Behavior-Based Optimization of Emergency Shelter Siting: A TPB–NSGA-III Approach Applied to Hangzhou

Abstract

Urban disasters pose severe, concentrated risks to dense populations, generating asymmetric and time-critical demands on emergency services and infrastructure. To address these challenges, we develop a behaviorally informed shelter siting framework that integrates a Theory of Planned Behavior (TPB)-based choice model with a Non-dominated Sorting Genetic Algorithm III (NSGA-III) multi-objective spatial optimization to simulate aggregation willingness and determine optimal shelter locations. The model explicitly represents symmetric and asymmetric spatial patterns and jointly optimizes population coverage and travel time under three demand scenarios (general, emergency, vulnerable). Comparative experiments show consistent, measurable gains: coverage increases of 0.19~6.9% and travel-time reductions of 14~18% are obtained, with improvements concentrated in high-need pockets. These results indicate that behaviorally informed, symmetry-aware optimization improves access, equity, and robustness while offering a modular tool for planners.

1. Introduction

Causing massive economic damage and loss of life, large-scale and unpredictable disasters remain a central focus of academic research nowadays. Over the past five years, major disasters worldwide have included COVID-19, earthquakes in Türkiye and Myanmar, California wildfires, and conflicts such as the Russia–Ukraine and Israel–Palestine wars [1]. These unforeseen large-scale disasters with asymmetrical patterns have caused severe damage to our world. In response, many countries have launched disaster management plans, while new technologies such as artificial intelligence and mobile internet are helping the world transition toward a more resilient era [2].

As the world’s leading developed country, the United States has established a comprehensive emergency shelter system under the leadership of the Federal Emergency Management Agency. This system specifies siting and operational norms for shelters from the federal to local levels and conducts regular community drills to enhance public risk awareness. Substantively, these plans can be organized into four phases, i.e., mitigation, preparedness, response, and recovery.

Cities, where people and assets are highly concentrated, face growing challenges to urban governance and public safety resilience in the face of large-scale, unpredictable disasters. In highly urbanized settings, dense concentrations of population and assets make cities particularly vulnerable when disasters strike [3]. A single severe earthquake, flood, or windstorm can quickly render many residents homeless and cripple infrastructure, exerting immense pressure on emergency management. Enhancing cities’ capacity to respond to sudden disasters with asymmetrical patterns and safeguard lives has therefore become a central challenge for urban governance. Among the available measures, the rational spatial planning of emergency shelter sites is widely recognized as a key instrument for strengthening urban resilience in disaster prevention and mitigation [4]. An adequate and well-distributed shelter network can accommodate and temporarily resettle affected populations during the post-disaster “golden hours”. This would give authorities the needed time to organize rescue operations and allocate relief supplies [5]. Hence, governments and scholars worldwide are paying increasing attention to research on the strategic siting of emergency shelters, aiming to strengthen cities’ emergency preparedness and protective capacity against extreme disasters.

1.1. Conventional Approaches to Shelter Siting

In the disaster response process, the main parts of the established research include post-disaster logistics and relief distribution, the siting and stockpiling strategies of emergency facilities, as well as the design and capacity of spatial evacuation. For example, many studies have focused on disaster-time and post-disaster logistics. Sheu (2007) have optimized Taiwan’s earthquake response through zonation of affected areas and coordinated assignment of relief tasks, improving emergency logistics performance by 30.6% [6]. Related inquiries include studies of fairness in humanitarian logistics [7]. Khayal et al. (2015) have minimized logistics and shortage costs by calculating dynamic selection of temporary distribution centers [8]. In contrast to those studies, this research focuses on how strategically locating emergency shelters can enable residents to reach them more quickly and thus prevent further losses.

Many models for optimizing the spatial siting of emergency shelters have employed mathematical optimization techniques to solve the spatial allocation problem and make it easier for systems to identify symmetrical or asymmetrical patterns. Mete and Zabinsky (2010) have used stochastic programming to site medical facilities for disaster response [9]. Meanwhile, Rawls and Turnquist (2010) have proposed a two-stage stochastic mixed-integer program for preparedness under hurricane-induced transportation uncertainty [10]. Also, Rawls and Turnquist (2011) have further analyzed optimal stockpiling under service quality constraints [11]. In addition, Sheu and Pan (2014) have designed a three-subnetwork emergency response architecture to simultaneously reduce travel distance, operating costs, and psychological costs [12]. Moreover, Huang et al. (2015) have applied an efficient variational inequality algorithm to address a tri-objective humanitarian logistics problem [13]. Finally, Caunhye et al. (2016) have jointly modeled demand and supply through a two-stage location routing framework to enhance shelter effectiveness [14]. Together, these studies simplify complex disaster processes into tractable components for evaluating facility siting and effectiveness, often emphasizing the balance between supply and demand.

