Research on Fire Evacuation in University Libraries Based on the Fuzzy Ant Colony Optimization Algorithm

Abstract

To study the impact of the psychological and behavioral characteristics of people, fire environment, and evacuation routes on fire evacuation efficiency, this study focuses on a university library as the research subject. A fuzzy logic algorithm is employed to analyze how psychological and behavioral traits influence initial evacuation speed during a fire. Also, fire data simulated using PyroSim software is integrated, with gas temperature, CO concentration, and visibility quantified through empirical formulas to adjust the reduction factor of evacuation speed, examining the effects of fire-generated products on evacuation performance. By incorporating fire environment factors into the heuristic function and refining pheromone update rules through iterative strategies, the ant colony algorithm is enhanced to achieve path planning. Results show that the psychological–environmental-route correction method improves evacuation efficiency by 16.2% compared to traditional methods without correction. This demonstrates that the proposed correction method can improve the efficiency of building fire evacuation and provides theoretical support and technical solutions for future library fire safety management.

1. Introduction

University libraries are characterized by multifunctionality, high occupancy, and various flammable items, which significantly increase the risk of fire incidents. Such spaces are prone to fire breakouts, which may lead to delayed rescue and evacuation, resulting in deaths, damage to collections, and property loss [1]. On 2 March 2003, Egypt’s famous Library of Alexandria suffered an electrical short-circuit fire, resulting in at least 35 injuries. Subsequently, on 17 December 2011, a case of arson at the Egyptian Scientific Research Institute Library caused 2 fatalities, multiple injuries, and the destruction of numerous books and archival documents. One of the most devastating incidents occurred on 30 January 2015, when an electrical malfunction triggered a catastrophic fire at the Library of the Russian Academy of Sciences. This event, often termed the “Chernobyl of Russian Science,” claimed the life of one firefighter, injured multiple personnel, and led to the irreversible loss of over 1 million volumes, including rare scientific works, historical archives, and ancient manuscripts. In recent years, the universities and many books as possible fuel sources have led to the frequent incidence of library fires at higher-education institutions. Therefore, seeking effective evacuation procedures in library fire is crucial for improving evacuation efficiency and keeping safety.

Currently, the human behavior modeling during evacuation is divided into: evacuation simulation models such as Building Exodus [2] and Pathfinder [3]; microsimulation models such as Agent-Based Modeling (ABM) [4,5], BP neural network models [6] and Cellular Automata [7]; and improved ant colony algorithm (IACO) [8], vehicle-augmented evacuation integer programming model [9] and other dynamic environmental planning models. Recent academic research has focused on the impact of environmental variables on evacuations. Numerical simulations using Pyrosim (https://www.thunderheadeng.com/pyrosim/, accessed on 1 July 2025) analyze variations in visibility, temperature, and toxic gas inside burning buildings, and Pathfinder simulates people’s evacuation to find out the minimal safe evacuation time, thereby formulating effective evacuation overall plans [10,11,12]. During real fire incidents, psychological reactions, including terror and avoidance behaviors, substantially influence evacuation results. Yan et al. [13] proposed that evacuation methods must include psychological characteristics and behavioral patterns, which may be clarified by evacuation exercises and comprehensive surveys. This study displays that people’s characteristics, cognitive capacities, and social influences cause significant differences in evacuation performance during fire emergencies. Kobes et al. [14] identified fire products, psychological emotions, and architectural layout as essential factors affecting evacuation, evaluating their influence on emergency reactions. Siyam et al. [15] used agent-based simulations of pedestrian evacuation, demonstrating that behavioral characteristics affected by gender and training substantially impact evacuation durations in fire scenarios. In summary, this research underscores two principles psychological and behavioral effects on fire evacuation: the influence of available safe evacuation time (ASET), and the psychological condition of evacuees affecting their responses. IACO’s building graph is a topological network, which lacks physical details such as road widths and corners, and iterative pheromone optimization in large-scale scenes is time consuming. While Pathfinder is a geometric-space-based shortest-path search, it ignores hazards in evacuation and is unable to respond in real time to threats such as the spread of fire. Considering the limits of both, this study will combine Pathfinder’s ability to handle complex spaces and crowd behavior with IACO’s ability to receive PyroSim fire data in real time to plan dynamically evacuation routes for different areas.

Empirical case investigations show the main cause of mortality in catastrophes is employees’ unfamiliarity with building layouts, which complicates identifying best exits and suitable evacuation routes [16,17]. Fire can cause fear among individuals, perhaps resulting in herd behavior or stampede accidents. Therefore, rapid decision making on evacuation routes and exit is crucial in emergency evacuations to minimize the danger of injury or death [18,19]. Thus, emergency path planning—calculating proper evacuation routes in real time according to current conditions—can direct individuals securely and effectively away from danger zones, reducing evacuation time and improving safety. Path optimization techniques are often divided into two categories: traditional algorithms, such as the simulated annealing algorithm [20,21], Dijkstra’s algorithm [22,23], and the A* algorithm [24], and bio-inspired intellect algorithms, including the whale optimization algorithm [25,26], the ant colony optimization algorithm [27,28,29], and artificial fish swarm algorithms [30,31].

