the resultant fireline. In this problem, four firefighting crews are assumed to be working at a constant rate. Each and every firefighting agent builds a fireline, which is represented by quadratic equations with different parameters. When any crew finishes its assigned task of fireline building, it helps the next crew to complete its assigned task. In this case, Genetic Algorithm has 12 parameters to optimize which consists of the (x,y) locations of the four fire fighting agents and the “ b ” parameters in equation (4) of the four firelines .

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Increasing the size of each grid results in the decrease of the number of total grids and hence the search space for the GA. However, this results in decrease of the resolution of the solution. A trade-off is required between the resolution of the solution and the search space for the GA. A moderate grid size of “3x3” square units is chosen in this paper for the simulation purpose which provides a fairly good resolution of the solution as well as manageable search space. In each iteration, the GA generates a population of solution vectors consisting of the initial locations of the four crews and the parameters of the four curves that the crews will be building. Once the solution vector is generated by the GA, a travelling salesman problem algorithm is utilized to obtain the proper order of the solution points. Simulation-Optimization technique is then used to generate populations in subsequent generations and eventually obtain the optimal solution.

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FIGURE 11. PERFORMANCE INDEX VS NUMBER OF GENERATIONS FOR STRATEGY 2

Figure 12 shows the final firefront and the final fireline generation by the four crews.

Since the search space for the GA is large in this case, 300 generations and a population size of 301 are used in the GA. Similar to the first strategy, the mutation probability is

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strategy for fireline construction for minimum burnt area. We have compared two optimal fireline construction strategies that make better resource allocation and helps in reducing the damage due to forest fires. Among the two proposed strategies, it is evident that the second strategy reduces the total burned area to a higher extent. One of the major contributions of this paper is to apply the GA based simulation-optimization technique to a wildfire fighting scenario and demonstrate that such techniques can be used to arrive at better resource utilization decisions. The availability of accurate fire propagation models, new technologies to gather and process information, and accurate weather prediction models can be used with simulation-optimization techniques as proposed for more efficient decision making in complex wildfires. The future work in this direction will focus on applying the proposed technique to more complex and uncertain situations and using the currently available software such as FARSITE, which can accurately simulate forest fire propagation under varying landscape, weather and wind conditions.

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FIGURE 12. FIRELINE GENERATION

Fig. 12 shows the fire is properly contained without escape. The red grids here represent final firefornt while the blue grids are the fireline. To compare the effectiveness of both the strategies, the simulation was performed using the same conditions for both the cases, such as time at which fire suppression begins the line production rate of the firefighting crews and the number of resources. In both the cases, the fire suppression effort begins at time t = 4 time units. The cumulative fireline production rate is 120 unit lengths per time step. For the firefighting crew using strategy 2, their cumulative line production rate is (120/3) = 40 grids per time step, and hence for each crew it is (40/4) = 10 grids per time step.

REFERENCES [1] http://www.nifc.gov/fire_info/nfn.htm [2] David L. Martell, Dennis Boychuk, James I.M., Barbara M.S. and Rica Saporta, 1994, “Decision Analysis of the Level of Forest Fire Protection in Ontario,” Proceedings of 1994 Symposium on Systems Analysis in Forest Resources, 138-149. [3] http:// www.eufirelab.org

Fig. 8 and Fig. 9 show the performance of the firefighting agents using strategy 1. For strategy 1, the area burned is evaluated as 3952 square unit length and for strategy 2, it is 3222 square unit length (equal to 358 grids). It is clear from the simulation results that strategy 2 yields better solution than strategy 1. This is expected because using the strategy 2, more flexibility is allowed to the fire crew in terms of initial deployment and curve generation.

[4] David Caballero, “FOMFIS: A Computer Based System For Forest Fire Prevention Planning,” In proc. of 3rd Intl. Conf. on Forest Fire Research, November. [5] A. Ollero, J.R. Martinez-de dios and B.C. Arrue, 1998,“Integrated Systems for Early Forest-Fire Detection,” International Confer. on Forest Fire Research 14th Conference on Fire and Forest Meteorology, II, pp. 19771988. [6] Gwynfor D. Richards, 1990, “An Elliptical Growth Model of Forest Fire Fronts and Its Numerical Solutions,” International Journal for Numerical Methods in Engineering, 30, pp. 1163-1179. [7] Goldberg, D., Genetic Algorithms in Search, 1989, “Optimization & Machine Learning”, Addison Wesley Longman, Inc. [8] Miachalewicz, Z., 1996, “Genetic Algorithms + Data Structure = Evolution Programs”, Springer Verlag. [9] Garg, D. and Kumar, M., “Optimization Techniques Applied To Multiple Manipulators for Path Planning and Torque Minimization”, Journal for Engineering Applications of Artificial Intelligence, Vol. 15, 2002, pp. 241-252.

The GA generates a population of several solutions that gets evaluated in each generation via simulation of the fire propagation model. All these calculations make the proposed GA based simulation-optimization technique computationally extensive. In-spite of this, real time applicability of this technique is not of much concern because of time scale in which wildfires are fought and also due to the fact that the proposed technique can be easily adapted to facilitate parallel computations.

CONCLUSION In this paper, a Genetic Algorithm based simulationoptimization framework for generating intelligent wildfire fighting strategies has been developed for the better containment of wildland fires. This optimization framework uses an advanced fire propagation model to determine the best

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[10] Sung-Do Chi, Ye-Hwan Lim, Jong-Keun Lee, Jang-Se Lee, Soo-Chan Hwang, and Byung-Heum Song, 2003, “A Simulation Based Decision Support System For Forest Fire Fighting,” Springer Berlin / Heidelberg, Advances in Artificial Intelligence, Vol 2829/2003, pp 487-498 [11] Fiorucci, P., Gaetani, F., Minciardi, R., Sacil, R., Trasforini, E., 2004, “Dynamic resource allocation for

forest fire risk management,” Database and Expert Systems Applications, Proceedings 15th International Workshop, pp 603-607. [12] Mark A. Finney, 2004, “FARSITE: Fire Area SimulatorModel Development and Evaluation,” United States Department of Agriculture, Research paper RMRS-RP-4

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