A GIS‑Based Multi‑Objective Optimization Strategy for Urban Automated External Defibrillator Deployment

A GIS‑Based Multi‑Objective Optimization Strategy for Urban Automated External Defibrillator Deployment | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article A GIS‑Based Multi‑Objective Optimization Strategy for Urban Automated External Defibrillator Deployment Jia Wang, Jingyi Zhou, Shaohua Wang, Min Zhang, Jie Shen, Tianhao Zhao, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8600130/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 10 You are reading this latest preprint version Abstract Background Out-of-hospital cardiac arrest (OHCA) remains a critical urban health challenge due to persistently low survival rates and uneven access to automated external defibrillators (AEDs). Existing deployment strategies often rely on heuristic decisions, limiting their ability to address spatial disparities in emergency response. This study aims to develop a spatially informed, data-driven framework to optimize AED placement and improve urban emergency response capacity. Methods Using Qinhuai District in Nanjing as a case study, we applied Geodetector to identify the spatial determinants of OHCA risk. High-risk population density and its interaction with resident density emerged as dominant factors, informing the construction of a high-resolution AED Demand Index for candidate site selection. We then formulated a multi-objective optimization model to balance service coverage, perceived accessibility, and cost-effectiveness. The model was solved using an enhanced NSGA-II algorithm incorporating tabu search and 2-opt mutation. Results The optimized layouts demonstrated substantial improvements over existing AED configurations. The maximum service distance decreased by 55.3%, and overall satisfaction reached a near-optimal level of 0.997. The enhanced algorithm also achieved notable computational gains compared with standard approaches. Conclusions The proposed GIS-based optimization framework provides a scalable and evidence-based tool for improving AED deployment in dense urban environments. By integrating spatial risk detection with multi-objective optimization, this approach supports urban planners in reducing spatial inequities and strengthening emergency response systems. Automated External Defibrillators (AEDs) spatial accessibility Geodetector multi-objective optimization NSGA-II emergency response planning health equity Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 1. Introduction Out‑of‑hospital cardiac arrest (OHCA) is a major global public health challenge and a leading cause of premature mortality. Defined as the abrupt cessation of cardiac mechanical activity, OHCA often occurs without warning, and without immediate intervention, irreversible brain injury or death can occur within minutes. Globally, millions of OHCA cases occur annually, yet survival‑to‑discharge rates in most countries remain below 10% despite advances in emergency medical services (EMS) and resuscitation science [ 1 ]. In resource-limited countries, the chain of survival for OHCA faces significant barriers. Public awareness and training in cardiopulmonary resuscitation (CPR) remain low, often hindered by cultural norms and legal concerns, resulting in minimal bystander intervention. EMS are frequently underdeveloped, with delayed response times or, in some regions, no formal system at all [ 2 ]. In China, the situation is equally concerning. The Report on Cardiovascular Health and Diseases in China 2023 indicates a continuous rise in cardiovascular disease prevalence, with coronary heart disease mortality increasing steadily since 2012 [ 3 ]. In China, the OHCA treated by emergency medical services is approximately 97.1 per 100,000 population. Although public awareness of CPR has improved, the survival-to-discharge rate remains critically low at 1.2%, with bystander CPR performed in only 17% of cases [ 4 ]. These figures highlight persistent gaps in emergency response infrastructure, public training, and post-resuscitation care. Nationwide registry data from the BASIC‑OHCA study, covering 32 monitoring sites and approximately 9% of the Chinese population, further estimate over one million OHCA cases annually, with 76.85% occurring at home, a mean patient age of 65.8 years, and survival‑to‑discharge of only 1.15% [ 5 , 6 ]. In contrast, countries with mature public‑access defibrillation systems, such as Japan and the United States, report bystander CPR rates exceeding 40% and survival rates above 8–10% for shockable rhythms[ 7 , 8 ], underscoring a substantial performance gap. To address these spatial disparities in OHCA outcomes, it is essential to examine the deployment and accessibility of life-saving interventions such as Automated External Defibrillators (AEDs). Despite the proven life‑saving value of AEDs, their deployment in Chinese cities faces systemic challenges. National policy frameworks for AED allocation were introduced relatively late and financial constraints—including the costs of equipment procurement, routine maintenance, and public training—have