Ant colony algorithms provide significant benefits over other techniques in addressing, discrete path planning challenges, owing to their scattered nature and adaptable abilities, making them effective for grid-based optimization and route planning. Wang et al. [32] improved ant colony optimization by using an integrated route optimization algorithm and a marine platform grid model to draw up path planning model for fire conditions. Zheng et al. [33] aimed to improve evacuation safety and efficiency during fire incidents by integrating elements associated with fire products into an improved heuristic function. They used a hybrid local and global pheromone update technique to change pheromone levels for fire path planning, while their model failed to include dynamic fire factors.

Researchers have studied the impact of psychological characteristics, behavioral, fire environment, and evacuation routes on fire evacuation; however, they have not performed a quantitative study of how psychological, behavioral, and environmental affect evacuation speed. The evacuation models mostly use shortest-path methods, ignoring the real effects of fire. This research presents a psychological–environmental-route optimization method for finding out the influence of evacuees’ psychological and behavioral traits, fire conditions, and evacuation routes on fire evacuation efficiency. The method incorporates library arrangements, evacuees’ psychological and behavioral traits, and variable fire factors. A fuzzy logic technique is used to quantify psychological and behavioral characteristics into initial evacuation speed. Using PyroSim software simulates fire situations to analyze real-time temperature, CO concentration, and visibility in various zones. The fire data are quantified using the formula method to change evacuation speeds properly. Further, by adding fire environment variables into the heuristic function and adjusting pheromone update rules in IACO, the approach optimizes evacuation routes among several influencing factors.

2. The Impact of Psychological Factors on Evacuation Speed

Psychological factors strongly affect evacuees’ speed and route choices during a fire. According to research on the psychological and behavioral characteristics of people in a fire, these are the main factors affecting the evacuation speed. Evacuation speed is not a constant variable, which is influenced by behavioral, psychological, and environmental factors. MATLAB 2021 version’s fuzzy logic algorithms quantify these to calculate modified initial evacuation speed.

2.1. Factors Affecting Evacuation Psychology

When a fire breaks out in a building, inadequate awareness of the situation and a shortage in emergency evacuation experience might provoke fear and avoidance behaviors among evacuees. These psychological reactions compromise judgment, obstruct quick route and exit selection, and can trigger “herd behavior” [34], resulting in crowding at evacuation locations, delays at exits, diminished egress efficiency, and delayed evacuation times. The main psychological factors affecting evacuation are encapsulated in

Table 1. Factors affecting the psychology of evacuation.

Factors	Concept
Frequency of training	Increasing the frequency of evacuation education and training for individuals enhances their confidence in evacuation knowledge and broadcast orders, reduces panic levels, and improves their ability to evacuate [35].
Risk perception	Risk perception has a substantial beneficial influence on evacuation behavior. As personnel’s risk perception increases, the evacuation characteristics become more evident [36].
Environmental familiarity	Enhanced environmental familiarity will reduce the spread of fear and promote crowd evacuation [37].
Panic level	Following a fire in a building, a lack of awareness of the fire circumstances and insufficient evacuation experience may easily arouse fear, which impairs judgment and results in the phenomena of crowd gathering and unthinkingly following others through the evacuation process [38].
Altruism psychology	It is a psychological tendency of evacuees to give assistance to those who need it during evacuation regardless of other factors, and helping behavior can improve the efficiency of evacuation to a certain extent [39].
Expected speed	The required evacuation speed of individuals may significantly change owing to differences in their physical health and psychological behavior [40].

.

2.2. Correction for Evacuation Speed

When people are subjected to outside information and are aware of the fire, people develop a negative psychology toward the situation, which affects their evacuation behavior and initial evacuation speed. The degree of influence depends on the degree of acceptance of the message “fire is happening” by the people, which is related to the awareness and social characteristics of the people [41]. To quantify the extent to which the “fire is happening” affects the initial speed of people, a mathematical correlation should be established between psychological information about people and the speed of evacuation.

The psychological and physiological characteristics of people under fire are abstract and complex, and it is difficult to quantify them directly into an accurate mathematical relationship with the evacuation speed, so this paper will quantify their effects through fuzzy logic. Fuzzy logic is a mathematical theory to deal with uncertainty and fuzziness, and its core idea is to extend the traditional binary logic to continuous affiliation through affiliation function. Applying the domain, fuzzy set, affiliation function and fuzzy rules for reasoning, and realizes fuzzy synthesis judgement by simulating the way of human thinking to solve the fuzzy rules which are difficult to be dealt with the conventional methods [42].

