Fire evacuation path optimization algorithms play a critical role in emergency management during fires, with the primary goal of providing the safest and most effective evacuation routes for people during a fire event, thereby minimizing loss of life and property. Traditional path optimization methods typically rely on Geographic Information Systems (GIS) and classic graph-based algorithms, such as Dijkstra’s and A* algorithms, which can efficiently find the shortest paths in static environments (Chen et al., 2020; Wang et al., 2025a). However, these methods struggle to adapt to the real-time requirements of path safety and responsiveness in the rapidly changing conditions of a fire disaster, leading to limited practical application effectiveness (Kodipalli et al., 2023).

In recent years, with the advancement of deep learning and intelligent optimization algorithms, fire evacuation path optimization has gradually incorporated data-driven and intelligent optimization approaches to address the complexities of dynamic fire scenarios (Sharma et al., 2020; Wang et al., 2025b). Graph Neural Networks (GNNs) have emerged as a valuable tool in disaster management due to their advantages in processing graph-structured data. They can model complex geographical environments as graph structures and analyze the risks and fire spread in different areas, thus providing support for dynamic path planning (Salami et al., 2023). Meanwhile, intelligent optimization algorithms, such as Particle Swarm Optimization (PSO) and Ant Colony Optimization (ACO), exhibit strong global search capabilities in path optimization, enabling the identification of safe routes in risk environments created by fire spread (Bouguettaya et al., 2022). Nevertheless, relying solely on deep learning or optimization algorithms still presents limitations in practical fire evacuation path optimization, primarily due to a lack of dynamic updating mechanisms that can effectively respond to the rapid expansion of fire.

Furthermore, to enhance the intelligence and real-time capabilities of path planning, this paper primarily explores the application of Multi-Agent Reinforcement Learning (MARL) in evacuation path optimization. By simulating various evacuation strategies through the collaboration of multiple agents in dynamic environments, the model can dynamically adjust path planning to adapt to the rapid changes in fire conditions.

In disaster management, Synthetic Aperture Radar (SAR) imagery has become an essential tool for monitoring natural disasters due to its all-weather, all-hour observation capabilities. SAR imagery can penetrate clouds and smoke, providing high-resolution surface information suitable for real-time monitoring of various disaster scenarios, including floods, earthquakes, and wildfires. Particularly in wildfire management, SAR imagery can clearly capture the areas affected by fires, the direction and rate of spread, offering robust data support for comprehensive monitoring and assessment of fire situations (Gupta et al., 2021; Tlijani et al., 2023). Traditional disaster management methods rely on ground sensors and video surveillance, which are limited in their application to large-scale fire scenarios and struggle to cover distant or dense fire areas. In contrast, SAR imagery not only provides real-time observations over a broader range but also acquires high-precision surface information, such as the location of fire sources, fire boundaries, vegetation density, and other critical features (Karimzadeh et al., 2022; Subramanian et al., 2023). By processing this SAR data, researchers can rapidly analyze fire dynamics after an outbreak, providing an accurate information foundation for disaster emergency decision-making (As shown in Figure 1).

In recent years, with the advancement of deep learning and intelligent analysis technologies, the accuracy and efficiency of SAR image processing have been greatly enhanced. Leveraging deep learning models such as Graph Neural Networks (GNN) and Convolutional Neural Networks (CNN), SAR imagery can be transformed into visual charts of fire situations, thereby supporting dynamic modeling of disaster scenarios (Pi et al., 2020; Wang and Wang, 2024; Yu and Zhenhua, 2024). However, many current studies still focus on the application of SAR imagery in disaster detection and monitoring, with less exploration of its potential in disaster evacuation path optimization. Although SAR imagery can provide precise information on fire spread, integrating it effectively into real-time decision-making for path planning remains an underexplored technical challenge (Alsamhi et al., 2021). Therefore, fully leveraging the data support role of SAR imagery in disaster management and combining it with evacuation path optimization models is an important direction for enhancing the speed and quality of wildfire emergency response and decision-making.

In the field of path planning, hybrid optimization algorithms have gradually become an effective tool for path planning in complex environments due to their combination of global search and local optimization capabilities. These algorithms typically integrate various optimization methods, such as Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO), and Genetic Algorithms (GA), and leverage machine learning models to enhance the adaptability and efficiency of the algorithms (Hu X. et al., 2023). By combining the strengths of different algorithms, hybrid optimization algorithms excel in multi-objective optimization, making them particularly suitable for dynamic path planning in complex disaster scenarios. In wildfire scenarios, path planning must consider not only conventional factors such as path length and time but also the potential threats of fire spread to the routes in real-time. Traditional path planning algorithms (like A*, Dijkstra) can find the optimal path in static environments but struggle to cope with the real-time changes in fire conditions (Xu et al., 2022). To address this issue, researchers have begun to introduce hybrid optimization algorithms to improve the flexibility of path planning. These methods dynamically adjust the weight coefficients and sampling strategies in path selection, enabling the generation of safer and more stable evacuation routes in complex fire environments.