hindered comprehensive implementation [ 9 , 10 ]. On a per‑capita basis, AED density in mainland China remains far below that of developed countries: fewer than 100 units per 100,000 population nationally, compared with approximately 700 units in the Netherlands, 550 units in Japan, and 300 units in the United States [ 11 ]. Spatially, large Chinese cities often exhibit a “dense‑in‑central‑areas, sparse‑in‑peripheries” clustered distribution pattern, leaving high‑OHCA‑risk peripheral areas underserved. For example, a spatial analysis of Nanjing’s central districts found that the average observed nearest‑neighbor distance between AEDs was 195.99 m—significantly shorter than the expected random distance of 258.47 m—indicating clustering in central zones but potential service blind spots in outlying areas [ 12 ]. Moreover, many current deployment strategies rely on heuristic placement strategies—such as prioritizing transportation hubs or commercial complexes—rather than data‑driven spatial correlation analyses between OHCA incidence and influencing factors (e.g., population density, EMS accessibility), limiting both the rationality and equity of AED placement [ 13 ]. Building on this analytical framework, AED deployment can be formulated as a multi-objective spatial optimization problem, enabling data-driven strategies that better align with clinical and operational needs. AED deployment can be modeled as a multi-objective spatial optimization problem, with the ultimate goal of meeting public rescue needs in the event of cardiac arrest. In an urban context, the analysis process typically consists of three stages: candidate area selection, multi‑objective optimization model construction, and model solution. Traditional multi‑objective optimization approaches often assign weights to each objective function and combine them into a single aggregated objective. However, weight selection can significantly affect results, limiting generalizability and practical applicability [ 14 ]. The Genetic Algorithm (GA) [ 15 ], with its strong global search capability and adaptability, has been widely applied in optimization problems and can effectively address these limitations. As multi-objective optimization tasks become increasingly prevalent, researchers have developed evolutionary algorithms to address trade-offs among competing objectives. Notable examples include the Multi-Objective Genetic Algorithm (MOGA) and the Non‑Dominated Sorting Genetic Algorithm (NSGA) [ 16 ]. Among them, the NSGA‑II algorithm [ 17 ] enhances convergence and solution diversity through fast non‑dominated sorting and crowding‑distance calculation. While NSGA‑II performs well for problems with two or three objectives, its efficiency declines in high‑dimensional objective spaces. To overcome this, the NSGA‑III algorithm was proposed. By introducing a reference‑point mechanism, NSGA‑III can generate a uniformly distributed Pareto‑optimal solution set in high‑dimensional spaces, demonstrating superior performance in complex, real‑world multi‑objective optimization scenarios [ 18 ]. To validate the proposed framework, a case study was conducted in Qinhuai District of Nanjing. In this study, Qinhuai District of Nanjing was selected as the case area. Standard deviational ellipse and other spatial analytical techniques were employed to examine existing issues in the spatial allocation of AEDs. Based on a systematic review and synthesis of relevant AED policy guidelines, the key influencing factors for urban AED deployment were identified and quantitatively defined. The Geodetector method was then applied to determine the weights of these factors, enabling the calculation of an AED urban spatial allocation demand index. Subsequently, a time-loss function was incorporated into a location–allocation framework to quantify the objective function of the AED deployment model. Constraints were formulated in accordance with the OHCA chain of survival to ensure clinical and operational relevance, resulting in the construction of a multi-objective AED allocation model. Accordingly, we propose an improved NSGA-II algorithm that integrates a tabu-list-based evolutionary mechanism to enhance solution diversity, improve local search, and prevent premature convergence. Based on this approach, the optimized AED deployment scheme was obtained. This research offers both theoretical contributions and actionable strategies for improving AED deployment in urban environments. 