The TSK model [43] is a system modeling method based on fuzzy logic proposed by Japanese scholars Takagi, Sugeno and Kang. It expands the structure of the high-order Sugeno type fuzzy system by adding fuzzy rule antecedents and high-order polynomial consequents. Its core feature is that the antecedent part is represented by fuzzy logic, and the fuzzy rule consequent is fitted by adding fuzzy systems and linear functions. The output is a linear combination of the input, and the output is an exact value. The construction method of the 6th-order Sugeno fuzzy system is as follows:

Determine each input linguistic variable $x_i(i=1,\cdots ,6)$. Construct their fuzzy sets separately $A_j^{(k)}(j=1,\cdots ,6)$. By means of fuzzy rules, a nonlinear function of $f_k(x)$ the output quantity Z can be derived, where k is the number of rules, k = 1, …, M.

Its antecedent part is:

$${\mu }_i={\mu }_{A_1^i}(x_1)\times {\mu }_{A_2^i}(x_2)\times \cdots \times {\mu }_{A_n^i}(x_n)$$

(1)

The rear piece part is:

$$P^i={a_0}^i+\stackrel{n}{\sum _{k=1}}{{\displaystyle a}}_k^i{x}_k+\stackrel{n}{\sum _{k\le 1}}{{\displaystyle b}}_{kl}^i{x}_k{x}_l+\stackrel{n}{\sum _{k\le l\le m}}{{\displaystyle c}}_{klm}^i{x}_k{x}_l{x}_m+\dots$$

(2)

The weighted output of all rules is:

$$f(x)={\displaystyle \frac{{\sum }_{i=1}^M{\mu }_i\cdot f{(x)}^i}{{\sum }_{i=1}^M{\mu }_i}}$$

(3)

where $u_i$ is the number of paradigms and $A_j^{\mathrm{i}}$ is ${\mu }_{A_j^i}(x_j)$ the degree of affiliation.

A questionnaire survey was conducted to gather people’s information. The data were then summarized to identify the input factors, which involve frequency of training, risk perception, environmental familiarity, panic level, altruistic psychology, and expected speed. Evacuation speed was identified as the outcome variable. The Sugeno fuzzy system is used to calculate the workflow of the fuzzy system, as shown in Figure 1.

This research addressed a university and used a random sample approach to give out 300 questionnaires, resulting in 230 valid replies received. The returned questionnaire data were combed and statistically analyzed. The domains, sets of fuzzy variables and plurality of each input, and the results are shown in

Table 2. Summary of data for each input.

Factors	Domain (Math.)	Fuzzy Sets (Plurality)
Frequency of training	(0, 4)	Rarely (0), Ever (1.5), Often (3.5)
Risk perception	(0, 1)	Low (0.3), Medium (0.75), High (0.96)
Environmental familiarity	(0, 1)	Unfamiliar (0), Average (0.5), Very Familiar (0.95)
Panic level	(0, 1)	Low (0.05), Medium (0.5), High (1)
Altruism psychology	(0, 1)	Low (0.05), Medium (0.5), High (1)
Expected speed	(1, 4)	Low (1), Medium (2.5), High (4)

. The domain, fuzzy set and plurality of each input in Table 2 were combined with the literature [44] to plot the different input affiliation functions as shown in Figure 2.

In this paper, fuzzy rules are formulated based on the empirical literature [35,36,37,38,39,40] and current research on the psychological behavior of evacuating people, as shown in Figure 3. MATLAB 2021 version was used to establish the Sugeno fuzzy system, and we imported the above data for calculation, and obtained the fuzzy algorithm, as shown in Figure 4 and Figure 5. Red line indicates the position of the current input value on the input variable affiliation function. Yellow area indicates the activation strength of each rule based on the current input value that will be used to scale the rule rear’s affiliation function.

3. The Impact of Fire Environment Factors on Evacuation Speed

3.1. The Effect of Fire Products on Evacuation

A fire can produce an enormous emission of heat, smoke, and dangerous substances. Factors such as smoke temperature, visibility, and toxic gas concentration affect the psychological condition of evacuees—triggering panic and avoidance behaviors—and cause direct physiological damage, including poisoning and respiratory complications, which may consequently decrease evacuation efficiency.

Smoke temperature substantially influences evacuation speed. As the fire develops, rising temperatures may harm people’s respiratory systems, mouths, and skin, significantly hindering evacuees’ speed.

Visibility fall hinders evacuation efficiency by limiting the field of sight at the fire site because of the thick black smoke. This hinders individuals’ ability to maneuver through obstacles and precisely identify escape routes, so decreasing total evacuation efficacy.

Toxic gases such as carbon monoxide negatively hinder evacuation efficiency. Inhalation of dangerous quantities impairs physiological functioning, decreasing cognitive ability and muscle coordination, so hindering normal walking and substantially delaying evacuation.