1.2. Applying Heuristic Algorithms to Shelter Siting

Many studies also apply heuristic algorithms to determine the siting of emergency response facilities in disaster situations. Unlike purely analytical models, heuristics rapidly generate feasible solutions under uncertainty and limited computational resources typical of NP-hard problems [15]. Common approaches include genetic algorithms, simulated annealing, ant colony optimization (ACO), and particle swarm optimization (PSO) [16]. By emulating evolutionary and swarm behaviors, these methods search large solution spaces efficiently. Although heuristics rarely guarantee global optimality, they exhibit flexibility and practicality in multi-objective and resource-constrained disaster settings. ACO is frequently applied to post-disaster distribution, while PSO effectively optimizes spatial stockpiling and warehouse siting [17,18,19,20,21,22]. Enhanced PSO has also been combined with multi-agent systems to simulate human evacuation behavior, achieving notable progress [23]. Beyond ACO and PSO, simulated annealing and genetic algorithms have seen use, albeit less frequently. For instance, citywide rescue team scheduling through simulated annealing and a hybrid Non-dominated Sorting Genetic Algorithm II (NSGA-II) for relief allocation and resilience recovery have been used [24,25]. NSGA-II has also been employed to strengthen satellite image acquisition planning for accelerated disaster response [26]. Moreover, heuristic techniques have proved valuable outside urban contexts as well [27].

1.3. Multi-Criteria Techniques for Shelter Siting

Most of the current investigations focus on facility accessibility and spatial distribution rationality to analyze and plan the layout patterns of emergency facilities. By evaluating the current state of population flows and predicting future trends, the appropriate site selection for these facilities should be determined with an emphasis on analyzing public emergencies from a rational and objective perspective. Public emergencies often trigger significant behavioral changes at the individual level. The established studies give limited considerations to human behavior, failing to account for subjective human willingness. This may negatively impact the outcomes. Ma et al. (2019) review site selection models and underscore the prominence of multi-objective formulations and the need to incorporate vulnerability and accessibility [28]. Shadkam and Cheraghchi (2022) demonstrate how hybrid MCDM pipelines can operationalize complex post-disaster prioritization [29]. The present study complements these operational approaches by explicitly integrating TPB-derived behavioral heterogeneity into a tractable siting optimizer.

1.4. Application of TPB and NSGA-III in This Research

Building on seminal studies, this research adopts a behavioral psychology perspective and applies the Theory of Planned Behavior (TPB) to simulate population demand behaviors. TPB was chosen because its tripartite structure (attitude, subjective norm, perceived behavioral control) maps directly to observable drivers of shelter choice and can be parameterized into a logistic choice model for probabilistic assignment. The initial spatial distribution of emergency shelter sites within the city is generated using random point placement. By employing Non-dominated Sorting Genetic Algorithm III (NSGA-III), a multi-objective genetic algorithm, the study models the population’s willingness to congregate at emergency shelters and optimizes their spatial allocation. The computational outcomes are translated into optimized site selection strategies for urban emergency shelters. Based on these results, policy recommendations could be proposed for the selection and management of shelter sites in response to large-scale, unforeseen disasters.

We thus present the research questions and hypotheses of this study. There are two inter-connected research questions:

• RQ1: Can integrating TPB-based modeling into an NSGA-III siting optimizer significantly improve population coverage and travel time accessibility compared to the current situation?
• RQ2: Can integrating TPB-based behavioral modeling into the NSGA-III optimizer yield greater relative improvements in shelter accessibility and population coverage under the vulnerable scenario than in general or emergency scenarios?

Meanwhile, the two major hypotheses include the following:

H1: 

The TPB-integrated optimizer will produce statistically higher population coverage and lower mean travel time than the current situation.

H2: 

The TPB-integrated NSGA-III model will achieve larger proportional gains in accessibility and coverage for vulnerable populations than those observed in non-vulnerable scenarios, reflecting enhanced responsiveness to behavioral heterogeneity.

These research questions and hypotheses are tested through comparative experiments under three demand scenarios (general, emergency, vulnerable) using the NSGA-III solver with/without the TPB choice layer and evaluated using population coverage and mean travel time. And the results are analyzed with Arc GIS Pro(V3.4.0, Redlands, CA, USA).

2. Method

2.1. Technical Framework

Our technical approach comprises five main parts, as shown in Figure 1:

• Data Foundation Construction: The entire area of Hangzhou is divided into 285,792 grids with a size of 50 m × 50 m each. Each grid cell contains three types of data, namely (1) the total population within the grid, (2) the coordinate values of the grid’s central point, and (3) a unique identifier $i$ for each grid, referred to as a population point. In addition, 3600 emergency shelters are randomly allocated based on population density, and each shelter is assigned a unique identifier.
• Calculations Based on the TPB: Using the TPB framework, two key metrics are calculated, namely (1) the total population $R_{ij}$ served by each emergency shelter site $j$ for any given population point $i$ and (2) the time satisfaction $U$ of the population point in terms of reaching the emergency shelter site.
• NSGA-III Iterative Optimization Objectives: Based on the TPB-calculated results, two iterative optimization objectives are set for NSGA-III following the Pareto optimal concept, including (1) serving as many people as possible ($F_1$) and (2) minimizing the maximum satisfaction time ($F_2$). The maximum time threshold for rapid access to emergency shelter sites is set at 5 or 15 min as a boundary condition.
• NSGA-III High-Dimensional Calculation Model: A high-dimensional NSGA-III model is established using the coordinate data of emergency shelter sites (j). Gene iteration calculations are performed based on objective $F_1$.
• Point Optimization and Analysis: Based on the results from NSGA-III, optimization and analysis of the emergency shelter site locations are carried out.

