Evacuation Route Determination in Indoor Architectural Environments Based on Dynamic Fire Risk Assessment

Abstract

The enclosed nature of indoor building spaces during fires creates complex fire environments and restricted evacuation routes, substantially elevating the risk of mass casualties. Traditional static evacuation routes not only overlook the complexity of fire scenarios but also fail to satisfy safety requirements for evacuation. To address this issue, this study proposes an enhanced A* algorithm to determine evacuation paths based on dynamic fire risk assessment. A dynamic fire risk assessment model is established using key fire environment parameters (e.g., temperature, visibility, and toxic gas concentration) and their corresponding personnel harm thresholds. This model quantifies fire risks within a discrete space. The A* algorithm is improved by integrating fire risk values and initial direction constraints into its heuristic function and path update strategy, thereby increasing the algorithm’s accuracy and efficiency. Using a subway station fire as a case study, the simulation results indicate that the improved algorithm can update evacuation paths in line with the dynamic evolution of fire risks. It also identifies evacuation routes by balancing fire risk, distance, and initial direction. This approach maintains the original path direction while substantially reducing path risk, achieving an approximate 70% reduction in individual evacuation path risk. This method can guide building fire safety design and the formulation of emergency evacuation plans. It also serves as a reference for path guidance during emergencies.

1. Introduction

Indoor buildings are characterized by enclosed environments and limited escape routes. During fires, the complex environment and dispersed crowds can lead to casualties and rescue difficulties. According to statistics, about 65% of casualties in building fires are due to failed evacuation routes [1]. Thus, rapidly evacuating people from dangerous to safe areas during fires and creating dynamic evacuation guidance strategies that adapt to fire progression is a critical issue in building safety. This has drawn many scholars’ attention to research on fire risk assessment and evacuation path planning in buildings.

To effectively reduce fire risks and enhance personnel safety, scholars have analyzed and assessed the main risk factors of indoor buildings using comparative analyses, computer simulations, and case analyses. Structural features and fire risks of buildings are the main factors affecting safe evacuation [2,3]. Johnson [4] presented a fire safety assessment model for large spaces, offering theoretical support for engineering practice. Ju et al. [5] proposed a hybrid weighting model based on game theory and TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) to quantify multi-dimensional fire risks. Lu et al. [6] combined FDS (Fire Dynamics Simulator) and CA (Cellular Automata) to develop a coupled model for assessing fire risks in university multi-story dormitories. Ye et al. [7] focused on the impact of fire products (e.g., smoke, heat radiation) on pedestrian behavior, enhancing the physical–social coupled mechanism of risk assessment. Research shows that fire environment risks greatly affect personnel safety during evacuation. Fire combustion products can cause physiological and psychological stimuli to individuals, further impacting evacuation behavior and outcomes.

During indoor fires, the irregular spread of fires and affected human behavior directly impact evacuation safety. Static environment information at a single moment cannot meet actual evacuation needs. Traditional static model-based evacuation path solutions are gradually being replaced by dynamic optimization algorithms. For example, Wang et al. [8] developed a multi-objective great ape optimization algorithm to balance evacuation time and congestion risks. Wang et al. [9] created an optimal phased evacuation strategy to improve resident safety during high-rise building fires. Ding et al. [10] studied real-time dynamic optimal evacuation route planning to enhance emergency management by increasing the utilization of evacuation exits. Regarding fire spread, Liu et al. [11] used an IACO (Improved Ant Colony Optimization) algorithm for time-varying path planning. He et al. [12] designed a risk perception-based chemical multi-hazard path planning method for better environmental adaptability. Choi et al. [13] established an optimal path model based on hazard prediction data. Feng Z et al. [14] considered the trade-off between fire risks and distance costs to provide evacuation path planning for stranded individuals. DENG et al. [15] optimized path planning by integrating safety and evacuation time in a fire evacuation model to dynamically avoid fire-affected route nodes.