3.2. Quantification of the Diminution in Evacuation Speed Due to Fire Products

Measuring the reduction variables related to smoke temperature, visibility, and CO concentration reflects their influence on evacuation speed. Fridor et al. [45] proposed computing distinct effect factors for smoke temperature, CO concentration, and visibility, then multiplying these factors to obtain a comprehensive speed reduction factor. In consideration of the abrupt occurrence of fires and the possibility of public panic, Qiu et al. [46] increased the human tolerance limits for smoke temperature and harmful chemicals by 40%. The critical temperature increased from 120 °C to 168 °C, while the dangerous concentration of poisonous gasses rose from 0.25% ($2.5\times {10}^{-5} {\mathrm{kg}/\mathrm{m}}^3$) to 0.35% ($3.5\times {10}^{-5} {\mathrm{kg}/\mathrm{m}}^3$). These adjustments are suitable for actual circumstances, and the updated formula is as follows.

$$v=v_0\cdot f_1(K_c)f_2(\rho )f_3(T)$$

(4)

$$\delta =f_1(K)f_2(\rho )f_3(T)$$

(5)

$$f_1(K_c)=\min (1,\max (0.2,1-0.324\times (3-K)))$$

(6)

$$f_2(\rho )=\left\{\begin{array}{c}1\\ 1-(0.2125+1.788\rho )\rho t\\ 0\end{array}\right.\hspace{1em}\begin{array}{c}\rho <0.1\%\\ 0.1\%\le \rho \le 0.35\\ \rho >0.35\%\end{array}\%$$

(7)

$$\begin{array}{l}{f}_3(T)=\left\{\begin{array}{cc}1& (T_0<T_s<T_{cr1})\\ {\displaystyle \frac{(v_{\max }-1.2){\left(\left.\frac{T_s-T_{cr1}}{T_{cr2}-T_{cr1}}\right)\right.}^2}{v_0}}+1& (T_{cr1}<T_s<T_{cr2})\\ {\displaystyle \frac{v_{\max }}{1.2}}\left. [1-\left({\left.{\displaystyle \frac{T_s-T_{cr2}}{T_{dead}-T_{cr2}}}\right)}^2\right.\right]& (T_{cr2}<T_s<T_{dead})\end{array}\right.\end{array}$$

(8)

where $\delta$ is velocity impairment; $K_c$ is the extinction coefficient, ${\mathrm{m}}^{-1}$; $\rho$ is the volumetric concentration of CO, %; $f_1(K_c)$ is the influence coefficient of visibility; $f_2(\rho )$ is influence coefficient of gas CO; $f_3(T)$ is the influence coefficient of temperature; $t$ is the exposure time (s); $v$ is current speed, m/s; $v_0$ is normal walking speed (set as 1.0 m/s); $v_{\max }$ is the maximum walking speed (set as 4.0 m/s); $T_s$ is temperature at the fire scene (°C); $T_{cr1}$ is temperature causing a discomfort (set as 30 °C); $T_{cr2}$ is temperature causing an injury (set as 60 °C); $T_{dead}$ is death temperature (set as 168 °C).

4. Path Optimization Based on ACO

4.1. Fundamentals of ACO

Ant Colony Optimization (ACO) is a bionic optimization algorithm that simulates the foraging behavior of ant colonies in nature, and its core idea is to simulate the ants to find the shortest path in the process of searching for food through the positive feedback mechanism of pheromones [47].

The ant’s choice of the next node conforms to the state transfer rule, $P_{\mathrm{ij}}^k$ denotes the transfer probability of ant k moving from node i to node j as.

$$\begin{array}{l}{P}_{ij}^k\left(t\right)=\left\{\begin{array}{l}{\displaystyle \frac{{[{\tau }_{ij}\left(t\right)]}^{\alpha }\cdot {[{\eta }_{ij}\left(t\right)]}^{\beta }}{{\displaystyle \sum _{s\in allowe{d}_i}{\left. [{\tau }_{ij}\left(t\right)\right]}^{\alpha }\cdot {[{\eta }_{ij}\left(t\right)]}^{\beta }}}},j\in allowe{d}_i\\ 0,j\notin allowe{d}_i\end{array}\right.\\ {\eta }_{ij}\left(t\right)={\displaystyle \frac{1}{d_{ij}\left(t\right)}}\end{array}$$

(9)

where ${\tau }_{ij}(t)$ is the pheromone concentration on the path between node i and j; ${\eta }_{ij}$ is degree of expectation of ants from node i to j; $\alpha$ is the pheromone heuristic factor; $\beta$ is the expected heuristic factor; $d_{ij}$ is the distance between points i and j.