2. Data and Methods 2.1. Study Area This study focuses on Qinhuai District, located in Nanjing, Jiangsu Province, China. Geographically, Nanjing spans 31.23°–32.62°N, 118.37°–119.23°E, situated in the southwestern part of Jiangsu. Qinhuai lies at the core of Nanjing’s urban area and serves as the city’s political, economic, cultural, and historical center (Fig. 1 ). Qinhuai has a high population density, with approximately 800,000 permanent residents and a substantial floating population. The district is characterized by intense human activity, including frequent commercial, cultural, and tourism events, which contribute to elevated public health risks and increased demand for emergency response services. Rapid urbanization has driven significant economic growth, positioning Qinhuai as one of the city’s most economically active regions. Its infrastructure includes multiple metro lines, wide road coverage, and a dense network of public facilities such as hospitals, schools, shopping centers, and cultural venues. According to local registry data, Qinhuai reports approximately 380 cases of OHCA annually, with a majority occurring in residential and commercial zones. As shown in Fig. 1 , OHCA incidents are spatially concentrated in densely populated urban blocks, particularly near transportation hubs, commercial centers, and residential clusters. These patterns reflect elevated public health risks and highlight the urgency of improving emergency response capabilities. In response to this demand, an increasing number of public places have installed AEDs. Although Qinhuai hosts a high concentration of medical institutions, traffic congestion and spatial heterogeneity in facility distribution pose challenges to timely emergency access. Scientifically optimizing AED deployment to improve response efficiency has become a pressing public safety concern, and Qinhuai—characterized by its strategic location, population density, economic vitality, and robust public infrastructure—offers substantial potential for such research. 2.2. Data The datasets used in this study were obtained from a diverse range of institutions and platforms, encompassing spatial, demographic, and transportation-related information essential for optimizing emergency medical services. A summary of dataset formats and sources is provided in Table 1 . The specific datasets are described below. (1) OHCA Data OHCA records were obtained from the Jiangsu Provincial Health Development Research Center. Each record includes the geographic coordinates, timestamp, and age of the individual involved, covering incidents that occurred within Nanjing. (2) AED Data AED deployment data were also provided by the same institution. This dataset contains the locations of all installed AEDs across the city, reflecting the current spatial coverage and distribution of emergency defibrillation resources. (3) Road Network Data Road network data were sourced from OpenStreetMap (OSM), covering Nanjing and its surrounding areas. The dataset includes geometric attributes (e.g., road length, connectivity) and classification types (e.g., highways, arterial roads, secondary roads), which were used to evaluate road density and accessibility. (4) Public Facility Data Point-of-interest (POI) data for public facilities were retrieved from the Gaode (Amap) Developer Platform. This dataset includes major urban amenities such as transportation hubs (e.g., metro stations, bus stops, railway stations), public buildings (e.g., schools, hospitals, shopping centers), and recreational venues (e.g., cinemas, museums). (5) Population Data Population estimates were obtained from the WorldPop project, which integrates remote sensing and statistical modeling to produce high-resolution global population rasters. For this study, 100 m-resolution data for different age groups in Nanjing were used to assess population exposure and vulnerability. (6) GDP Data Gross Domestic Product (GDP) data were acquired from the Resource and Environment Science Data Platform. These data reflect the economic development level of each region and serve as an important reference for assessing AED deployment needs and prioritization. To enable spatial analysis, the study area was divided into 200 m × 200 m grid cells. Population-related factors—including resident and susceptible population densities—were calculated as population-to-area ratios. Road network density was computed as the total road length per unit area, while medical accessibility was evaluated using an origin–destination (OD) cost matrix [ 19 ]. Kernel density analysis was applied to public places, with service radii assigned according to facility type (e.g., 1000 m for metro stations) [ 20 ]. GDP values were normalized to a [0, 1] range to ensure comparability and integration into the analytical model. Table 1 Description of datasets used in the study, including format and source. Data Name Time Format Data Source Historical OHCA Incident Data 2023 .xlsx Jiangsu Institute of Health Development AED Device Data in Nanjing 2024 .xlsx Jiangsu Institute of Health Development Population Data 2020 .tif WorldPop website Road Network Data 2023 .shp OpenStreetMap website Public Facility Data 2023 .shp Amap Open Platform GDP Data 2023 .xlsx Resource and Environment Science Data Platform 2.3. Methods Based on a multi-objective optimization framework, this study conducts research on the optimal allocation of urban AEDs (Fig. 2 ). Firstly, it establishes an empirical foundation by integrating multi-dimensional data such as OHCA records and urban infrastructure indicators. Secondly, it applies techniques including Geodetector and demand index modeling to quantify spatial heterogeneity and identify high-priority AED deployment areas. Subsequently, a multi-objective optimization model is constructed, with objective functions and constraints designed to "maximize service satisfaction and coverage while minimizing treatment costs". Finally, the improved NSGA-II algorithm is used for model solution, generating diverse and high-quality deployment schemes to effectively resolve the complex trade-off issues in AED allocation. 