In recent years, numerous scholars have established fire evacuation models and proposed optimized or optimal evacuation plans [16,17,18]. However, existing fire evacuation models and commercial software programs like Building Exodus (Version 6.3) and STEPS (Version 2023) mainly focus on analyzing factors affecting evacuation. These models often use the shortest path algorithm and seldom consider dynamic fire risks and multiple environmental factors in complex settings [19,20,21]. Research by Huang et al. [22,23,24] shows that people’s path choices are closely related to fire evolution. Most passengers initially head for the nearest exit, but as the fire develops, evacuation paths diversify, reflecting dynamic environmental influences on decision making. Studies by Haghani et al. [25,26,27] indicate that individuals’ wayfinding in dangerous environments is constrained by movement inertia. Wang et al. [28] used agent-based modeling to simulate underground building fire evacuations, confirming the feasibility of multi-factor interactions and providing a theoretical basis for evacuation models in complex environments.

Based on existing research, this study proposes an enhanced A* algorithm for dynamic evacuation path planning during fire emergencies, considering the limitations in dynamic risk response and multi-objective path optimization. The algorithm takes into account the characteristics of indoor building spaces and the evolution of fire risks, dynamically adjusts evacuation routes through real-time environmental risk updates, and generates adaptive evacuation path solutions that integrate factors such as dynamic fire risks, distance, and initial path direction. It provides a theoretical basis for architectural fire safety design, emergency plan formulation, and intelligent evacuation system development.

2. Dynamic Fire Risk Assessment Method

2.1. Environment Modeling Method

When a fire occurs in an indoor building environment, different areas are affected by the fire to different degrees. It is difficult to achieve adaptive evacuation planning and building function assessment without considering the regional characteristics. In previous studies, the uneven demand for regional evacuation was often ignored, leading to significant deviation between evacuation planning and safety assessment results and the actual situation. To consider the characteristics of local areas, this paper conducts grid processing of the building scene for personnel evacuation, and superimposes terrain information, fire environment information, and personnel information for each grid according to the evacuation demand. The discrete environment state under the unified time corresponds to the evacuation behavior to simulate the process of personnel evacuation.

2.2. Fire Risk Quantification Based on Multi-Parameter Fusion

To describe the impact of multiple environmental parameters on personnel in the fire scenario, we integrated and quantified the risk of several typical fire parameter indicators. According to the hazard of several typical fire environmental parameters to personnel [29,30], including the toxicity of combustible combustion products, the reduction in action ability caused by high temperatures and hypoxia in the fire environment, the fire environment is divided into four risk levels, namely, no risk, potential risk, medium risk, and high risk. In addition to the above fire factors, smoke visibility seriously affects the speed of personnel evacuation. This paper defines that when the area visibility reaches less than 3 m, the corresponding area risk level is level 4 with high risk, and constructs a fire risk level function, as shown in Formula (1):

$$Fs=\max \left\{ f \left(T\right), f \left(co\right), f \left(oxy\right), f \left(visi\right)\right\}$$

(1)

where f(T), f(co), f(oxy), and f(visi) are the risk levels of current temperature, carbon monoxide, oxygen concentration, and visibility, respectively.

Considering the level of human injury caused by fire risk factors in a relatively short period, the classification and attribute summary of fire risk are shown in

Table 1. Classification of fire hazard levels.

Degree of Danger	Temperature (℃)	CO Concentration (ppm)	Oxygen Concentration (%)	Visibility (m)	Risk Level (Fs)	Risk Value (r)	Area Access Sign
Safety	<42	<50	17~21	>3	1	0	Safe passage
potential danger	42~50	50~200	14~17		2	1/3	Accessible, affected by fire
danger, numbness	50~80	200~2000	11~14		3	2/3	Accessible, affected by fire
extreme danger, death	>80	>12,000	<11	<3	4	1	Inaccessibility/casualties

[1,31,32].

2.3. Path Risk Assessment Based on the Fusion of Multiple Environmental Parameters

When quantifying the fire environmental risk, it is necessary to consider the time-varying characteristics of multiple fire parameters. The time-varying temperature, toxic gas concentration, visibility, and other environmental parameter changes in each evacuation area in the building are quite different, so discrete risk assessment is required for each area [33]. Build a risk matrix. The matrix of the environmental parameters of the k-th level is shown in Equation (2). The level can be selected at the platform level, the human eye height of the station hall level, or other plane heights. Thus, the degree of injury to personnel during the entire evacuation process and the degree of danger at different locations of the station can be measured.

