Visualization of Real-Time Forest Firefighting Inference and Fire Resource Allocation Simulation Technology

Abstract

In recent years, the increasing frequency of forest fires has threatened ecological and social security. Due to the risks of traditional fire drills, three-dimensional visualization technology has been adopted to simulate forest fire management. This paper presents an immersive decision-making framework for forest firefighting, designed to simulate the response of resources during fires. First, a fire resource scheduling optimization model for multiple fire stations is proposed. This model integrates the characteristics of fire spread with a mixed-integer linear programming (MILP) framework, aiming to minimize response time and firefighting costs. It enables flexible resource scheduling optimization under various fire spread scenarios and constraints on firefighting resources. Second, the ant lion optimization algorithm (ALO) is enhanced, incorporating multiple firefighting weighting factors such as the density, distance, and wind direction of burning trees. This improvement allows for the dynamic selection of priority firefighting targets, facilitating the precise allocation of resources to efficiently complete fire suppression tasks. Finally, a three-dimensional virtual forest environment is developed to simulate real-time actions and processes during firefighting operations. The proposed framework provides an immersive and visualized real-time fire simulation method, offering valuable support for decision-making in forest fire management.

1. Introduction

Forest fires, whether caused by human or natural factors, have severely disrupted the ecological balance and pose significant threats to human property and life safety. The complexity of forest fires makes it challenging for fire departments to make effective decisions and take timely action. Additionally, traditional drills are costly, spatially constrained, and carry inherent risks, which complicates the development of efficient firefighting plans [1]. To address these challenges, 3D visualization technology is employed to create virtual environments that replicate real forest fire scenarios, visualize various firefighting strategies, and provide a scientific basis for informed decision-making. For instance, vFireVI enables multi-user collaboration and dynamic forest fire simulations [2], while the FFSimulator visualizes the impact of multiple variables on fire spread [3]. Moreover, the integration of geographic information systems (GISs) with remote sensing technology serves as an effective tool for managing forest fire risk [4]. Currently, the application of 3D visualization technology in forest fire management primarily focuses on simulating fire equipment and developing training systems [5]. However, it lacks a comprehensive approach to coordinating multiple sites and resources in actual firefighting operations and managing fire spread, thereby failing to fully capture the complex challenges of real-world scenarios.

Forest firefighting primarily involves prediction, monitoring, and fire suppression tasks. Fire suppression tasks encompass not only decisions about actions taken after arriving at the fire scene but also pre-arrival decisions on resource allocation [6]. In forest firefighting strategies, resource scheduling is critical to ensuring firefighter safety and optimizing the use of firefighting resources. It generally includes single-resource and multi-resource scheduling, with a particular emphasis on time and cost management [7]. Current research predominantly treats firefighting resources as a unified whole for scheduling, rather than differentiating by resource type, and lacks the flexibility to adapt to real-time conditions at the fire scene. Effective allocation of firefighting resources is essential for controlling fire spread and minimizing losses. However, existing studies still pay limited attention to resource allocation during active fires and the potential for resource coordination [8]. In real-world environments, forest fire spread is influenced by multiple factors—including wind direction, wind speed, vegetation type, environmental conditions, and firefighting measures—resulting in uneven and dynamic changes in fire behavior [9]. Consequently, firefighting resource allocation can be viewed as a dynamic task allocation problem, enabling adaptation to the evolving environment and demands during fire spread.

Currently, research on forest firefighting decision-making primarily relies on two-dimensional maps, which overlook terrain complexity and the three-dimensional spatial distribution of fire sites, limiting the ability to intuitively display the dynamic effects of firefighting resources during operations. Three-dimensional visualization technology, however, can effectively address these limitations by fully utilizing three-dimensional spatial information to provide multi-perspective insights into fire site conditions, offering decision-makers a more intuitive understanding of the fire response process [10]. The challenge remains to achieve effective dispatch and organization of firefighting resources in a three-dimensional environment, thereby ensuring both the scientific validity and practical applicability of the decision-making model.

Based on virtual reality and visualization technology, this paper develops a dynamic decision-making framework for firefighting resource management within a three-dimensional virtual forest environment. Firefighting resources are dispatched efficiently, taking into account both response time and firefighting costs. Upon the arrival of firefighting resources at the scene, they are dynamically allocated and organized to fully capture and represent firefighting operations in the forest environment.

In summary, the key contributions of this paper are as follows:

(1)

A fire resource scheduling model for multiple fire stations was developed. By integrating forest fire spread characteristics with a mixed-integer linear programming (MILP) model, flexible resource scheduling was achieved across various fire scenarios and resource constraints, to minimize response time and firefighting costs.

(2)

A dynamic task allocation algorithm within a virtual environment was designed. By enhancing the ant lion optimization algorithm (ALO) and incorporating fire-related weighting, factors such as the density, distance, and wind direction of burning trees, priority firefighting targets were precisely selected, and resource allocation was optimized, thereby improving fire suppression efficiency.