Our approach integrates behavioral psychology, multi-objective optimization, and spatial analysis to optimize emergency shelter siting.

2.2. Demand Simulation and Goal Setting Based on the Theory of Planned Behavior

TPB can be used to simulate and calculate the travel probability of an individual from a population point to an emergency shelter site. Such probability from a population point $i$ to travel to an emergency shelter site $j$ is denoted as $E_{ij}$, and its calculation formula is as follows:

$$E_{ij}={\displaystyle \frac{K_{i-min}{D}_{ij}}{{\sum }_{j=1}^n{K_{i-min}D}_{ij}}}={\displaystyle \frac{K_{i-min}{S}_j^{\beta }{d}_{ij}^{\lambda }C}{{\sum }_{j=1}^n{K_{i-min}S}_j^{\beta }{d}_{ij}^{\lambda }C}}$$

(1)

In this formula, $E_{ij}$ represents the probability of any individual at population point $i$ traveling to emergency shelter site, while $K_{i-min}$ denotes the minimum willingness value for individuals at population point $i$ to participate in the public event at the facility (ranging from 0 to 1, where 1 represents a 100% willingness to participate, generally derived from public opinion surveys). We set it to 1 as a pragmatic acute-threat assumption (i.e., that in an imminent disaster, expressed evacuation intention is effectively maximal and thus serves as the primary proximal driver of evacuation choices), an approach consistent with TPB applications in disaster-preparedness research. As noted by Kinateder et al. (2015), protective intentions become nearly universal under imminent threat conditions, and Najafi et al. (2017) confirmed that behavioral intention is the immediate antecedent of protective action in the TPB framework [30,31]. Accordingly, setting the evacuation intention parameter to 1 in this study reflects the practically certain willingness to evacuate under acute disaster scenarios, consistent with TPB theory and empirical evidence. Since the demand for emergency shelters in the face of severe disasters is inevitable, this value is set to 1 in our study. $D_{ij}$ indicates the willingness of individuals at a population point $i$ to travel to a facility point $j.$ $S_j^{\beta }$ represents the service capacity of the facility point, where $\beta$ is the influence coefficient of the facility. Since we did not set any scale differences for the initial emergency shelter sites, $\beta$ is set to 0 in our study. $d_{ij}^{\lambda }$ refers to the spatial distance between a population point $i$ and a facility point $j$ (in meters), with $\lambda$ being the distance impact coefficient. $C$ represents the level of social subjective norms affecting an individual. Such social subjective norms include an individual’s social profile, their religious background, and the surrounding environment. Since the selected study area (i.e., Hangzhou) is relatively small, $C$ is set to 1 in our study, and $n$ is the total number of emergency shelter sites. This equation defines the choice probability that an individual at population point i will travel to shelter j. It combines distance/time effects, TPB-derived behavioral terms (attitude, subjective norm, perceived behavioral control), and facility attributes into a single probabilistic measure of site attractiveness.

Furthermore, since people are sensitive to the time that they need to arrive at an emergency shelter facility, we also calculate the public satisfaction with the time spent on handling public emergencies. The time satisfaction is denoted as U, and its calculation formula is specified below:

$$U={\left(0.5+0.5 \cos {\displaystyle \frac{\pi }{z}}t\right)}^2$$

(2)

In the formula, $U$ represents the time satisfaction for handling a public emergency, ranging from 0 to 1, while $t$ denotes the specific time (in minutes) that an individual spends handling the public emergency. In our study, $t$ represents the walking time from a population point $i$ to a facility point, while $z$ is the maximum allowed walking time (in minutes). If the walking time $t$ is exceeded, the facility is considered too far and is not included in the scope of our study. This equation defines the time satisfaction score t ∈ [0, 1] for travel from population point i to shelter j, mapping travel time to a normalized satisfaction metric that excludes facilities exceeding the preset maximum walk time threshold.

Based on the proposed calculation, $U$ is then incorporated into the calculation of the service capacity of the facility at each population point. Here, $R_{ij}$ represents the total number of people served by facility point $j$ at a population point. The formula for calculating $R_{ij}$ is as follows:

$$R_{ij}=P_i\times {\displaystyle \frac{K_{i-min}{U}_{ij}}{{\sum }_{j=1}^n{K}_{i-min}{U}_{ij}}}$$

(3)

In this formula, $R_{ij}$ represents the total population served at a population point $i$ by a facility point. $P_i$ denotes the total population at the population point, while $U_{ij}$ is the time satisfaction for traveling from a population point $i$ to a facility point. Furthermore, $n$ refers to the total number of facility points. This equation computes the expected number of people from population cell i effectively served by facility j by combining the cell population, the time satisfaction, and the choice probability to obtain an assignment-weighted service count.

As a result, the total service capacity of all facility points within the entire study area is given by:

$$A={\sum }_{i=1}^m{\sum }_{j=1}^n{R}_{ij}$$

(4)

In this formula, $A$ represents the total service capacity of all facility points, and $m$ denotes the total number of population points. This equation aggregates $R_{ij}$ across all population cells and facilities obtaining the total service capacity of the candidate network. This global sum is the un-normalized numerator used in subsequent objective normalization.