The pheromone update rule is given in the following equation:

$$\left\{\begin{array}{l}{\tau }_{ij}\left(t+1\right)=\left(1-\rho \right)\cdot {\tau }_{ij}\left(t\right)+\Delta {\tau }_{ij}\\ \Delta {\tau }_{ij}={\displaystyle \sum _{k=1}^n\Delta {\tau }_{ij}^k}\end{array}\right.,0<\rho <1$$

(10)

$$\Delta {\tau }_{ij}(t,t+n)=\left\{\begin{array}{l}{\displaystyle \frac{Q}{L_k}}\\ 0\end{array}\right.$$

(11)

where $\rho$ is the pheromone volatilization factor; $Q$ is pheromone constant; $L_k$ is the total length of the path traveled by ant k; $L_{ij}$ is the total length of the path from node i to j.

4.2. Improvement of ACO

4.2.1. Improvement of the Heuristic Function

In the conventional Ant Colony Optimization (ACO), the heuristic function is often represented as the inverse of the distance between node i and j. During a fire incident, byproducts of combustion and the surrounding environment interact, resulting in a disturbance that can lead to a local optimum for the colony. To address this limitation, this paper incorporates coefficients reflecting the impact of carbon monoxide concentration, smoke temperature, and visibility on evacuation. These coefficients enhance the heuristic function and facilitate the dynamic path search in fire scenarios. To assess the impact of visibility, toxic gas, and smoke temperature on evacuation, the visibility influence function $f_1\left(K_c\right)$, the CO volume fraction influence function $f_2\left(\rho \right)$, and the smoke temperature influence function $f_3(T)$ are incorporated into the heuristic function to establish the quantification formula for their effects on human evacuation.

$$E_{ij}=f_1\left(K_c\right)\cdot f_2\left(\rho \right)\cdot f_3(T)$$

(12)

For the evacuation problem of people under fire scenario, the shortest route does not represent the ideal option, as the effective path length accounts for the impact of fire-related hazards on the evacuation process:

$$L_{ij}=d_{ij}\cdot E_{ij}$$

(13)

Hence, the improved heuristic function formula:

$${\eta }_{ij}={\epsilon }_1{\displaystyle \frac{E_{ij}}{d_{ij}}}$$

(14)

where ${\epsilon }_1$ is the correction factor.

4.2.2. Enhancement of the Pheromone Update Method

The conventional pheromone update model has shortcomings since it ignores the impact of psychological variables, such as Personnel retrograde and herd mentality, on the evacuation process. This study aims to enhance pheromone updating approach and develop a pheromone updating model that better aligns with crowd evacuation, as defined in Formula (15).

$$\begin{array}{l}{\tau }_{ij}\left(t+\Delta t\right)=\left(1-\rho \right){\tau }_{ij}\left(t\right)+\Delta {\tau }_{ij}\left(t\right)\\ \rho \left(t+1\right)=\left\{\begin{array}{l}0.9\rho \left(t\right),\rho \left(t\right)>{\rho }_{\min }\\ {\rho }_{\min },else\end{array}\right.\\ \Delta {\tau }_{ij}\left(t\right)={\displaystyle \sum _1^{\mathrm{m}}\Delta {\tau }_{ij}^k\left(t\right)}\\ \Delta {\tau }_{ij}^k\left(t\right)=\left\{\begin{array}{l}\lambda \cdot {\displaystyle \frac{L_{N-\max }-L_k}{L_{N-\max }}}\cdot {\displaystyle \frac{Q}{L_k}}\\ 0,\hspace{1em}\mathrm{else}\end{array}\right.,ant \mathrm{k} passes through(\mathbf{i},\mathrm{j})\end{array}$$

(15)

where $L_{N-\max }$ is the maximum value of the path travelled by all ants during each iteration; $\lambda$ is the adjustment factor.

4.3. Simulation Experiments and Analysis

In IACO, the calculation results depend on the number of ants M, the pheromone heuristic factor $\alpha$, the expected heuristic factor $\beta$, the pheromone volatilization factor $\rho$, and the pheromone intensity Q. However, currently, there is no strict theoretical basis for setting these algorithm parameters, nor a universal method for determining the optimal parameter combination [48]. The most common approach involves obtaining statistical data through software simulations to identify the optimal configuration. This study employs MATLAB 2021 to construct a 50 × 50 grid graph. Using a single exit as a case study, simulation calculations are performed to determine the optimal parameter set. In the figure, the black areas represent obstacles, as shown in Figure 6.

To minimize the number of simulation experiments, setting the parameter values according to the existing literature and methodology, the initial parameters are assigned to $(\alpha = 0.5, \beta = 1, \rho = 0.4, Q = 1, M = 50)$, and through the control variable method, only one parameter value is changed at a time while other parameters are kept constant [49]. For each group of parameters, 10 times values of simulation are performed to take the average value to obtain the optimal result.

(1)

Combination of $\alpha$ and $\beta$

Taking $\alpha \in \{0.5, 1, 2, 4, 6, 8\}$ and $\beta \in \{1, 3, 5, 7, 9\}$, different combinations of $\alpha$ and $\beta$ are simulated. To prevent the occurrence of chance, each group and parameter combination is simulated 10 times, the average value is taken for a total of 300 simulations to obtain the optimal result [50]. Further simulation results of different combinations of $\alpha$ and $\beta$ are shown in

Table 3. Different $\alpha$ and $\beta$ simulation results of parameter combinations.