(3)

A visual simulation of the forest firefighting response process was realized. Through the simulation of a virtual three-dimensional forest scene, incorporating three-dimensional models of trees, terrain, the environment, and firefighting resources, the movement of firefighting resources, firefighting actions, and water flow effects were accurately simulated, providing a more intuitive and effective method for forest fire suppression.

2. Related Research

2.1. Disaster 3D Visualization

Three-dimensional visualization technology is now widely applied in fields beyond gaming and entertainment, particularly in scenarios that are challenging to operate in practice due to resource limitations or operational risks [11]. The primary advantage of virtual environments lies in their high degree of immersion, enabling users to simulate various situations and translate these simulated experiences into real-world response strategies [12]. For instance, in recent years, Li Wenting et al. have leveraged three-dimensional visualization technology to explore a variety of disaster scenarios. By modeling urban underground structures and buildings, the impact of above-ground structures on underground infrastructure during earthquakes is demonstrated, effectively assessing earthquake risks and providing a scientific foundation for improving building design and disaster response strategies [13]. In addition, Lin Minglang et al. utilized the discrete element method (DEM) in combination with PFC3D to perform three-dimensional modeling of damaged structures in the Shigang District. Their research investigated the mechanisms by which ground deformation contributes to structural damage [14]. Similarly, for flash flood early warning systems, Fujimi T et al. conducted randomized controlled trials using three-dimensional visualization to simulate different intervention scenarios, thus promoting the development of timely evacuation strategies [15]. Alene G H et al. applied this technology to debris flow disasters, simulating the temporal and spatial evolution of events to construct a digital mudslide model [16]. Additionally, for visually challenging hurricane disasters, Fusco et al. proposed a damage visualization method within a customized virtual reality experience, allowing users to intuitively understand the potential structural damage and utility disruptions caused by hurricanes, thereby enhancing risk awareness [17].

Three-dimensional visualization technology offers an immersive environment for high-risk tasks, mitigating uncontrollable damage—an enormous advantage in many fields [18]. In firefighting, 3D visualization technology provides real-time simulation training and a highly immersive experience, enabling firefighters to navigate complex fire scenarios and ultimately reduce disaster losses. For instance, Lian Haojie and colleagues reconstructed realistic fire training environments by combining NeRF and 3D Gaussian sputtering technology, generating high-fidelity physical environments and fire equipment models. They implemented multi-user collaborative training using the Photon PUN2 network framework, demonstrating that this approach significantly enhances training effectiveness [19]. The findings of this research underscore the vast potential of 3D visualization technology in creating realistic physical environments. Additionally, Tao Rui and colleagues developed a ship fire training simulator using three-dimensional modeling and physics-based simulation technology, achieving the first physics-based real-time smoke simulation. This innovation offers a more immersive and comprehensive operational environment for maritime firefighting training [20]. The aforementioned research highlights the tremendous potential of 3D visualization technology in generating realistic physical environments and its application value in complex fire situations.

In forest firefighting, the unknown and dynamic nature of fire environments presents significant challenges. As such, the application of 3D visualization technology plays a crucial role in addressing these complexities. Calandra et al. combined a fire extinguisher interface with real-time fire simulation logic to explore the use of virtual reality training simulation (VRTS) in forest firefighting training. Their approach, which complements traditional video-based training methods, was shown to significantly improve the learning experience [21]. Similarly, MS Clifford et al. applied virtual reality in aerial firefighting training, creating a realistic training environment where helicopters are used to extinguish large wildfires. This technology helps air attack supervisors (AASs) manage the mental and physical stress associated with decision-making during firefighting operations [22]. These studies illustrate the broad application potential of 3D visualization technology in the fire protection field, providing robust support for improving overall firefighting efficiency and addressing complex fire scenarios.

2.2. Fire Resource Scheduling Model

The primary challenge in forest fire resource scheduling is how to efficiently allocate firefighting resources to the fire site with the lowest possible cost and in the shortest time while maximizing the resource needs of the fire site. Existing research often focuses on optimizing resource scheduling by adhering to specific constraints [23]. Response time is the primary objective in forest fire resource scheduling, and it plays a critical role in enhancing the overall effectiveness of forest firefighting operations [24]. For example, Wang Lubing et al. proposed a method that combines the artificial bee colony (ABC) algorithm with the variable neighborhood search (VNS) algorithm. This approach employs the ABC algorithm to simulate bee foraging behavior, seeking the global optimal solution through the coordinated roles of employed, onlooker, and scout bees. Concurrently, the VNS algorithm dynamically adjusts the solution’s neighborhood structure to further refine the paths from multiple fire stations to the fire scene, thereby minimizing the total response time for firefighting tasks [25]. On the other hand, the C+NVC (cost plus net value change) model combines the objectives of minimizing resource usage costs and reducing total fire suppression losses [26]. In actual forest firefighting operations, decision-makers often aim to simultaneously reduce both firefighting costs and response time. As a result, it is necessary to establish a multi-objective optimization model to find the optimal resource scheduling solution. For instance, G. Tian et al. proposed a multi-objective discrete gravitational search algorithm that prioritizes minimizing response time and the number of fire trucks deployed, optimizing resource allocation from a single fire station to multiple fire sites [27]. Similarly, Pan Weijun et al. applied the non-dominated sorting genetic algorithm II (NSGA-II) to optimize resource scheduling for multiple aircraft from various assembly points to multiple fire sites, to enhance aircraft firefighting efficiency and further reduce firefighting costs [28]. Shahparvari et al. developed an optimization model for bushfire suppression aimed at minimizing both completion time and total cost while adhering to resource constraints. The model utilizes an enhanced weighted Chebyshev method to manage the highly complex operational responses involved in aerial firefighting for bushfire suppression [29].