Furthermore, with the development of Multi-Agent Reinforcement Learning (MARL) technology, hybrid optimization algorithms have been increasingly applied to multi-agent collaborative path planning. MARL’s application in fire scenarios can simulate the cooperation of multiple evacuation teams, adjusting routes in real-time to avoid collisions and adapt to the dynamic changes in fire conditions (Yang et al., 2022). However, although the combination of hybrid optimization algorithms and MARL can enhance the flexibility and dynamic adaptability of path planning, most existing studies focus on the theoretical aspects of the algorithms, lacking practical application explorations supported by multi-source data (Poudel and Moh, 2021). How to effectively integrate hybrid optimization algorithms with fire data (such as SAR imagery, fire emission data) to meet the path planning needs in wildfires remains a significant technical challenge.

This study proposes the GreyGNN-MARL model, which aims to provide an intelligent solution for evacuation path optimization in grassland fire scenarios. The core goal of the model is to achieve real-time planning and adjustment of dynamic evacuation paths under fire environments by combining multi-source data with intelligent algorithms. The GreyGNN-MARL model consists of multiple modules, mainly including graph neural networks (GNN) modules, gray wolf optimization (GWO) modules, and multi-agent reinforcement learning (MARL) modules. Through the collaborative work of these modules, the model can optimize evacuation paths in real time in complex and dynamic fire environments. Figure 2 shows the overall architecture of the GreyGNN-MARL model, covering the complete process from multi-source data input to path planning output.

At the input layer of the model, GreyGNN-MARL combines multi-source data from Sentinel-1 SAR images, global fire emission data (GFED), vegetation index, etc., and structures the fire scene through data preprocessing. These data are processed by GNNs, where each path (track1, track2, track3) represents a different data processing flow. GNNs and SAR encoders are used to extract geographic and fire information from multi-source data to form a graph structure of the fire scene. In this process, nodes represent different geographical locations or evacuation areas, while edges represent the connection between nodes based on risk propagation or traffic accessibility. Through this graph structure, the model can dynamically capture the spread of fire and regional fire risk information.

After the graph structure is constructed, the model enters the GWO module, which performs preliminary optimization of the path based on the graph feature matrix of GNN. The GWO algorithm simulates the hunting strategy of gray wolf groups and uses adaptive sampling density to dynamically adjust the weights in path selection to generate multiple candidate evacuation paths. Compared with traditional path planning methods, the GWO module can prioritize avoiding high-risk areas and improve the safety and efficiency of path selection.

Then, the MARL module further optimizes the evacuation path through multi-agent collaboration. In a fire environment, the MARL module uses multiple agents to adjust the evacuation strategy in real time to cope with the dynamic changes caused by the spread of fire. Each agent represents an evacuation team, which ensures that each group of evacuees can avoid high-risk areas and adjust the evacuation path in real time by sharing information and collaborating. In a complex environment where the fire is dynamically expanding, the MARL module can continuously optimize the path to ensure that the evacuation process is more adaptable and intelligent.

Through the organic combination of GNN, GWO and MARL modules, the model forms a multi-level intelligent evacuation path optimization system that can dynamically optimize the path in a fire environment and improve the safety, real-time and adaptability of the evacuation path.

The Graph Neural Network (GNN) module is the core component of the GreyGNN-MARL model used for constructing and analyzing the fire environment. Its main task is to convert fire scenes into graph structure representations based on multi-source data (such as SAR images, fire emission data, and vegetation indexes) to capture fire spread and regional risks at the node and edge levels. Through the GNN module, the model can effectively extract and process spatial and risk information in the fire environment, providing accurate fire risk and regional information support for the path optimization module (Chae et al., 2022; Sannidhan et al., 2023; Wang et al., 2022). As shown in Figure 3, the architecture of the GNN module includes data preprocessing, feature initialization of nodes and edges, message passing, and aggregation steps.