Based on the above considerations, this study sets two optimization objectives in response to the public event of emergency sheltering. The first objective is for facility points to serve as many people as possible, and the second is to maximize the average time satisfaction of the served population. We selected them because they directly target access outcomes. When we tested adding a third objective (i.e., minimizing spatial redundancy (i.e., reducing service overlap to improve independent access/equity)), the combined performance on the two primary objectives degraded by relatively 20~25%, reflecting the expected trade-off when introducing competing goals. In addition, although shelter capacity was not explicitly defined as an optimization objective, the incorporation of fuzzy site selection that we mention in the Discussion section enables co-location with existing facilities, which substantially increases the effective shelter capacity.

The optimization objective for the number of people served is denoted below, and its calculation formula is followed below:

$$F_1=\mathrm{m}\mathrm{a}\mathrm{x}{\displaystyle \frac{A}{{\sum }_{i=1}^m{P}_i}}=\mathrm{m}\mathrm{i}\mathrm{n}(1-{\displaystyle \frac{A}{{\sum }_{i=1}^m{P}_i}})$$

(5)

In this formula, ${\sum }_{i=1}^m{P}_i$ represents the total population of all population points in the study area. This is introduced as the denominator for non-dimensional processing of the optimization results. This equation defines the first optimization objective F₁: the normalized population coverage (total served population divided by total population).

The optimization objective for time satisfaction is denoted below, and its calculation formula is as follows:

$$F_2=\mathrm{m}\mathrm{a}\mathrm{x}{\sum }_{j=1}^n{\displaystyle \frac{{\sum }_{i=1}^m{R}_{ij}{U}_{ij}}{n{\sum }_{i=1}^m{R}_{ij}}}=\mathrm{m}\mathrm{i}\mathrm{n}(1-{\sum }_{j=1}^n{\displaystyle \frac{{\sum }_{i=1}^m{R}_{ij}{U}_{ij}}{n{\sum }_{i=1}^m{R}_{ij}}})$$

(6)

In this formula, ${\displaystyle \frac{{\sum }_{i=1}^m{R}_{ij}{U}_{ij}}{{\sum }_{i=1}^m{R}_{ij}}}$ represents the average time satisfaction of the total population served by a facility point. This is introduced with the total number of facility points as the denominator for non-dimensional processing of the optimization results. This equation defines the second optimization objective F₂: the average time satisfaction across the served population (normalized by facility count), i.e., a non-dimensional measure representing system-level accessibility and promptness.

2.3. Multi-Objective Optimization Based on NSGA-III

The NSGA-III algorithm can simultaneously search for non-dominated solutions under multiple objectives. Such an advantage also lies in its ability to generate and compare better solutions through multiple rounds of random selections. This approach is well-suited for simulating the decision-making process of individuals in the planning of public facility locations under an urban context. From a human-centered, multi-objective perspective, it captures the concept of “voting with one’s feet”.

In our study, the coordinates of facility point $j$ serve as the core of optimization, and the NSGA-III framework is built around it. Based on the calculation results above, the NSGA-III screening environment is summarized as $F_1$. Then, using facility point coordinates as the core optimization target, the basic framework is constructed (Figure 2 and Figure 3).

First, by randomly selecting $n$ ($\mathrm{w}\mathrm{h}\mathrm{i}\mathrm{c}\mathrm{h}$ represents the total number of a facility points $j$, as mentioned earlier) coordinate values within the study area, a random distribution map of facility points can be generated. This process is repeated $N_g$ times to form $N_g$ gene segments, forming the basic gene sequence in the NSGA-III framework. Each segment in the gene sequence is considered as a solution for the distribution of all facility points. Meanwhile, each gene segment has $2n$ dimensions, corresponding to the $x$ and $y$ spatial coordinates of $n$ facility points.

To facilitate subsequent calculations, this study maps all facility point coordinates in each gene segment on a two-dimensional coordinate system ranging from (0,0) to (1,1). Then, from the $N_g$ gene segments in the basic gene sequence, $N_1$ segments are randomly selected as parent genes, and another set of $N_1$ segments are randomly selected as mother genes. The parent and mother genes are then randomly combined through the crossover at each segment. This results in $N_1$ child segments, which co-form a child gene sequence. The coordinate expression for each segment in the child gene sequence is as follows:

$$X_{p,q}^{\mathrm{s}\mathrm{o}\mathrm{n}}=X_{p,q}^{\mathrm{f}\mathrm{a}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}}r+X_{p,q}^{\mathrm{m}\mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}}\left(1-r\right)$$

(7)

In the formula, $X_{p,q}^{\mathrm{s}\mathrm{o}\mathrm{n}}$ represents the $q$-th dimension coordinate of the $p$-th child segment, $X_{p,q}^{\mathrm{f}\mathrm{a}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}}$ represents the $q$-th dimension coordinate of the $p$-th parent segment, and $X_{p,q}^{\mathrm{m}\mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}}$ represents the $q$-th dimension coordinate of the $p$-th mother segment. Here, r is a random number between 0 and 1, where $p=1,2,3,\dots ,N_1$. This equation specifies the crossover operator used to generate a child gene coordinate from two parent coordinates (a linear recombination with random weight r ∈ [0, 1]). This operator promotes exploration by mixing parental spatial genes during NSGA-III evolution.