Despite the progress mentioned above, the uncertainty in fire scale and the deployment and availability of firefighting resources continue to constrain the effective dispatch of forest firefighting resources [30]. As the complexity of constraints increases, traditional heuristic algorithms exhibit limitations in addressing such challenges. Specifically, they tend to have high computational complexity and slow convergence when handling large-scale problems and may fail to identify the global optimal solution in multi-objective optimization scenarios [31]. In recent years, mixed-integer linear programming (MILP) models have been increasingly applied to optimization problems due to their ability to handle both linear and nonlinear constraints while achieving optimal solutions through precise mathematical modeling. For instance, Wang Lubing et al. investigated the resource-constrained forest fire emergency dispatch problem, to simultaneously minimize total transportation distance and firefighting rescue time. By establishing a multi-objective MILP model, they derived the optimal firefighting dispatch plan for multiple fire sites [32]. Similarly, O. Ozkan developed a mathematical approach to forest fire detection, incorporating a drone range constraint into the problem formulation. The model sought to minimize the number of drones and their flight distance to mitigate the risk of forest fires [33]. Li Xiang et al. constructed a MILP model aimed at optimizing the total path from multiple locations to fire sites while minimizing the overall forest fire losses. Their model accounted for constraints such as the limited flight range and payload capacity of unmanned aerial vehicles (UAVs) [34]. N Skorin-Kapov et al. developed a MILP optimization model for aerial resource scheduling in large-scale wildfires, aiming to maximize both the minimum target completion and total water output in the region, with priority given to achieving the target water flow [35]. These studies demonstrate the significant advantages and practical relevance of applying mixed-integer linear programming to forest fire resource scheduling problems, highlighting its potential for providing more efficient and accurate resource allocation solutions.

2.3. Dynamic Task Allocation

The dynamic task allocation problem is a well-researched field, with applications spanning areas such as production and manufacturing [36], the service industry [37], traffic and transportation management [38], and disaster relief [39]. Task allocation methods predominantly include those based on traditional linear programming, dynamic market mechanisms, advanced artificial intelligence reinforcement learning, and various heuristic algorithms [40]. The linear programming-based approach transforms the task allocation problem into a mathematical model, deriving the allocation plan by solving this model. For instance, to address the challenges of a highly mobile environment in vehicular fog computing (VFC), Chao Zhu et al. proposed an optimization model based on linear programming to make task allocation decisions according to system requirements [41]. Market-based task allocation methods simulate market mechanisms to allocate resources or tasks, treating them as commodities that are distributed through bidding or negotiation processes. Duan Xiaojun et al. introduced a novel hybrid “two-stage” auction algorithm that integrates hierarchical decision-making with a centralized-distributed auction structure to optimize UAV task allocation [42]. With continuous advancements in artificial intelligence technology, researchers have increasingly applied reinforcement learning to task allocation challenges. Zhao Xinyi et al. proposed a fast task allocation (FTA) algorithm based on Q-learning, addressing the task allocation problem of heterogeneous UAVs in uncertain environments through neural network approximation and prioritized experience replay [43]. Han Qie et al. developed a multi-agent system using the multi-agent deep deterministic policy gradient (MADDPG) algorithm, enabling drones to perform real-time operations when the locations of targets and threat areas are known [44].

For forest fire resource allocation problems, the aforementioned methods primarily focus on centralized control or global models, which can be less effective when addressing the uncertainty and dynamic nature of forest fires. Heuristic-based task allocation, on the other hand, leverages prior experience to inform decision-making, offering faster computation times and making it more suitable for large-scale dynamic scenarios. Common heuristic algorithms include the greedy algorithm [45], ant colony optimization (ACO) algorithm [46], particle swarm optimization (PSO) algorithm [47], and simulated annealing algorithm (SA) [48]. For example, Liu Xinlin et al. proposed an enhanced genetic algorithm (GA) based on the fireworks algorithm (FWA) to address the task allocation problem of UAVs in forest fire reconnaissance, aiming to optimize the balance between solution efficiency and effectiveness [49]. Specifically, Gao Sheng et al. proposed a grouped ant colony optimization algorithm to address multi-UAV reconnaissance task allocation by considering the varying performance of UAVs and the heterogeneous characteristics of their targets [46]. Huo Lisu et al. introduced an exchange judgment simulated annealing algorithm and extended the 3D vehicle routing problem (VRP) model by incorporating virtual nodes, significantly improving the search efficiency for approximate optimal solutions in discrete combinatorial optimization problems [50]. Additionally, Zhang Hongguang et al. accounted for factors such as fire edge suppression, continuity of combustion units, and wind direction, and proposed a particle swarm optimization algorithm for firefighting aircraft task allocation in forest fire rescue [51].