Initially, the GNN module converts key geographical information and fire status in the fire scenario into a graph structure G = ( V , E ) , where V represents the set of nodes, indicating different geographical locations or evacuation areas, and E represents the set of edges, connecting different nodes through travel or risk relationships. The initial features h v ( 0 ) of each node v ∈ V are initialized using the following formula: h v 0 = MLP x v + Embedding Risk v , Vegetation v where x v is the geographical feature of the node, Risk ( v ) denotes the fire risk level of the node, and Vegetation ( v ) indicates the vegetation coverage. Through a multi-layer perceptron (MLP) and embedding layer, the GNN module transforms this information into an initial node feature vector suitable for message passing.

During the message passing phase, the GNN module propagates and aggregates fire and risk information through edges between each node, constructing dynamic features of the fire scenario. In the l -th layer of message passing, the feature vector h v ( l ) of node v is updated by the weighted aggregation of neighbor node features, with the formula being: h v l + 1 = σ W l h v l + ∑ u ∈ N v α u v l W e l h u l where W ( l ) and W e ( l ) are the weight matrices for nodes and edges, respectively, N ( v ) denotes the set of neighboring nodes of node v , α u v ( l ) is the attention weight for edge ( u , v ) , measuring the influence of node u on node v , and σ is the activation function.

To further enhance the accuracy of risk propagation in fire scenarios, the GNN module introduces an attention mechanism in message passing to dynamically adjust the weights α u v ( l ) of edges, prioritizing the influence of high-risk nodes during fire spread. The attention weights α u v ( l ) are calculated using the following formula: α u v l = exp LeakyReLU a ⊤ W l h u l   ‖   W l h v l ∑ k ∈ N v ⁡ exp LeakyReLU a ⊤ W l h k l   ‖   W l h v l where a is the learned attention parameter vector, ‖ represents vector concatenation, and LeakyReLU is the activation function. This mechanism adaptively focuses on key nodes and high-risk edges in the fire scenario, ensuring more precise fire risk assessment during path optimization.

After multiple layers of message passing and feature aggregation, the GNN module outputs the final node features h v ( L ) and edge feature matrices, reflecting the risk levels of various regions and their connectivity in the current fire scenario. The resulting graph structure information H is then input into the Grey Wolf Optimization (GWO) module to support further path planning and optimization.

The GNN module forms a high-dimensional feature representation of the fire scenario through multi-layer feature aggregation, dynamic adjustment of attention weights (Ge et al., 2022), and embedding of fire risks. This module not only effectively captures the spatial relationships in the fire environment but also dynamically models the fire spread process, laying a solid data foundation for real-time path planning in the GreyGNN-MARL model.

The Grey Wolf Optimizer (GWO) module in the GreyGNN-MARL model is responsible for generating preliminary path optimization in fire scenarios. Inspired by the hunting behavior of grey wolves, the GWO algorithm dynamically adjusts path sampling density and weight coefficients to provide global search and optimization capabilities for evacuation routes (Sun et al., 2024; Wei et al., 2024; Agarwal et al., 2023). In fire environments, the GWO module utilizes the graph feature matrix generated by the Graph Neural Network (GNN) to preliminarily plan multiple candidate paths, ensuring that evacuation routes can avoid high-risk areas as much as possible. As shown in Figure 4, the GWO module includes key steps such as path initialization, dynamic sampling, and iterative optimization.

The GWO module initializes three main search agents: the alpha wolf (Alpha), beta wolf (Beta), and delta wolf (Delta), each playing different roles in path optimization. The positions of these three agents represent the coordinates of candidate evacuation routes, with the initialization formula as follows: X α 0 = Initialize X start , X goal , X β 0 = RandomInit () , X δ 0 = RandomInit () where X α ( 0 ) represents the initial position of the alpha wolf, initializing the path through the start and goal points, while X β ( 0 ) and X δ ( 0 ) are the random initial positions for the beta and delta wolves, respectively. This initialization ensures that the path search process can begin with multiple candidate paths, increasing path diversity.

During the path optimization process, the GWO module improves the evacuation route’s risk avoidance effect by dynamically adjusting the sampling density. Specifically, the alpha, beta, and delta wolves repeatedly calculate the distances between each other to update their respective path positions. The path update formula for the t -th iteration is as follows: X t + 1 = X α t − A ⋅ C ⋅ X α t − X t where A and C are control coefficients that adjust the convergence and exploration capabilities of the path. The coefficient A is dynamically calculated using the following formula: A = 2 ⋅ a ⋅ r − a , a = 2 − 2 t T where T is the maximum number of iterations, and r is a random number controlling the dynamic changes in sampling density and search range. By continuously adjusting the values of A and C , the GWO module can increase sampling in high-risk areas, thereby avoiding areas with strong fire spread and enhancing the safety of the path.