Parameter Value	Average Length
	$\mathit{\beta }=1$	$\mathit{\beta }=3$	$\mathit{\beta }=5$	$\mathit{\beta }=7$	$\mathit{\beta }=9$
$\alpha =0.5$	28.50	25.82	24.67	24.42	24.13
$\alpha =1$	27.10	24.93	23.96	24.09	23.91
$\alpha =2$	24.49	24.20	23.64	24.09	23.92
$\alpha =4$	25.90	24.31	24.57	24.45	24.28
$\alpha =6$	25.25	24.40	24.76	24.37	24.64
$\alpha =8$	27.10	24.97	24.50	24.66	24.66

.

(2)

Combination of $\rho , Q, M$

Through the above simulation experiments, the optimal values of $\alpha$ and $\beta$ are determined. In this experiment, the fixed values of $\alpha =2$ and $\beta = 5$ are used. Taking $\rho \in \{0.4, 0.5, \mathrm{s}0.6\}$, $\mathrm{Q}\in \{1, 50, 100, 150\}$, $M\in \{50, 100, 150\}$. Numerical simulations are carried out using different combinations of $\rho$, $Q$, and $M$, each combination is simulated for 10 times to take the average value, and a total of 360 simulations are performed. The simulation results are shown in

Table 4. Simulation results for different combinations of $\rho$, $Q$, and $M$.

Parameter Value	Average Length
$\mathit{\rho }$	Q	M = 50	M = 100	M = 150
0.4	1	24.06	23.59	23.65
	50	24.36	24.01	23.45
	100	24.61	23.97	23.95
	150	24.87	24.26	23.72
0.5	1	24.14	23.98	23.55
	50	24.72	24.23	24.12
	100	24.26	24.25	24.02
	150	24.21	23.78	24.03
0.6	1	24.17	23.89	23.51
	50	24.91	24.01	24.03
	100	24.84	23.87	23.66
	150	24.56	24.64	23.96

.

Determine the parameter combination as $\alpha =2, \beta =5, \rho =0.4, Q=50, M=150$, The optimal evacuation paths and exits for different regions are selected by comparing the simulation results of ACO and IACO. The evacuation path diagram is shown in Figure 7. The colored lines are evacuation routes, the red areas indicate fire zones and The blue signs usually represent critical nodes. The simulation results are shown in

Table 5. Algorithm data comparison.

Starting Point	Exit	Distance for ACO	Number of Iterations for ACO	Distance for IACO	Number of Iterations for IACO
A	1	17.99	21.49	17.99	21.49
	2	31.11	35.14	30.71	35.38
B	1	23.05	27.31	22.99	26.49
	2	25.18	28.73	24.51	28.14
C	1	95.52	50.03	92.29	47.5
	2	43.45	39.7	40.14	36.42
E	1	62.79	52.78	57.72	47.63
	2	64.69	51.56	64.45	48.53

and Figure 8, Figure 9, Figure 10 and Figure 11. By selecting the optimal path length and the minimum number of iterations, it is known that Exit 1 is selected for evacuation in areas A, B, E and Exit 2 is selected for evacuation in area C.

5. Practical Cases

5.1. Building Information

This research uses a university library as a case study. The building consists of four levels, measuring 82 m in length, 67.8 m in breadth, and 18.1 m in height, covering a footprint of 3690 square meters. The main building is divided into parts for faculty offices, book storage, reading zones, and study rooms. A 1:1 scale digital model was constructed in Revit. And importing the IFC format file is imported from Revit into PyroSim 2019. The room temperature is established at 20 °C. After many scenario experiments, the fire point is arranged on the first floor, which has a greater impact on evacuating the crowd. After fieldwork, a part of the doors and windows are opened in the software of fire simulation, and the fire materials are wooden bookshelves and books, the green icons are monitoring devices, as shown in Figure 12. The heat release rate was designated as 6 MW; the fire type was categorized as fast fire. The fire growth coefficient was 0.044 ${\mathrm{kw}/\mathrm{s}}^2$, the fire source reached a steady state after 369.27 s, fire duration set to 600 s. Base cells of dimensions 0.5 × 0.5 × 0.5 m are designed, creating a grid of 164 × 135 × 40 cells, amounting to a total of 885,600 base elements. Wall surfaces were represented as gypsum, the flooring as ceramic tiles, and the study desks and chairs as yellow pine. Monitoring devices were positioned at a height of 2 m to capture environmental information. The ignition point was situated on the first level, with detecting sites positioned around stairs and hallways. Based on the fire model set up, simulations can be performed to obtain data and pictures of visibility, temperature, and CO concentration at various monitoring sites; (1) is the pictures of visibility, (2) is the pictures of temperature, and (3) is the pictures of CO concentration as illustrated in Figure 13.