Although heuristic task allocation methods offer fast computation speeds, their global optimization capabilities are limited, and they are prone to becoming trapped in local optima. In 2015, Mirjalili introduced the ant lion optimizer (ALO), which mimics the hunting mechanism of ant lions in nature and has demonstrated excellent performance in avoiding local optima and achieving fast convergence [52]. Building on this foundation, subsequent researchers have further applied and refined the ant lion algorithm to solve various practical problems. For instance, E.S. Ali et al. applied the ant lion optimization algorithm (ALO) to optimize the allocation and shaping of distributed generation in radial distribution systems [53]. Yao Yindi et al. proposed a virtual force-guided ant lion optimization algorithm (VF-IALO) to address the coverage hole problem caused by the random deployment of wireless sensor networks (WSNs). By dynamically adjusting the number of ant lions and using virtual force guidance, they achieved efficient task allocation and global optimization [54]. Moreover, Kavitha J et al. designed an ant lion-based autoregressive optimization (ALAO) strategy, which integrates an autoregressive model to dynamically adjust resource allocation in cloud infrastructure, ensuring system performance stability while meeting user demands [55]. In summary, while the ant lion algorithm has been seldom applied in the context of forest fires, its strong global search capabilities and adaptability make it well-suited to addressing the complexities of forest fire scenarios. It has the potential to enhance resource allocation strategies by better adapting to the dynamic and uncertain nature of forest fires.

3. Overview

This paper presents a firefighting decision-making framework based on a virtual three-dimensional forest environment, designed to optimize resource allocation and dynamic task scheduling, as illustrated in Figure 1. When a fire occurs, firefighting resources are initially dispatched. Taking into account the fire scene’s scale, terrain complexity, and resource distribution within the virtual environment, a mixed-integer linear programming (MILP) model is developed to minimize firefighting costs and response time, thereby optimizing the scheduling strategy for firefighting resources. Upon the arrival of firefighting resources at the fire scene, they are allocated and organized. By integrating fire spread dynamics with the ant lion algorithm (ALO) and accounting for the evolving conditions of the fire scene and firefighting expertise, a real-time adjustment strategy is designed and implemented to optimize the allocation of firefighters’ tasks. Finally, the movement of firefighting resources and firefighting animations are simulated to visualize the entire decision-making process within the virtual three-dimensional forest environment.

4. Models and Algorithms

The virtual forest fire decision-making framework encompasses the construction of three-dimensional forest scenes, the development of a fire resource scheduling model, and the dynamic allocation of forest fire resources.

4.1. Firefighting Resource Allocation Model

To address the problem of firefighting resource dispatch, a mixed-integer linear programming (MILP) model is formulated. When a fire occurs, resource dispatch from either a single or multiple locations is considered, with the primary objective of minimizing response time and firefighting costs.

First, two decision variables are defined: Firefighting resources primarily consist of human resources and equipment resources. Human resources refer to firefighters, while equipment resources include fire trucks.

The objective function is defined as follows:

Minimize the total cost of forest firefighting, which is composed of two components, as shown in function (1). The first component represents the transportation cost of dispatching firefighting resources from the fire station to the fire scene, calculated based on response time and unit transportation cost. The closer the distance, the shorter the response time and the lower the transportation cost. The second component is the selection cost of firefighting resources, representing the fixed cost associated with selecting and utilizing these resources:

$$min\sum _{i=1}^N{C}_{transi}·x_i+C_{ti}·x_i+C_{ei}·y_i$$

(1)

The model is subject to the following constraints:

The total firefighting resource demand constraint:

$$t\sum _{i=1}^N(k·x_i+y_i)·v_e\ge \sum _{j=1}^t{v}_{fi}$$

(2)

The available resource constraint for each fire station:

$$i\in N{x}_i\le A_{fi}{y}_i\le A_{ei}$$

(3)

The fire truck capacity constraint:

$$i\in N{y}_i\le p·x_i$$

(4)

Constraint function (2) ensures that all resources arriving at the fire site are sufficient to control the fire, which means that the total number of trees extinguished by firefighting resources should be higher than the number of trees currently burning. Among them, $v_{fj}$ represents the growth rate of burning trees at the j-th moment, which is derived based on the forest fire spread speed and forest coverage. The forest fire spread speed is calculated based on Zhengfei Wang’s forest fire spread model [56], taking into account factors such as temperature, humidity, wind speed, and combustible type. Constraint function (3) represents the resource quantity constraint, which limits the number of fire trucks and firefighters available at each fire station. The resources dispatched from each station must not exceed the station’s capacity. Constraint function (4) limits the number of personnel per fire truck, ensuring that the total number of firefighters dispatched from each station does not exceed the capacity of the fire trucks.