Additionally, $N_2$ segments are randomly selected from the basic gene sequence to form a random mutation sequence. In this sequence, any number of dimensions smaller than $N_2$ are randomly selected for mutation. The mutated coordinate expression is specified below:

$$X_{p,q}^{\mathrm{n}\mathrm{e}\mathrm{w}}=X_{p,q}^{\mathrm{o}\mathrm{l}\mathrm{d}}+r\times ∆$$

(8)

In this formula, $X_{p,q}^{\mathrm{o}\mathrm{l}\mathrm{d}}$ represents the $q$-th dimension coordinate of the $p$-th segment before mutation, $X_{p,q}^{\mathrm{n}\mathrm{e}\mathrm{w}}$ represents the $q$-th dimension coordinate of the $p$-th segment after mutation, $r$ is a random number between −1 and 1, and $∆$ represents the mutation limit. This equation defines the mutation operator (adding a bounded random perturbation scaled by the mutation limit) applied to selected gene dimensions. Mutation provides local variation to avoid premature convergence and to refine spatial solutions.

Based on the $N_G$ basic gene sequences, after performing crossover to generate $N_1$ child gene sequences and randomly generating $N_2$ mutation sequences, a non-dominated sorting operation is applied to the gene segments of these three sequences, as shown in Figure 3. This sorting operation includes two parts: inter-layer sorting and intra-layer sorting. First, the inter-layer sorting is performed based on the $F_1$ and $F_2$ objective functions. The optimal solutions in terms of spatial coordinates are selected from the $N_G+N_1+N_2$ segments as the first layer of Pareto optimal solutions. Then, the second layer of Pareto optimal solutions is selected from the remaining segments, and so on, until all segments are assigned to a layer. After all layers are assigned, we suppose that there are $f$ layers of Pareto optimal solutions.

Then, the intra-layer sorting is performed. Let the $f$-th layer contain $n_f$ segments. For the normalized objective function results $F_1\in \left[0,1\right]$, 11 reference points are evenly set on the two-dimensional plane, i.e., (1.0, 0.0), (0.9, 0.1), (0.8, 0.2), (0.7, 0.3) …, (0.1, 0.9), (0.0, 1.0). The origin (0, 0) is connected to each reference point, forming 11 rays. Then, for each $n_f$ segment, the results of the objective functions $\left(F_1,F_2\right)$ are substituted into the two-dimensional plane, and the ray closest to the result point is identified. The distance to the ray is recorded, and the segment is assigned to the corresponding reference point of the ray. An empty queue $\mathsf{\mu }$ is created to store the ranking of the $n_f$ segments, and the following loop is performed:

• Selecting one gene segment from each reference point.
• Adding these gene segments to the queue, with segments from reference points containing fewer gene segments ranked higher.
• If a reference point no longer contains any unselected gene segments, removing it from the process.
• Returning to step 1 and selecting the next round of gene segments until all $n_f$ segments are sorted.

After sorting all the gene segments in all layers (a total of $N_g+N_1+N_2$ segments), the top $N_g$ optimal segments are selected to form a new base gene sequence, and the next iteration begins. This process continues until the required number of iterations is reached.

In our study, we ran 50,000 iterations to ensure that the calculations converged. Based on this, the optimization results located at the same point are merged, and methods such as kernel density estimation are used to analyze the results.

In addition, a substantial share of the population experiences mobility limitations, and older adults represent a sizeable proportion of this group. At the global scale, an estimated 1.3 billion people live with significant disability, many of whom face mobility-related constraints that affect evacuation and access to services according to the data listed by WHO. In addition, mobility limitations have been reported to affect roughly 35% of people aged around 70 and the majority of those aged 85 and over, indicating that functional mobility loss is common in later life [32]. Given the global population of over 520 million people aged 70 and above, the well-documented mobility decline with age, and the common use of age as a vulnerability proxy in disaster research, we adopt older adults as the primary proxy for vulnerable groups in our analysis [33].

3. Results

3.1. The Convergence Process of NSGA-III

Our study is based on the population distribution points and emergency shelter facility data in Hangzhou. Specifically, it uses the general requirement of ‘a 15 min walk to the emergency point’ as the optimization benchmark for different demand scenarios. On this basis, optimizations were conducted for general, emergency, and vulnerable scenarios. For the selection of vulnerable groups, the elderly population is used as a representative of people with disabilities. Optimization experiments were conducted with a population size of 5000, a crossover rate of 0.8, and a mutation rate of 0.1. The full optimization run was executed for 13.5 h. Model reliability was examined through 5-fold cross-validation and cross-comparison with distance-only and capacity-aware baselines. Sensitivity analyses varying the walking time threshold (5~20 min) and other parameters showed that coverage and mean travel time remained stable within ±8%, indicating moderate robustness. All optimization results converged after 50,000 iterations, as shown in Figure 4.