5.2. Personnel Initial Evacuation Speed Correction

Using the fuzzy algorithm of Figure 4 and Figure 5, the average values of each influencing factor in

Table 6. Mean values of each influencing factor.

	Frequency of Training	Risk Perception	Environmental Familiarity	Panic Level	Altruism Psychology	Expected Speed (m/s)	Initial Evacuation Speed
Man	2	0.87	0.37	0.44	0.67	2.9	1.2
Woman	2	0.85	0.36	0.58	0.68	3.0	1.12

is brought into the calculation to obtain the initial evacuation speed of 1.2 m/s for men and 1.12 m/s for women.

5.3. Derogation of the Speed of Evacuation

The consequences of building fires—specifically smoke temperature, visibility, and CO concentration—are critical determinants of evacuation times and deaths since they may markedly impede evacuation pace. The reduction factor δ for evacuation speed can be computed at different time intervals and locations using smoke data and relevant methodologies. During the first periods of a fire, visibility is comparatively high; smoke density is minimal; and temperatures have not significantly increased, leading to an insignificant effect on evacuation efficiency. Physiological and psychological impacts on individuals start when smoke temperature surpasses 60 °C, CO concentration attains 0.1% ($1\times {10}^{-5} {\mathrm{kg}/\mathrm{m}}^3$), and vision diminishes under 3 m. At 168 °C, carbon monoxide concentration attains 0.35% ($3.5\times {10}^{-5} {\mathrm{kg}/\mathrm{m}}^3$), and visibility of less than 0.6 m, resulting in a lethal hazard. Figure 13 illustrates that areas E and F remain unharmed under these settings. The speed reduction factors for each zone are listed in

Table 7. Speed reduction by district.

Area\Time(s)	60	120	180	240	300	360	420	480
A	1	1	1	1	1	1	1	0.83
B	1	1	1	1	1.02	1.14	1.24	0.93
C	1	1	1	1	1	1	1	1
D	1	0.79	0.3	0.4	0.66	0.62	0.57	0.54
E	1	1	1	1	1	1	1	1
F	1	1	1	1	1	1	1	1
1st floor stairs	1	1	1.32	2.97	1.48	0.67	0.34	0.02
2nd floor stairs	1	1.02	1.09	1.05	0.98	0.31	0.16	0.02
3rd floor stairs	1	1	1	0.58	0.55	0.66	0.62	0.64
4th floor stairs	1	1	0.88	0.44	0.55	0.65	0.61	0.62

.

5.4. Comparison of Results from Personnel Evacuation Simulation Analysis

Importing the IFC format file of the Revit architectural model into Pathfinder, define parameters for occupant evacuation scenarios, and create a simulation model involving individual dispersion, as shown in Figure 14. According to standard library occupancy statistics, the total number of evacuees across all levels is 930 individuals, with evacuation conditions specified in

Table 8. Evacuee parameters.

Type of Personnel	Height/m	Shoulder Width/m	1st Floor/Person	2nd Floor/Person	3rd Floor/Person	4th Floor/Person
Middle-aged men	1.667	0.433	4	3	4	2
Middle-aged women	1.560	0.405	6	5	3	4
Young men	1.686	0.427	105	133	114	73
Young women	1.580	0.391	115	127	126	87

. The library’s fire alarm system includes an infrared detector that normally activates a fire alarm signal within 30 s, with a maximum delay of one minute [51]. Observational data reveal that the library’s patrons are mostly young students, typically attentive, with a reaction time of 30 s. The evacuation beginning time is calculated to be 90 s.

This study selects the first to fourth floors of the library as the research subjects for evacuation simulation, using Pathfinder 2019 version to model evacuation behavior. The baseline evacuation speed is set between 0.76 and 1.27 m/s [52], with evacuation paths distributed uniformly according to the Steering. Building upon this base, this study incorporates a psychological–environmental-path correction method to account for physiological and psychological factors, as well as the effects of fire products.

Three adjustments are implemented: First, the initial evacuation speed is adjusted using a fuzzy logic algorithm. Second, the reduction in evacuation speed caused by fire products in each zone at specific time points is calculated via a formula, and the evacuation speeds are corrected accordingly to reflect realistic escape conditions. Third, IACO algorithm is employed to optimize and revise evacuation routes.

To confirm the possibility of the proposed optimization scheme, three comparative scenarios are established:

Scenario 1: The normal evacuation method, with individual speeds ranging from 0.76 to 1.27 m/s, and evacuation paths uniformly distributed using the Steering mode in Pathfinder.

Scenario 2: The ACO path correction method, with individual speeds ranging from 0.76 to 1.27 m/s. Evacuation routes are designated that populations in zones A, B, E, and F evacuate through Exit 1, while those in zones C and D evacuate through Exit 2.