Table 1. Indices, sets, parameters, and decision variables in the MILP model.

Indicator
i	The i-th fire station
j	The j-th time period
Set
t	Firefighting time period settings
N	Set of fire stations
Parameters
$C_{transi}$	Unit transportation cost of fire trucks
$C_{ti}$	Fire truck extinguishing cost
$C_{ei}$	Firefighter extinguishing cost
$v_{fj}$	Growth rate of burning materials in time period j
$v_e$	Firefighter extinguishing speed
k	Ratio of fire truck extinguishing speed to firefighter extinguishing speed
$A_{fi}$	Number of firefighters at the i-th fire station
$A_{ei}$	Number of fire trucks at the i-th fire station
p	Fire truck capacity
Decision Variables
$x_i$	Number of fire trucks dispatched from the i-th fire station
$y_i$	Number of firefighters dispatched from the i-th fire station

provides a summary of the symbols used in the MILP model. $C_{transi}$ represents the fire truck fuel consumption cost, calculated as 1.47 USD/h [57] multiplied by the response time. The firefighting cost of the fire truck, denoted as $C_{ti}$, is set at 480 USD/h [57], while $C_{ei}$ refers to the firefighting cost of a firefighter, set at 2 USD/h [58]. The firefighting speed, $v_e$, of the firefighter is set to 0.2 m/s [59]. The capacity of the fire truck selected in this paper is 4–6 people, so our fire truck capacity, p, is set to 5 people, and the unit firefighting manpower of a fire truck is equivalent to three firefighters [60], so k is set to 3. For detailed values of $A_{fi}$ and $A_{ei}$, please refer to

Table 2. Firefighting resources and distance to fire locations for each fire station.

Fire Station	Fire Trucks	Firefighters
Station 1	80	400
Station 2	180	1100
Station 3	150	700
Station 4	160	800

. There is no clear standard for the construction of fire stations, and the number of personnel is at least 6 [61].

In this study, Google’s open-source optimization library, OR-Tools [62], was employed to solve the mixed-integer linear programming (MILP) problem. OR-Tools is a highly efficient mathematical optimization tool that addresses complex problems such as linear programming, integer programming, and mixed-integer programming. It achieves this by mixing multiple meta-heuristic algorithms, offering a robust approach to solving these challenges.

4.2. Dynamic Allocation of Forest Firefighting Resources Based on the ALO Algorithm

When firefighting resources arrive at the fire scene, the ant lion optimization (ALO) algorithm is initially employed to incorporate firefighting weighted factors, including the continuity of burning trees, wind direction, and distance from firefighting resources, to compute the optimal list of target trees for firefighting. Following this, the task allocation of firefighters is dynamically adjusted based on the real-time fire conditions and the optimal list of firefighting targets. A data structure is used to store the allocation relationships between firefighters and their assigned target trees. During each update, the status of firefighters’ tasks is reviewed, and the allocation is adjusted to ensure that firefighters are always directed to extinguish the most optimal trees. Figure 2 below illustrates the process of the proposed method.

The main process of the ant lion optimization (ALO) algorithm is as follows:

(1) Data initialization: The number of ants and ant lions, as well as the dimension of the variables, are determined. Their positions are randomly initialized within the feasible domain, and the corresponding fitness values are calculated.

The fitness function is weighted for forest firefighting problems, as shown in function (5). It takes into account factors such as the continuity of burning trees, wind direction, and the distance from firefighting resources. These factors are used to apply firefighting weights to the fitness function, allowing the algorithm to select a group of trees with higher fitness values, which then guide the search direction of the particles:

$$F=\alpha ·TotalPriority-\beta ·ATreeD-\gamma ·AfighterD-\delta ·AngleW$$

(5)

The parameters $\alpha$, $\beta$, $\gamma$, and $\delta$ represent the heuristic weights of each relevant attribute. Specifically, $\alpha$ represents the weight of total priority, $\beta$ represents the weight of the density of burning trees, $\gamma$ represents the weight of the distance between trees and firefighting resources, and $\delta$ represents the weight of the angle between the fire spread direction and the wind direction. $TotalPriority$ denotes the total priority (assumed to be constant), $ATreeD$ represents the average distance between trees, $Afighter$ represents the average distance between trees and firefighters, and $AngleW$ denotes the average angle between the trees and wind direction. These weights are used to heuristically adjust the allocation of firefighting resources. The initial setting of these parameters in this paper is based on the empirical values in the relevant field literature [51], and is adjusted based on my observations of the initial performance of the algorithm. Each weight value is 1.0 to achieve a balance between the factors.

(2) Determination of elite ant lions: The individual with the best fitness value from the initialized ant lion population is selected as the elite ant lion.