$$R_k(t)=\left[\begin{array}{cccc}{r}_{\mathrm{1,1}}(t)& r_{\mathrm{1,2}}(t)& \dots & r_{1,m}(t)\\ r_{\mathrm{2,1}}(t)& r_{\mathrm{2,2}}(t)& \dots & r_{2,m}(t)\\ ⋮& ⋮& \ddots & ⋮\\ r_{n,1}(t)& r_{n,2}(t)& \dots & r_{n,m}(t)\end{array}\right]$$

(2)

where suppose m_i,j,k (t) indicates whether the evacuation area of row i and column j of the kth floor is traversed by people at time t, which is recorded as follows:

$$m_{i,j.k}\left(t\right)=\left\{\begin{array}{c}\begin{array}{cc}0& Personnel bypass the area at time t\end{array}\\ \begin{array}{cc}1& Personnel cross the area at time t\end{array}\end{array}\right.$$

(3)

The risk Z of the total route from the start of evacuation (t = t₀) to the safe evacuation (t = t_k) is as follows:

$$Z={\sum }_{t=t_0}^{t_k}{\sum }_{i,j,k}{r}_{i,j.k}(t)\cdot m_{i,j.k}(t)$$

(4)

3. Improved A* Algorithm Path Planning Based on Dynamic Fire Risk

3.1. Path Updating Principle and Algorithm Optimization

As a path search method integrating a greedy strategy and heuristic function, the A* algorithm can reduce the search space and improve efficiency through the heuristic function, and can solve the shortest path satisfying constraints such as obstacle avoidance in the state space graph. However, the traditional A* algorithm only models for static environment, and does not consider the impact of dynamic disasters (such as fire spread) on path planning, resulting in significant deviation between planning results and actual emergency scenarios. Therefore, this paper proposes a dynamic improvement strategy: first, generate the initial path under the static environment, and then dynamically update the path based on the fire evolution information.

The process of fire evolution is discretized into state changes in a period, and dynamic fire risk information is introduced based on the advantages of the traditional static A* algorithm. The implementation steps of the algorithm include the following: (1) The discrete time segment is incorporated into the A * algorithm as a time factor to obtain a dynamic environment model. (2) For paths affected by fire risk, path nodes in high-risk areas are updated to the non-optimal node set in the state space to achieve the real-time risk avoidance behavior of personnel. (3) For other risk areas affected by fire, the algorithm introduces fire risk factors and the direction constraints of the initial route to achieve comprehensive consideration of environmental risk, the shortest path, and the pre-selected path direction when people choose the path.

Considering the contradiction between the computational complexity of the algorithm and the real-time information, an optimization method for the search efficiency of the algorithm is proposed including the following: (1) Heuristic improvement: use more accurate heuristic functions and add constraints to reduce the search space. (2) Dynamic update: only local re-planning is carried out for the path of the fire-affected area, and the static path calculation results are reused in combination with the cache mechanism to reduce repeated operations.

Differently from the limitation of the traditional A* algorithm to minimize the path length in the static map, this paper maps the continuous evacuation space into a state space through the discretization method, where each state corresponds to a position node in the risk matrix, and realizes the synchronous simulation of dynamic disaster scenarios and evacuation behavior through the time-varying state correlation mechanism. The algorithm supports rapid path updating driven by real-time fire data, and improves the search efficiency on the premise of ensuring path reliability through heuristic fusion of risk coefficient and direction constraint, which can meet the real-time requirements of fire evacuation simulation.

3.2. Path Search Rules Affected by Fire

In this paper, eight neighborhood traversal is used as the basic moving rule, and dynamic fire risk information is integrated to optimize the path search algorithm. When searching path nodes, first judge the risk status of the neighborhood grid, and then proceed to the next step of path decision that integrates multiple factors:

(1)

When there is no risk in the neighborhood (Figure 1a), search for the shortest path in the default eight neighborhood direction.

(2)

When some locations in the neighborhood are in the high-risk area, the grid location in the high-risk area is considered as an obstacle treatment, as shown in Figure 1b. The locations in P4, P6, and P7 directions are at high risk, and are not considered as the next optional path area; the residual neighborhood path selection comprehensively evaluates the risk value, distance, and direction constraints. Figure 1c is taken as the schematic diagram to illustrate the direction constraint. Take the connecting line of the current position and the initial exit as the reference direction (positive direction of y-axis in Figure 1c), and calculate the deviation angle Δ of each candidate path. The larger the included angle of deviation from the original path, the greater the constraint. The direction deviation angle can be integrated into the range of [0°, 180°] to unify the measurement when making angle comparisons.