Scenario 3: The psychological–environmental-path correction method, with initial speeds set at 1.2 m/s for men and 1.12 m/s for women. The speed reduction values because of fire products are detailed in Table 7. Evacuation routes are designated that populations in zones A, B, E, and F evacuate through Exit 1, while those in zones C and D evacuate through Exit 2.

As shown by

Table 9. Comparison of data from the three programs.

Scenario	Total Evacuation Time\s	Anyone Trapped	Evacuation Efficiency (Curve Slope)	100–220 s (Curve Slope)	100–300 s (Curve Slope)
1	426	no	High in the first half of slope	−4.947 ± 0.032	−1.948 ± 0.022
2	313.3	no	Always high	−5.222 ± 0.032	−3.688 ± 0.030
3	356.8	no	High in the second half of slope	−4.430 ± 0.027	−3.200 ± 0.289

and Figure 15, the total evacuation time for Scenario 1 under normal evacuation conditions is 426 s. Since the emergency, the psychological characteristics of personnel in a fire scene were not considered, the evacuation efficiency in the early phase was rather high. However, without path optimization, personnel congestion occurred at evacuation exits, leading to blockages that reduced overall evacuation efficiency in the latter phase. The evacuation time of Scenario 2, the ACO path correction method, is 313.3 s. The evacuation efficiency (curve slope) of Scenario 2 is the same as that of Scenario 1 in (100–125 s), and its (curve slope) is higher than that of Scenario 1 after 125 s, because it uses ACO for route planning. In Scenario 3, after carrying out the psychological–environmental-path correction, the evacuation time was reduced to 356.8 s, which is 69.2 s shorter than the evacuation time of Scenario 1, and 43.5 s more than Scenario 2. Because Scenario 3 takes into the reduction in speed caused by psychological panic and the fire environment. Although the path is optimized, the actual speed decreases, leading to a slightly longer total time. The evacuation efficiency (curve slope) during the 100–220 s interval was lower than that of Scenario 1 and Scenario 2, attributable to the influence of fire produce and negative psychological factors. Nevertheless, the effective IACO path optimization avoids congestion at the exits, and the evacuation efficiency surpasses that of Scenario 1 after 220 s.

Figure 16 shows Pathfinder evacuation density for three scenarios, where the color gradient indicates the density size (red represents the high-density area). The results show that Scenario 1 has obvious single-exit congestion, and all the evacuees are concentrated in one stairway, so the evacuation is slowing down and the evacuation efficiency (curve slope) becomes smaller, while Scenario 2 and Scenario 3 both achieve double-exit diversion, and the crowd distribution is more balanced, so their evacuation efficiency (curve slope) is larger. At t = 200 s, Scenarios 1, 2 and 3 have evacuated the evacuation of 484, 518 and 450 people, respectively. Scenario 3 has a relatively lower evacuation rate in the early stage due to the impact of fire products, but after path optimization by IACO, its evacuation numbers surpassed those of Scenario 1.

In summary, Scenario 1 and Scenario 2 show significant deviations when simulating personnel behavior. Conversely, the psychological–environmental-path correction method comprehensively accounts for evacuation challenges in fire scenarios by exploring the influence of the complex psychological, behavioral characteristics, and fire products on the people’s evacuation. It adjusts evacuation speed and employs IACO to optimize evacuation routes. Through broadcast-guided regional evacuation, this approach more accurately reflects real-world conditions.

6. Conclusions and Outlook

The psychological–environmental-path adjustment method corrects the evacuation rate by quantifying the effects of personnel behavioral characteristics, psychological characteristics, and fire products on personal speed, and optimizes the evacuation path using the improved ant colony algorithm. Using the fuzzy algorithm and formula method for quantification, and IACO to optimize the evacuation path, the research results show that the method can improve the evacuation efficiency and avoid causing casualties.

The fuzzy algorithm can determine the initial evacuation speed based on factors such as gender, frequency of training, risk perception ability, environmental familiarity, panic level, altruistic psychology, and expected speed.

The formula method is used to quantify the reduction in fire products to the personal evacuation speed, which is corrected to be more in line with the actual situation under the fire.

The evacuation model is established by using ACO. IACO considers the influence of fire environment on personal evacuation, path length and other factors to restore the real scene of fire evacuation as much as possible. The path planning of IACO is better than the routes of Pathfinder. IACO can simulate the paths of the crowds in different areas, and evacuates in different regions to avoid the pile-up of people and improve the use rate of the exits.

This study is intended as a simulation template, which can serve as a foundation for future empirical or experimental research, but has not yet been validated with real-world data. Subsequently, the simulation model will be continuously optimized by comparing the simulation data with the data of real evacuation scenarios, to be closer to the actual situation in the field. In the future, we will investigate the effect of other fuzzy-based ACO or hybrid evacuation models on the evacuation efficiency in the hybrid evacuation model, and further improve the evacuation model.