(3) Updating the position of ants and ant lions: For each ant, an ant lion is selected through the roulette method, and the search range is updated. Each ant performs a random walk around both the selected ant lion and the elite ant lion. The average result of these walks is taken as the new position of the ant. The updated formula is as Formula (6):

$$An{t}_i^{t+1}={\displaystyle \frac{R_A^t+R_E^t}{2}}$$

(6)

The variables $R_A^t$ and $R_E^t$ represent the values generated by the ant’s random walk in the t-th iteration. Specifically, $R_A^t$ corresponds to the value generated by the random walk around the ant lion selected in the t-th iteration, while $R_E^t$ is the value generated by the random walk around the elite ant lion during the same iteration.

(4) Recalculation of fitness value and update of ant lion: After each iteration, the fitness values of both the ant and the ant lion are recalculated. The ant lion’s position is updated based on the ant’s position and its fitness. The position with the best fitness is then designated as the new elite ant lion position.

(5) Termination of iterations: Check whether the maximum number of iterations has been reached. If the limit is reached, output the final result and terminate the iteration; otherwise, return to step (3) and continue the process.

5. Algorithmic Implementation

Based on the theoretical framework described in the previous section, this paper explores the visualization methodology for simulating forest fire suppression. First, a three-dimensional forest environment was constructed using a virtual engine, and the detailed process of fire resource scheduling was elaborated. Subsequently, the dynamic allocation algorithm for forest firefighting resources, based on the ant lion optimization algorithm (ALO), was implemented. The complete visualization process from resource scheduling to fire extinguishment was demonstrated. The study utilized the Unity3D engine for simulation, with C# serving as the primary programming language. All experimental simulations were conducted on an ASUS computer equipped with an Intel(R) Core i5-12400F CPU, 32 GB of RAM (Intel Corporation, Santa Clara, CA, USA), and running the Windows 11 Professional operating system.

5.1. Scene Construction

We constructed the scenario in accordance with the provisions of The Forest Fire Prevention Regulations [63] and NFPA 1710 [61].

In accordance with NFPA 1710, when developing fire department plans and allocating resources, it is required that the travel time of firefighting resources to the fire scene should not exceed 4 min. In practical forest firefighting operations, the average speed of fire trucks is typically around 30 km/h  [64], which results in a coverage area of approximately 12 km² for each fire station. To evaluate the robustness, scalability, and effectiveness of the proposed framework under varying fire conditions, we constructed a three-dimensional virtual forest scene covering an area of 50 km², with four fire stations strategically placed. Table 2 provides the details of the firefighting resources available at each fire station. By simulating different meteorological conditions, we generated various fire scenarios to visualize the decision-making process for firefighting. The forest scene constructed for this study is depicted in Figure 3.

The Forest Fire Prevention Regulations classify forest fires into four categories based on the affected forest area and the number of casualties, as outlined in

Table 3. Classification of forest fire intensity.

Fire Intensity Level	Affected Area (km2)	Number of Casualties
General Forest Fire	≤0.01	1–10
Large Forest Fire	0.01–1	10–50
Major Forest Fire	1–10	50–100
Particularly Major Forest Fire	≥10	≥100

. These categories are as follows: general forest fire, large forest fire, major forest fire, and particularly major forest fire.

5.2. Dynamic Allocation of Forest Firefighting Resources Based on ALO

Upon the arrival of firefighting resources at the fire scene, Algorithm 1 is executed to achieve the dynamic allocation of firefighting resources. First, the ant lion optimization algorithm is employed to generate a list of trees prioritized for extinguishment. Each firefighter is then assigned to the nearest unassigned tree, and the allocation relationship between firefighters and trees is stored. Once a task tree is fully extinguished, the task is cleared, and the tree is removed from the list. The system checks if all trees have been extinguished. If so, the process terminates; otherwise, the process is repeated.

5.3. Ant Lion Optimization Algorithm for Searching Optimal

Algorithm 2 provides a specific implementation of the ant lion optimization (ALO) algorithm. In this algorithm, each ant is represented as a list of tree indices, with the ant lions following a similar structure. The fitness of both ants and ant lions is determined by a fire-weighted fitness function. During each iteration, the position of each ant is updated relative to the ant lion selected through the roulette selection operator and the elite ant lion. This updated position is derived by conducting two random walks around the selected ant lion and the elite. As all ants perform random walks, their fitness is evaluated using the fitness function. If an ant achieves a higher fitness than any ant lion, its position will be considered as the new position of the corresponding ant lion in the subsequent iteration. The best ant lion is continually compared with the elite ant lion identified during the optimization process and replaced if necessary. This process is repeated until the maximum number of iterations is reached, at which point the final result is returned, and the iteration terminates.