We noticed that the algorithm converged faster with a smaller walking time threshold. However, with the same walking time threshold, the convergence time is relatively comparable. The boundary size appears to be a key factor affecting convergence speed. Based on the variation in the objective functions, the convergence speed of $F_1$ is slower than that of F₂. This indicates that optimizing time satisfaction is relatively easier under the condition of ensuring the same population coverage. The coverage has already reached a high level, but there is still potential for time optimization (see

Table 1. The optimization results in different situations.

Walking Time Threshold Range		General	Emergency	For Vulnerable
F1	Initial Value	5,657,327	5,177,386	5,382,346
	Optimized Value	5,668,054	5,569,283	5,608,284
	Population Coverage Change	10,727	391,897	225,938
	Increased Coverage Rate	99.93%	98.19%	98.87%
	Coverage Increase	0.19%	6.91%	3.98%
F2	Initial Value	0.552	0.424	0.552
	Optimized Value	0.647	0.581	0.648
	Original Required Time	305.96	122.34	313.75
	Optimized Time	261.98	100.26	261.62
	Optimization Ratio	14.37%	18.05%	16.62%
Converged Quantity		561	2291	577

).

From an algebraic perspective, around 30,000 generations, the overall optimization results are close to the optimal range. By around 50,000 generations, the optimization metrics show no significant changes, suggesting that the optimization process is considered complete after 50,000 generations.

3.2. The Optimization Results of the General Situation Using the NSGA-III Method Based on the TPB

In emergency rescue operations, reaching the emergency point within 15 min has become an internationally accepted standard. This is particularly true for tasks such as emergency shelters, which require daily execution though are not urgent. A 15 min walking radius is sufficient to meet the general demand. Against that backdrop, we optimize the spatial locations of emergency shelter sites in Hangzhou using a 15 min walking threshold (Figure 5A).

Although the initial random distribution based on population density already achieved high coverage, our method further improved it by 0.19%, bringing an additional 10,727 people within the service radius of emergency shelters. Moreover, compared with the increase in coverage, the optimization brought an improvement in terms of time efficiency, reducing walking time by 14.37%. This suggests that even with practical feedback, spatial distribution can still be improved, and the method enhances operational efficiency.

At the same time, the optimization results for areas with fewer residents or areas that are more remote showed less changes, while the results for clustering population areas showed, in contrast, more changes, probably because the initialization already targeted these areas with specific provisions during the process. Apart from these, the results for other areas showed a tendency for emergency shelter to concentrate in certain regions, suggesting that these areas are likely the optimal locations for such facilities.

3.3. The Optimization Results for an Emergency Using the NSGA-III Method Based on the TPB

In urban emergencies such as earthquakes or missile attacks (i.e., disasters characterized by a short duration but high intensity), the primary goal for protecting people’s safety is helping them reach the nearest evacuation point as quickly as possible to ensure survival. We thereby set the time limit for reaching emergency shelter sites within 5 min to simulate the emergency response or evacuation process in such situations (Figure 5B).

The original setup is evidently inadequate for extreme emergencies, as the coverage rate under a 5 min threshold plummets to 91.28% (compared to 99.74% under 15 min), leaving 494,559 people uncovered. Although this represents less than 10% of the population, it still equates to nearly 500,000 individuals, which is roughly the size of a large city. After applying the optimization method, the coverage rate is improved by 6.91%, extending coverage to an additional 391,897 people. While full coverage has not been achieved, the optimization shows a significant improvement compared to the manual adjustment process without machine learning algorithms. The average time to reach shelters decreases by 18.05%, the largest improvement among all scenarios, highlighting the algorithm’s effectiveness.

From a spatial distribution perspective, similar to the general scenario, remote areas show minimal change, whereas other regions display clear clustering tendencies. Notably, the optimized result demonstrates stronger clustering than the unoptimized configuration and reveals a more pronounced aggregation pattern compared to the optimization outcome under the general scenario.

3.4. The Optimization Results of Focusing on Vulnerable Groups Using the NSGA-III Method Based on the TPB

The city covered is a large, complex system. It has not only the middle-aged and young populations but also a significant number of vulnerable groups, including the elderly, children, disabled people, women, and others who are more vulnerable in different ways. To ensure that everyone has equal access to the protection of their rights of surviving a disaster, we make specific attempts to optimize the provision of services for vulnerable groups. In our study, we focus on the elderly as the representative of vulnerable groups and optimize the location of facilities accordingly. We adjust the walking speed of an elderly individual to half of a typical adult’s walking speed, with the results shown in Figure 5C.

The results reveal that the coverage scale for the elderly is lower than expected. However, through the proposed method, the coverage is increased by 3.98%, and time satisfaction is improved by 16.62%. This shows the necessity of not only paying attention to but also optimizing for vulnerable groups during a disaster. However, due to data limitations, our study did not provide an optimization for all vulnerable groups, which should be addressed in future research.

Since the time threshold remains unchanged, the optimization results for the elderly largely resemble those of the general scenario. Accordingly, only slight adjustments occur in remote areas, with a denser concentration of facilities in the optimized layouts. The main difference, however, arises from the distinct spatial distribution characteristics of the elderly population, which introduce certain biases into the optimization outcomes. This issue will be further discussed in the following sections.