Additionally, to ensure the stability of the optimization process and the global nature of path selection, the GWO module comprehensively evaluates the path distances between the alpha, beta, and delta wolves in each iteration. The comprehensive path evaluation formula is as follows: Fitness X = w 1 ⋅ Distance X + w 2 ⋅ Risk X + w 3 ⋅ Smoothness X where w 1 , w 2 , and w 3 are weight coefficients that control the proportion of path distance, fire risk, and path smoothness in the optimization. Through this formula, the GWO module can balance path length and risk avoidance, achieving multi-objective path optimization.

After multiple iterations and dynamic sampling, the GWO module generates a set of optimized candidate paths, with the selected paths having high safety and shorter evacuation times. These paths will serve as the initial path input for the Multi-Agent Reinforcement Learning (MARL) module, further supporting dynamic adjustment and real-time optimization of the paths. The GWO module provides an efficient preliminary path optimization method for the GreyGNN-MARL model through adaptive path sampling and multi-objective optimization strategies.

Multi-Agent Reinforcement Learning (MARL) extends traditional reinforcement learning to environments where multiple agents interact. Each agent learns to optimize its strategy by receiving feedback from the environment while considering the presence and actions of other agents. In MARL, agents operate in a shared environment, learning to cooperate or compete to achieve individual or collective goals. Each agent simulates an “evacuation team,” which refers to a group of individuals who need to evacuate urgently during a fire, usually residents walking, residents riding bicycles, or families driving small vehicles (such as cars). We assume that these evacuation teams are small in size to allow for more flexible route adjustments and avoidance of high-risk areas for fires. Larger-scale transportation vehicles (such as buses) and large-scale team evacuations are not within the scope of this study’s assumptions. The model focuses on the rapid evacuation of small-scale teams. As shown in Figure 5, the MARL module includes the state space definition of the agent, the reward function design, and the policy update process.

In the MARL module, the state s t of each agent is composed of characteristics such as its position, fire risk information, and distances to neighboring agents, with the state defined by the following formula (Zhang et al., 2022): s t = Position x t , y t ,  Risk x t , y t ,   ∑ j ∈ N Distance s t , s j where Position ( x t , y t ) is the coordinate of the agent’s current position, Risk ( x t , y t ) is the fire risk coefficient at the current position, and N denotes the set of neighboring agents. This state description allows agents to perceive changes in the surrounding fire and distances to neighbors in the dynamic environment, supporting path optimization.

Each agent selects an evacuation path by performing an action a t . The set of actions includes basic operations such as moving forward, turning, and waiting, and agents choose action a t based on the current state s t to avoid high-risk areas. The agents’ decisions follow a reinforcement learning-based policy update formula: Q s t , a t ← Q s t , a t + α r t + γ max a ′ Q s t + 1 , a ′ − Q s t , a t where Q ( s t , a t ) represents the state-action value function, α is the learning rate, γ is the discount factor, and r t is the immediate reward obtained by the agent at time t . This update formula allows agents to balance exploration and exploitation, gradually learning the optimal strategy to avoid high-risk areas.

To achieve efficient risk avoidance, the MARL module designs a comprehensive reward function that considers factors such as path safety, evacuation time, and distances between agents. The reward function is defined as: r t = w 1 ⋅ − Risk x t , y t + w 2 ⋅ − Time s t , a t + w 3 ⋅ ∑ j ∈ N Distance s t , s j where w 1 , w 2 , and w 3 are weight coefficients controlling the influence of risk avoidance, time minimization, and agent spacing in the reward. This reward mechanism provides agents with immediate feedback during the evacuation process, leading to the selection of efficient risk-avoiding paths.

During the training process of the MARL module, the model gradually optimizes path selection through the collaboration of multiple agents, enabling them to achieve dynamic path planning under changing fire conditions and uncertainties. Information sharing and state synchronization among agents also ensure global consistency in evacuation routes (Ünal et al., 2022; Hu Y. et al., 2023). To further optimize the strategy, agents update their decision policy using the following policy iteration formula: π t + 1 a | s = exp Q s , a / τ ∑ a ′ ∈ A ⁡ exp Q s , a ′ / τ where π t + 1 ( a | s ) represents the policy probability distribution, and τ is the temperature coefficient controlling the level of exploration. By soft-maximizing the Q -values, agents can explore a broader range of path choices while favoring the optimal strategy with higher Q -values.

In summary, the MARL module enables the GreyGNN-MARL model to achieve intelligent evacuation route optimization in dynamic fire environments through collaborative learning and real-time decision-making among multiple agents, providing reliable technical support for real-time risk avoidance in complex disaster scenarios.