Algorithm 1 Dynamic allocation algorithm

Input: $F=$ list of firefighters, $T=$ list of burning trees, $A=$ firefighter-tree allocation dictionary, $S_{\mathrm{assigned}}=$ list of assigned trees, $L_{\mathrm{complete}}=$ list of unassigned firefighters Output: $TargetTree=$ firefighter’s assigned tree 1: For each t in T: 2: Obtain $T_{\mathrm{best}}$ through the ALO algorithm 3: For each f in F: 4:    If f is not assigned or $A\left[f\right]$ is null: 5:       Find the tree closest to f, $T_{\text{best\_closest}}$, in $T_{\mathrm{best}}$ 6:       If $T_{\text{best\_closest}}$ is not null: 7:          $A\left[f\right]=T_{\text{best\_closest}}$ 8:          Add $T_{\text{best\_closest}}$ to $S_{\mathrm{assigned}}$ 9:          $f.targetTree=T_{\text{best\_closest}}$ 10:          Firefighter f proceeds to $targetTree$ to extinguish the fire 11:       End if 12:    End if 13: End for 14: Initialize $L_{\mathrm{complete}}$ 15: For each $(f,t)$ in A: 16:    If t is fully extinguished: 17:       Add f to $L_{\mathrm{complete}}$ 18:       Remove t from $S_{\mathrm{assigned}}$ 19:    End if 20: End for 21: For each f in $L_{\mathrm{complete}}$: 22:    Clear the allocation relationship $A\left[f\right]$ 23: End for 24: End for

Algorithm 2 ALO algorithm searches for the best list of trees

Input: $F=$ list of firefighters, $outburningTrees=$ list of external burning trees, $selectedTreeCount=$ size of the optimal tree list Output: $BestTrees=$ list of optimal trees 25: If $selectedTreeCount\le outburningTrees.Count$: 26:    Initialize ants 27:    Initialize ant lions 28:    For each iteration do: 29:       Set the ant lion with the highest fitness as the $globalBestantlion$ 30:       Update the maximum and minimum values of ant variables 31:       For each ant in ants do: 32:          Select an ant lion using $RouletteWheelSelection\left(\right)$ 33:          Calculate new ant position using RandomWalk() based on $selectedantlion$’s position and $globalBestAntlion$’s position 34:          Calculate the average value as the ant position using Equation (6) 35:          Update the ant’s fitness and position using Equation (5) 36:          If the ant’s fitness > ant lion’s fitness then: 37:             Update the ant lion to the ant 38:          End if 39:       End for 40:    End for 41: Else if $selectedTreeCount\le outburningTrees.Count$: 42:    Set $bestTrees$ to $outburningTrees$

6. Results and Discussion

This section presents and analyzes the experimental results in detail. To comprehensively assess the effectiveness of the fire resource scheduling model and the dynamic allocation algorithm, the scheduling schemes and algorithm performance under various fire levels and wind speed conditions are first introduced. This analysis illustrates the impact of different conditions on fire resource demand. Subsequently, a comparison is made between fire extinguishing strategies based on the ant lion optimization (ALO) algorithm and traditional methods, highlighting the advantages of the dynamic allocation algorithm in enhancing fire extinguishing efficiency. Finally, the constructed three-dimensional virtual forest scene is utilized to simulate and visualize the fire resource response process during forest fires, offering researchers and decision-makers an intuitive understanding of fire dynamics and firefighting strategies. Through a comprehensive analysis of the experimental outcomes, this section provides an in-depth discussion of the model’s universality and its potential for practical application.

6.1. Firefighting Resource Dispatch and Scheduling Model

The wind is a primary driving factor in forest fires and significantly influences the rate of fire spread [65]. To illustrate the generalizability of the proposed model, we simulated fire scenarios with varying levels of severity under two different wind speeds: 0.3 m/s and 1.6 m/s. The specific dispatching strategies derived from these simulations are presented in

Table 4. Firefighting resources at a wind speed of 0.3 m/s.

Fire Severity Level	Fire Area (km2)	Fire Stations	Fire Trucks	Fire Fighters
General Forest Fire	0.01	1	1	4
Moderate Forest Fire	0.5	1	10	49
Major Forest Fire	5	2	85	422
Severe Forest Fire	11	2	152	760

and

Table 5. Firefighting resources at a wind speed of 1.6 m/s.

Fire Severity Level	Fire Area (km2)	Fire Stations	Fire Trucks	Fire Fighters
General Forest Fire	0.01	1	4	16
Moderate Forest Fire	0.5	1	52	254
Major Forest Fire	5	3	326	1629
Severe Forest Fire	11	4	500	2497

.

As the fire area expands, the demand for firefighting resources increases significantly. Specifically, in cases of major and particularly severe forest fires, the number of fire trucks and firefighters escalates exponentially. This indicates that as the fire severity level increases and the affected area grows larger, more firefighting resources are required. Furthermore, under conditions of lower wind speeds, resource allocation for each fire level is relatively minimal, suggesting that fires can be effectively controlled with fewer resources when the spread is slower. Conversely, at higher wind speeds, resource dispatch becomes more proactive, with greater numbers of fire trucks and firefighters deployed. This underscores the need for more flexible and scalable resource allocation strategies under extreme weather conditions. Although the number of fire stations does not significantly change between general and major forest fires in both tables, the second table illustrates that more fire stations are allocated for major and particularly severe fires. This reflects the importance of additional fire stations in providing broader and faster coverage, reducing response time, and effectively controlling the fire.