(3)

When the neighborhood is full of high risk (Figure 1d), ignore the risk of the current layer and expand one layer of domain nodes outward as candidate nodes. As shown in Figure 1d, the grid locations of P10, P12, P14, P16, P18, P20, P22, and P24 are regarded as the current optional path nodes, and the current location node is recorded as the evacuation bottleneck node.

3.3. A* Algorithm Path Search Heuristic Function Optimization

The traditional A* algorithm uses the evaluation function to evaluate the shortest distance from the starting node to the target node, and selects the next node to be searched according to the evaluation value. By comprehensively considering the actual distance and the estimated distance, it maximizes the speed of finding the shortest path. The moving cost evaluation function from the starting point to the target point is shown in Formula (5):

$$f(n)=g(n)+h(n)$$

(5)

where n represents the current node position in the path search process, and g(n) represents the actual moving distance from the starting node position to the current node position. h(n) represents the estimated distance from the current node position to the target node position, that is, the heuristic function.

The A* algorithm is calculated by the Euclidean distance, as shown in Equations (6) and (7):

$$g(n)=g(f)+\sqrt{(x_n-x_f{)}^2+(y_n-y_f{)}^2}$$

(6)

$$h(n)=\sqrt{(x_g-x_n{)}^2+(y_g-y_n{)}^2}$$

(7)

where ($x_n$,$y_n$) is the position coordinate of the current node n; ($x_f$,$y_f$) is the position coordinate of the parent node f of the current node n; and ($x_g$, ${\mathrm{y}}_g$) is the location coordinate of the target node g. The cost from the current node position to the target node position is calculated by the Euclidean distance, which can meet the requirements of the shortest path, so that the A* algorithm can obtain the shortest path while reducing the number of search nodes.

To consider the dynamic fire environment, fire risk factors are introduced into the heuristic function of the traditional A* algorithm. Based on the dynamic fire risk information, path planning to avoid fire risk is realized. The optimized heuristic function $h^{\prime }(n)$ is shown in Formula (8):

$$h^{\prime }(n)=c\times r(t)d_{ij}$$

(8)

where $r(t)$ is the fire risk value at node j at the current time t, and $d_{ij}$ is the Euclidean distance from node i to j. C is the constraint of the search direction in the heuristic function h’(n), which can be expressed by Formula (9).

$$c=k_c\times (1-\mathit{cos}\theta )$$

(9)

where the angle deviating from the initial direction is θ = min(|Δ|, 360° − |Δ|), so that θ ∈ [0°, 180°], and k_c is the normal number, representing the constraint strength coefficient.

3.4. Local Path Updating Method Under Fire Risk

When the A* algorithm generates an initial path, there may be some nodes that are greatly affected by fire and are not suitable for use as evacuation paths. To solve this problem, the path and risk matrix are intersected, and the local path affected by the fire is updated and improved. Considering the calculation efficiency of the algorithm, the method of further optimization based on the generated path is adopted to evaluate and adjust only the path nodes in the path that are affected by the environment, and then screen the path nodes by increasing the fire impact and direction constraints, to improve the search efficiency and also be closer to the real situation of fire escape.

The implementation process is shown in Figure 2. In the figure, black is the obstacle area, the S node is the starting node, and the G node is the target node. The black solid line is the initial path, and the blue solid line is the optimized path. First, according to the static environmental conditions, connect S node and G node to generate the initial path, then overlay the real-time risk information, judge the risk degree at each grid location, further check whether there is a risk area on the initial path connection, and update the path of the risk area node. If there is no risk area affected by fire, then the connection between the S node and the G node is the final path.

If it exists, it is necessary to find the parent node P1 of the risk area node P2, re-select other neighborhood grid locations, find the P2’ node instead of the P2 node according to the movement rules and the optimized heuristic function, and adjust the subsequent path nodes to finally complete the optimization of the entire path. Due to the addition of constraints in the heuristic function, the updated path is close to the selected direction of the original path, and the new path can effectively avoid unnecessary fire risks.