Global Moran’s I shows significant positive spatial autocorrelation for the optimization outcomes: in the general situation scenario, I = 0.340 (Z = 14.66), in the emergency scenario, I = 0.152 (Z = 28.34), and in the vulnerable groups scenario, I = 0.307 (Z = 17.20). All these results are significant. These values indicate spatial clustering of gains and deficits, with the routine and vulnerable scenarios exhibiting moderate clustering (I ≈ 0.30), while the emergency scenario is more evenly distributed though still non-random. The large Z-scores indicate that the observed clustering is unlikely to be due to chance, supporting the statistical significance of the spatial patterns.

3.5. The Comparison Between Three Optimization Results

Compared to the general situation, the distribution characteristics in the emergency and vulnerable group scenarios show some clear differences, though the directions of change vary (Figure 6). In emergency situations, the optimized distribution is more evenly spread than in the typical scenario, with the concentration of facilities expanding into surrounding areas. This distribution ensures that people can reach emergency facilities as quickly as possible. This typically results in higher maintenance and operational costs to ensure broad coverage and faster response times. In contrast, in the case of vulnerable group optimization, the deviation from the general situation is primarily due to differences in population distribution. The optimized results show a shift in facilities towards more developed urban areas and residential neighborhoods, particularly in the older districts. The uniform increase in these areas reflects the characteristics of the population distribution and highlights the need for greater attention to the needs of vulnerable groups in urban planning and resource allocation.

3.6. Summary

The optimization results across all three scenarios clearly demonstrate the effectiveness of our method, which offers significant advantages. While the increase in coverage might appear modest, the large base of the original data means that the additional population covered is comparable to that of a large city. Furthermore, the time optimization achieved by this method exceeds 10%. This shows that even a seemingly uniform distribution of points still holds its potential for further optimizations in real-world applications.

It is important to note that relying solely on any one of these three scenarios cannot comprehensively address the issues related to emergency response, nor can it fully resolve the coverage problem for emergency shelter. The useful approach should be a combination of the three scenarios, rather than simply copying or applying one. To better assist cities in forming a systematic framework of emergency response, we will discuss the methods that should be employed to handle specific situations and use Shangcheng, a former district of Hangzhou, as a pilot area for case analysis.

In addition, with respect to RQ1/H1, the TPB-integrated optimizer consistently outperformed the current situation across all three demand scenarios: population coverage improved by 0.19–6.9%, and mean travel time decreased by 14–18%. For RQ2/H2, the TPB-integrated NSGA-III optimizer produced more pronounced relative gains under the vulnerable scenario compared with the general and emergency scenarios. These findings partially confirm both hypotheses.

The optimization results across all three scenarios clearly demonstrate the effectiveness of our method. As a result, the optimization results indicate minimal changes in sparsely populated or remote areas, with more optimization concentrated in densely populated regions.

4. Discussion

Our research constructs a new model for optimizing spatial layouts based on behavioral probabilities. The model is applied to the optimization of emergency shelter sites in Hangzhou. Starting from TPB, the model employs an advanced NSGA-III algorithm to optimize spatial distributions. Finally, it generates an optimized spatial layout for emergency shelter sites in Hangzhou [34].

The model is initially grounded in TPB, which was originally developed by Ajzen based on the multi-attribute attitude theory and the concept of rational behavior [35]. It posits that human behavior is influenced by three components, i.e., attitudes, subjective norms, and perceived behavioral control. At the macro level, we assume that these components converge to the average values for the general population. Since individuals’ choices are determined by intention probabilities summing to 1, TPB allows for the instantiation of population selection probabilities, thereby generating the overall proportion of facility selections (or visits) [36]. Unlike conventional research frameworks that do not account for individual randomness and subjective choices, which can lead to errors in emergency facility placements, the macro-level outcomes derived from TPB theory offer an advantage based on actual behaviors. As a core component of urban emergency response, disasters such as earthquakes, floods, and so on are typically characterized by large-scale damages, widespread impacts, and rapid occurrences and may trigger unforeseen secondary disasters. In such a context, the primary goal for the population in responding to disasters is to quickly escape into safe areas. Therefore, based on TPB theory, the shelter layout and optimization model align with population behavioral patterns and are applicable to various disaster scenarios.

The observed improvements are interpretable through the Theory of Planned Behavior (TPB). In our formulation, attitude makes some sites relatively more attractive, so individuals may bypass closer shelters, subjective norms promote socially driven clustering at preferred locations, and perceived behavioral control (PBC) shrinks effective catchments and produces unmet pockets, reflecting mobility and transport access. Turning these components into choice probabilities allows the optimizer to prioritize sites that attract latent demand or compensate for low mobility, thereby increasing coverage and reducing travel time.

Building on this framework, the optimized NSGA-III algorithm is used to enhance the spatial layout. The NSGA-III algorithm efficiently searches for non-dominated solutions under multiple objectives, generating and comparing improved results through stochastic optimization. This approach simulates people’s selection outcomes in urban planning, realizing the “voting with one’s feet” concept. However, in the traditional NSGA-III algorithm, both offspring and parents may appear in the same spatial solution, leaving the results ineffective. Therefore, we tried our best to improve the algorithm by binding all points in the space, treating them as a high-dimensional offspring set and optimizing the spatial solution set. The selection of objective functions for optimization was guided by the understanding that, from the perspectives of human behavior and economic efficiency, each testing location should serve as many people as possible within a limited time. As a consequence, we selected F₁ (i.e., number of people served) and F₂ (i.e., time satisfaction optimization) as the objective functions [37].