To ensure the practical application effectiveness of the GreyGNN-MARL model in grassland fire scenarios, this study selected high-quality public datasets that are multi-sourced and multi-dimensional, including the Sentinel-1 SAR dataset, the Global Fire Emissions Database (GFED), and the NASA LP DAAC vegetation index dataset. These datasets provide comprehensive fire scenario information, covering the geographical structure of the fire area, the spread trend of the fire, and the vegetation coverage, providing ample data support for path optimization in dynamic fire environments. Table 1 shows an overview of the datasets and their application scenarios.

The Sentinel-1 SAR dataset provides all-weather, all-hour synthetic aperture radar imagery. SAR imagery can penetrate clouds and smoke, accurately acquiring the location of the fire source, fire boundaries, and surface features during the fire (Lasaponara et al., 2023). This information is used to generate the base graph structure of the fire area, helping the GNN module capture geographical features and fire dynamics in the fire scenario, providing high-precision input for environmental modeling in path planning.

The Global Fire Emissions Database (GFED) provides data on carbon emissions, fire intensity, and spread trends during the fire. GFED data reflects the activity of the fire source and the type of combustion during the fire occurrence period, which helps to label high-risk areas and dynamically simulate the expansion of the fire (Oliva et al., 2020). The model uses GFED data for real-time updates of risk areas, ensuring that evacuation routes avoid high-risk areas of fire spread, enhancing the safety of the evacuation process.

The NASA LP DAAC Vegetation Index dataset provides vegetation indices (such as NDVI and EVI) for grassland areas, as well as ecological characteristics such as vegetation coverage and density (Huot et al., 2022). In fire scenarios, vegetation density and type directly affect the speed of fire spread and the level of fire risk. Through vegetation data, the GNN module can model the fire scenario accurately, further enhancing the support for risk avoidance strategies in path planning. Evacuation routes, and enhanced evacuation efficiency and safety.

The experiment was conducted in a high-performance computing environment to support large-scale data processing and efficient training of multi-module deep learning models. The hardware and software configurations and model parameter settings are shown in Table 2 covering detailed configurations of hardware devices, software platforms, key hyperparameters, and model modules.

To comprehensively evaluate the performance of the GreyGNN-MARL model in fire evacuation route optimization, this study designed multiple experimental metrics, including route planning time, risk avoidance success rate, route safety, route smoothness, and communication delay. These metrics quantitatively assess the model’s performance from aspects of efficiency, safety, and stability, ensuring its reliability and application value in actual fire scenarios.

Route planning time refers to the average time required for the model to generate evacuation routes, calculated in seconds, used to measure the model’s response efficiency. T avg = 1 N ∑ i = 1 N T i where T i represents the time for the i -th planning, and N is the total number of plannings. The shorter the route planning time, the faster the model’s response speed, the better it meets the real-time evacuation needs in fire scenarios.

Risk avoidance success rate refers to the frequency at which the model successfully avoids high-risk areas in the fire environment, expressed as a percentage, used to evaluate the safety of route planning. R safe = N safe N × 100 % where N safe represents the number of successful risk avoidances, and N is the total number of tests. A higher risk avoidance success rate means the model has a higher adaptability to changes in the fire, effectively avoiding high-risk areas.

Route safety assesses the cumulative fire risk in the evacuation route, calculated using the fire risk weight w risk and the risk values r i of each node on the route: S path = ∑ i = 1 L w risk ⋅ r i where L is the total length of the route. The lower the route safety, the more successful the route planning in avoiding high-risk areas, enhancing the safety of evacuation.

Route smoothness is used to measure the continuity and smoothness of the route, calculated by the angle changes between segments in the route: S smooth = ∑ j = 1 L − 1 θ j + 1 − θ j where θ j represents the angle of the j -th segment of the route. A smaller smoothness value indicates a more continuous and smooth route, reducing the number of emergency turns, which helps to improve the speed and safety of evacuation.

Communication delay refers to the delay time of the system in receiving and processing multi-source data, used to evaluate real-time responsiveness in IoT environments: D comm = 1 M ∑ k = 1 M d k where d k is the delay of the k -th data transmission, and M is the total number of transmissions. The lower the communication delay, the faster the model can obtain environmental information and adjust the route, helping to achieve efficient evacuation planning in fire environments.

These experimental metrics cover the model’s response speed, the safety and smoothness of the route, and communication efficiency, ensuring the GreyGNN-MARL model has comprehensive performance in fire evacuation route optimization.