3.5. Algorithm Steps

Step 1: Import the initial static map, perform initialization processing, set the personnel type, personnel starting point, and exit location, and complete the initial path planning under the static environment.

Step 2: Fire risk state matrix at superposition discretization time.

Step 3: For the path not affected by fire in the whole period, the output is the final path. For the path affected by fire, further analyze the fire-affected road sections on the path.

Step 4: For the path affected by the fire, first judge the degree of danger. The high-risk area is regarded as an obstacle. If no other (optional) path is found, return an error or alternative path (for example, cross the path with high-risk, and record that the path node is a trapped node and outputting the attribute information of the trapped personnel).

For areas with other risks, further analyze the adjacent nodes of the road section affected by the fire on the path, search the movement value of other optional nodes, and judge whether the movement cost is lower than that of the original path section (from xj to xk) in the travel direction.

Step 5: Calculate the cost and update the path: consider the distance cost between xj and the candidate node, the risk cost of the node, and the direction constraint of the initial exit. If the moving cost of the road segment is lower than that of the original path segment, the algorithm will replace the original path segment with the road segment and update the path. At the same time, due to the update of the path, the nodes for subsequent traversal need to be adjusted accordingly.

After the initial path planning algorithm based on A* algorithm, an algorithm for further updating the path is proposed, aiming to find a path that is more suitable for people’s choices under fire than the current path planning in a dynamically changing environment. The improved route is obtained by combining the results of dynamic fire risk and the constraint conditions of local directions. The implementation method of dynamic path planning is shown in Figure 3.

4. Algorithm Simulation Experiment

Taking a subway station platform fire as an example, the simulation platform uses an Intel i9 series 2.20 GHz processor with 32 GB of memory, and Python 3.8 is used as the simulation software platform.

4.1. Preparation of Simulation Parameters

• Evacuation scenario: Select the effective platform length L (113 m) and width W (11.8 m) of the subway station, with the location of the safe passage as the safety exit, and establish a grid map with an initial grid division size of 0.5 m × 0.5 m.
• Fire Information Modeling

This study employs PyroSim (Version 2024.1) fire dynamics simulation software to calculate smoke dispersion, temperature variations, and toxic gas concentration changes in complex environments. We simulate multiple potential fire scenarios for buildings and store the simulation results in a database. These results can serve for pre-fire safety assessments and, when combined with evacuation simulation outcomes, provide decision-making references for evacuation route guidance during fire incidents [34,35,36].

For the experimental case study, we selected a challenging fire scenario with a 7 MW fire source located on one side of the station platform, featuring extremely rapid fire growth. Following the two-phase fire development pattern (initial power increase followed by stabilization) specified in metro design fire scenarios, the simulation results reveal the fire progression process along with the spatial distribution and temporal evolution of temperature, gas composition, and visibility. Using the fire risk quantification method in Section 2.2, the obtained data are analyzed to reveal fire risk evolution. The fire spread process is transformed into fire risk changes on the map, providing data for evacuation path planning. High-risk, medium-risk, potential risk, and risk-free areas are visualized in red, orange, yellow, and no color. The fire risk evolution diagram is shown in Figure 4.

3.

Initial and Behavioral Attributes of Evacuees

Considering that the high temperatures, toxic gas concentration, and smoke visibility in fire environments can cause physiological and psychological stress to evacuees, significantly affecting their evacuation speed [35], Zuo et al. [37] introduced three effect functions, namely temperature effect function $R_1(T)$, visibility effect function $R_2(K_c)$, and carbon monoxide concentration effect function $R_3({\rho }_{co})$, to quantify the correlation between these factors and evacuation speed. The effective evacuation velocity under fire conditions $v_t$ is expressed as follows:

$$v_t=v_0\times R_1(T)\times R_2(K_c)\times R_3({\rho }_{co})$$

(10)

where $v_0$ represents the normal walking speed and $v_t$ denotes the equivalent evacuation speed under fire influence. This study adopts this model to calculate evacuation speeds during fires.