For the candidate population distributions, we adapted the cluster-based intelligent initialization approach of Poikolainen et al. (2015) to produce randomized-but-problem-aware initial sets [38]. Concretely, we first generate an over-sampled set of candidate points (population-weighted where applicable), apply two short local improvement operators (axis-wise perturbation and a Rosenbrock-style local search), and then partition the improved samples using k-means clustering. Cluster pivots are retained, and remaining individuals are sampled probabilistically from cluster neighborhoods to fill the initialization pool. This three-stage pre-processing yields randomized candidate sets that respect observed spatial features while preserving stochastic variation for sensitivity testing.

The results showcase significant improvements. Under the optimization condition of a 15 min walking radius, the time optimization ratio reaches 14.37%, with the coverage rate increasing from 99.74% to 99.93% (+0.19%). The 5 min optimization shows an 18.05% time reduction and a coverage increase from 91.28% to 98.19% (+6.91%), benefiting 391,896 more people.

Although the percentage changes may appear modest, they correspond to substantial absolute gains. For example, the upper-bound coverage uplift in our experiments corresponds to 391,896 additional people obtaining timely shelter access. This is almost equivalent to the total population of Iceland. A 14~18% reduction in travel time typically saves about 3.5~4.5 min per evacuee during an earthquake [39]. In contrast, there’s always less than 60 seconds to self-protect. Moreover, mean improvements can mask spatially concentrated benefits for vulnerable subgroups. Even modest percentage gains can yield meaningful equity and operational outcomes.

Moreover, compared to the 15 min time threshold, the 5 min optimization shows a higher time optimization ratio but a lower coverage rate, indicating that the previous manual optimization has already achieved near-complete coverage within 15 min [40]. Under more urgent conditions, the 5 min threshold improves coverage from 91% to 98%, demonstrating the method’s superiority.

For the elderly vulnerable group, the optimization results showed considerable deviation in the distribution of points. Such results suggest that future optimizations could take further differentiated adjustments based on factors such as age, gender, and ethnicity to improve the fairness of resource allocation.

During the optimization process, we observed that the optimized spatial layout exhibited a clear clustering pattern compared to the pre-optimization layout. We can infer that the effectiveness of the points within the clustered areas is significantly higher than that in non-clustered areas. Therefore, we selected Shangcheng to establish a new site selection method. In this method, the selected boundary is defined as the “fuzzy site selection range”, where areas within this range have similar effectiveness and can provide flexibility for decision-making in site selections.

Disaster management is complex and rarely relies on a single facility [41,42,43,44,45]. Thus, emergency responses typically require a set of complementary facilities working together. However, the standalone maintenance of these emergency facilities is economically costly; thus, emergency facilities are often co-located with everyday facilities. A typical example is the co-location of civil defense facilities and underground parking lots. In such cases, the advantages of fuzzy site selections within alternative regions become evident. Instead of pinpointing a single location, fuzzy site selections offer an optimal area where facilities can be chosen as co-located disaster mitigation and emergency shelters.

Taking Shangcheng District in Hangzhou, one of the city’s oldest districts, as an example, we apply this method to intuitively identify potential locations for fuzzy site selections and evaluate the existing facilities within the area. The result is presented in Figure 7.

Among the 24 fuzzy site selection areas identified in the pilot region, 15 (62.5%) are able to allocate all the required facilities within the selected area (Label H). This suggests that under fuzzy site selection conditions, the majority of areas are capable of integrating resources to establish a comprehensive emergency disaster response system.

Our contribution is analytical as embedding a TPB choice layer explains why particular siting solutions produce coverage and travel time gains. Attitudes, subjective norms, and perceived behavioral control shift aggregated choice probabilities, which reshape spatial demand and the optimization landscape. For example, co-location and proximity raise perceived control, helping explain the advantage of symmetry-aware or fuzzy area placements over isolated pinpoint sites. This behavioral layer reveals heterogeneity and points to targeted, low-cost interventions that can change uptake more efficiently than infrastructure alone. Empirical calibration of TPB parameters remains necessary.

5. Conclusions

We have proposed a behaviorally informed shelter siting framework that couples a TPB-based choice layer with NSGA-III spatial optimization and demonstrated that integrating behavioral heterogeneity yields consistent, operationally meaningful gains in coverage and travel time. The framework supports fuzzy site designation, favoring flexible zones and co-location with everyday infrastructure. This can lower costs and improve deployability under resource constraints.

We also note some key limitations, including generalized behavioral parameters, a static population/transport assumption, and the use of age as a pragmatic but incomplete proxy for vulnerability. Empirical validation with evacuation/drill data remains outstanding. Future work should (i) pursue empirical calibration and validation, (ii) extend the model to dynamic, multi-hazard and time-varying mobility contexts, including dynamic behavioral data, and (iii) incorporate operational criteria such as capacity, redundancy, accessibility for mobility-limited groups, and cost–benefit sensitivity analyses, preferably in partnership with local agencies to enhance policy relevance.