Through the continuous expansion of the fire area under both low and high wind speed conditions, it is evident that the model can adapt to fire scenarios of varying severity and complexity. Whether dealing with a small-scale initial fire or a complex, large-scale fire, the model is capable of flexibly dispatching firefighting resources to ensure a rapid response and arrival at the fire scene, all while minimizing costs under various challenging conditions. The model demonstrates strong versatility. Figure 4 and Figure 5 illustrate the visualization results of resource dispatch at fire sites for four severity levels of forest fires: general, large, major, and particularly severe forest fires, under wind speeds of 0.3 m/s and 1.6 m/s, respectively.

6.2. Dynamic Allocation Algorithm

In order to evaluate the effectiveness of the dynamic task allocation algorithm in forest fire management, this study compared three different firefighting strategies. The first strategy uses the improved ant lion optimization (ALO) algorithm, which integrates multiple firefighting factors to prioritize the firefighting areas. The second strategy uses the beluga whale optimization (BWO) algorithm [66] to achieve the allocation of firefighting resources. The third strategy uses a simpler method to select the trees on the outermost side of the fire boundary and allocate firefighting resources to them in a predetermined order. By comparing the firefighting effects of these three strategies, the advantages and potential of the improved ALO algorithm in forest fire scenarios are analyzed. The experimental visualization results are shown in Figure 6.

In this experiment, the dynamic allocation of forest firefighting resources was simulated and analyzed using a time step of 20 s. As shown in the real-time burning and extinguished tree number curve in Figure 7, the improved ant lion algorithm significantly reduced the firefighting time compared with the other two schemes, with an average reduction of about 40 s. Additionally, the number of trees extinguished by the improved ant lion algorithm within the same time frame is notably higher.

Overall, the application of the improved ant lion algorithm in forest firefighting demonstrates a substantial improvement in efficiency. This algorithm not only effectively reduces the total firefighting time but also greatly increases the number of trees extinguished within a given period. Compared with other strategies, the improved ant lion algorithm curbs the spread of fire more quickly and effectively, minimizing the impact on ecosystems and human communities. These results indicate that the improved ant lion algorithm offers significant advantages in complex forest fire scenarios, providing more scientific and efficient support for real-world firefighting decision-making.

6.3. Three-Dimensional Visualization

By constructing a three-dimensional virtual forest scene, we simulated and demonstrated the fire resource response process during forest fires, including fire spread paths, the deployment of firefighting resources, and the dynamic progression of firefighting actions, as shown in Figure 8. This 3D visualization not only provides an immersive experience of fire development and firefighting decision-making but also enables users to observe and analyze the effectiveness of firefighting resource allocation from multiple perspectives. Through this visualization approach, researchers and decision-makers can more intuitively comprehend the complexities of fire dynamics, assess the efficiency of various firefighting strategies, and make more informed decisions.

7. Limitations and Outlook

Finally, we propose several directions for future research. This study has several limitations. First, the model simplifies real-world forest fire dynamics by representing fires as individual burning trees, without considering the complex spread through forest fuels such as litter and undergrowth. Second, while wind is treated as a key meteorological factor in fire suppression, other environmental parameters that significantly influence fire behavior—such as temperature, humidity, and precipitation—are not fully accounted for. Third, the resource allocation values used in the study are primarily virtual and lack validation against real-world data. Moreover, the study employs a basic A* algorithm for path planning [67] without introducing significant improvements or addressing complex, real-world firefighting strategies, such as creating firebreaks. Additionally, the research focuses solely on single-point fire scenarios, leaving multi-point fires and various resource types unexplored. The computational efficiency and accuracy of the proposed algorithm in handling large-scale fires and real-time decision-making also require enhancement. Future research should integrate more realistic fire spread models, advanced firefighting strategies, improved path planning algorithms, and multi-location fire scenarios to further optimize the dynamic allocation algorithm and enhance its effectiveness in large-scale fire events. Incorporating historical fire data and advanced machine learning techniques can improve the analytical capabilities of fire resource allocation strategies, thereby enhancing the framework’s practicality and accuracy for real-world applications.

8. Conclusions

Forest firefighting decision-making is a multi-dimensional and complex process, encompassing critical aspects such as fire station selection, resource management and allocation, and task assignment. This study proposes a forest firefighting decision-making framework that integrates a mixed-integer linear programming (MILP) model with a dynamic allocation algorithm based on the ant lion algorithm (ALO). The framework’s applicability and effectiveness are validated through experiments conducted under diverse fire scenarios. The MILP model optimizes response times and firefighting costs across various forest fire propagation scenarios and resource availability, demonstrating significant flexibility and robustness. Meanwhile, the dynamic allocation algorithm ensures more dynamic and precise resource distribution by comprehensively considering factors such as the density of burning trees, distances, and wind direction. Furthermore, the development of a three-dimensional virtual forest scene provides intuitive and visual support for comprehending and evaluating firefighting strategies. In conclusion, the forest firefighting decision-making framework proposed in this study holds substantial theoretical and practical significance. It offers novel insights into forest fire response strategies and lays a foundation for future research in this domain.