To better characterize evacuation behaviors, we account for population diversity by establishing initial occupant classifications and attributes. Following the SFPE Handbook of Fire Protection Engineering [38], we define three occupant types, namely adults, elderly, and children, with initial movement speeds of 1.5 m/s, 0.5 m/s, and 1.0 m/s, respectively. The total number of evacuees is set to 100, with each agent uniquely numbered. Visual representations use green, purple, and blue dots for adults, the elderly, and children, respectively, while the fire source is marked with a red rectangle.

4.2. Analysis of Algorithm Path Planning Results

To evaluate the effectiveness of our algorithm in dynamically planning evacuation routes in fire scenarios, we conducted evacuation simulations integrated with fire evolution processes. Figure 5 captures the real-time progression of fire spread and personnel evacuation. Our algorithm triggers path updates only in fire-affected areas. Evacuees unaffected by fire use the shortest path, while those in affected areas update their routes based on real-time fire risk. By balancing fire risk, distance, and initial direction, evacuees exhibit risk-avoidant behaviors, such as detouring high-risk zones and moving through low-risk areas. The evacuation was completed within 55 s.

4.3. Comparative Analysis of Evacuation Path Planning

We further selected the two personnel with the longest evacuation time in this scenario for path trajectory and evacuation behavior analysis, explained the planned paths of Agent32 and Agent40 affected by the fire, and used the evacuation time, evacuation path length, and risk value of personnel as key indicators to verify the effectiveness of this method through comparison with static shortest path planning. As shown in Figure 6, the difference in the evacuation path trajectories of personnel under the influence of fire and without considering the influence of fire is displayed. Based on not changing the initial direction of personnel travel as much as possible, the path trajectories of the two personnel under the method proposed in this paper avoid the fire risk based on the original evacuation direction.

We further analyzed the two selected personnel samples based on evacuation time, path length, and path risk, and compared them with the traditional algorithm of static shortest path to demonstrate the effectiveness of our method in fire evacuation scenarios. The comparison between the evacuation parameters of the selected personnel and the traditional A* algorithm is shown in Figure 7.

Due to the influence of risk avoidance detours, the evacuation routes of Agent32 and Agent40 have been extended compared to traditional static routes, and the evacuation time of both individuals has increased, but the risk of evacuation routes has significantly decreased. This demonstrates that the personnel evacuation path planning under the method proposed in this article can provide suggestions for emergency evacuation guidance strategies in the event of a fire, and the algorithm simulation results are also closer to the characteristics of real personnel fire emergency behavior.

5. Conclusions

Based on a discrete fire risk model and considering computational complexity as well as the need for dynamic path updating in evacuation planning, this study enhances the path search strategy and heuristic function of the A* algorithm. The improved algorithm integrates fire risk, distance, and directional constraints to create an evacuation path plan that ensures path continuity while effectively reducing fire risks along evacuation routes.

(i)

A dynamic fire-risk evaluation model was developed. The model quantifies threat levels in a discretized environment using key parameters—ambient temperature, visibility, and toxic gas concentration—benchmarked against human-safety thresholds. This framework enables continuous, real-time updates of node-specific risk values as conditions evolve.

(ii)

Building on the classic A* search, we introduced a multi-criteria heuristic that fuses spatial distance, fire-risk coefficients, and directional continuity constraints. This fusion enables the algorithm to more rapidly converge on viable evacuation routes that prioritize both safety and computational efficiency, particularly under rapidly changing fire scenarios.

(iii)

Evacuation paths are continually reevaluated: nodes exceeding a critical risk threshold are excluded from consideration, while remaining candidates are ranked by a composite score of proximity, current risk, and trajectory alignment. This adaptive re-routing scheme maintains route connectivity and dynamically steers evacuees away from emergent hazards.

(iv)

Simulation studies demonstrate that our improved approach substantially lowers the cumulative risk exposure along evacuation routes compared to traditional methods. Moreover, the algorithm’s modular design and low computational overhead make it suitable for real-time deployment in buildings of varying sizes and layouts.

Currently, the model assumes a two-dimensional floor plan and does not incorporate vertical transitions (e.g., stairwells, elevators) or crowd dynamics. Future efforts will integrate multi-level connectivity data and agent-based crowd behavior into a digital rehearsal platform—combining virtual simulations with live drills—to further validate and refine the evacuation strategy under realistic conditions.