2.3.1. Analysis of AED Influencing Factors and Candidate Areas (1) Factor Selection and Quantification Based on a comprehensive review of national and municipal guidelines, as well as relevant literature, four primary categories of influencing factors were identified. These categories reflect the spatial characteristics of Qinhuai District and the current AED distribution pattern, and include: population-related factors (A), transportation-related factors (B), public facility-related factors (C), and economic factors (D). A total of 13 variables were selected across these four categories to represent the key drivers of AED deployment demand (Table 2 ). Population factors reflect potential demand intensity, including the resident population density (RPD) and the susceptible population density (SPD), which refers to individuals aged 55–80 who are most vulnerable to OHCA according to epidemiological studies. Traffic factors represent accessibility constraints, where Road network density (RND) measures total road length per unit area, with higher values indicating better access. Public venue factors capture spatial clustering of high‑footfall locations (e.g., transportation hubs, sports facilities, schools, shopping malls, cultural venues, offices, accommodations) that increase the likelihood of public cardiac arrest events. The service radii of these facilities were determined according to their functional characteristics (Table 3 ), which served as the basis for subsequent spatial analysis. Economic factors (GDP per unit area) serve as a proxy for urban development level, which may influence both AED deployment capacity and public activity patterns. Positive factors (where higher values indicate greater AED demand potential) were normalized using Eq. (1), and negative factors (where lower values indicate better conditions, e.g., shorter travel time to hospitals) were normalized using Eq. (2): $$\:\begin{array}{c}{X}_{norm}=\frac{\left(X-\:{X}_{min}\right)}{\left({X}_{max}-\:{X}_{\text{m}\text{i}\text{n}}\right)}\:\#\left(1\right)\end{array}$$ $$\:\begin{array}{c}{X}_{norm}=\frac{\left({X}_{max}-\:X\right)}{\left({X}_{max}-{X}_{\text{m}\text{i}\text{n}}\right)}\#\left(2\right)\end{array}$$ where \(\:X\) is the original value, \(\:{X}_{norm}\) is the normalized value, and \(\:\frac{{X}_{max}}{{X}_{min}}\) are the minimum/maximum values of the factor, respectively. All spatial datasets were projected to a common coordinate system (CGCS2000) and resampled to a 200 m resolution to ensure spatial alignment before normalization. Table 2 AED allocation influencing factors and their quantification. Category Factor Code Quantification Method Population Resident population density \(\:{a}_{1}\) People per km² (WorldPop data) High-risk population (55–80y) density \(\:{a}_{2}\) People per km² (WorldPop data) Traffic Road network density \(\:{b}_{1}\) Total road length per km² (OSM data) Medical facility accessibility \(\:{b}_{2}\) Average travel time to nearest hospital (min) Public Venues Transportation hub density \(\:{c}_{1}\) Kernel density (stations, airports) Sports facility density \(\:{c}_{2}\) Kernel density (gyms, stadiums) Elderly care facility density \(\:{c}_{3}\) Kernel density (nursing homes) School density \(\:{c}_{4}\) Kernel density (primary/secondary schools) Shopping mall density \(\:{c}_{5}\) Kernel density (shopping centers) Cultural venue density \(\:{c}_{6}\) Kernel density (museums, theaters) Office density \(\:{c}_{7}\) Kernel density (office buildings) Accommodation density \(\:{c}_{8}\) Kernel density (hotels, resorts) Economic GDP per unit area \(\:{d}_{1}\) GDP per km² (resource and environmental platform) Note: Eq. (1) applies to positive factors ( \(\:{\text{a}}_{2}\) , \(\:{\text{a}}_{2}\) , \(\:{\text{b}}_{1}\) , \(\:{\text{c}}_{1}\) – \(\:{\text{c}}_{8}\) , \(\:{\text{d}}_{1}\) ); Eq. (2) applies only to negative factor \(\:{\text{b}}_{2}\) (medical accessibility, lower values indicate better access). Table 3 Public venues, typical subcategories, and their service radius. Major category Typical subcategories Service radius (m) Transportation hubs Ports, airports, railway/high-speed rail stations, metro stations, passenger terminals, bus stops, cruise terminals 500–5000 Sports and fitness venues Stadiums, ball game facilities, gyms, and swimming pools 500–1000 Elderly care institutions Nursing homes, elder care centers, senior activity centers 500–1000 Schools Universities, high schools, middle schools, primary schools, and kindergartens 300–1000 Large shopping centers Metropolitan shopping centers, general malls 500–1000 Cultural and recreational venues Exhibition halls, museums, art galleries, libraries, theaters, concert halls, religious sites, bookstores 300–1000 Office facilities Office buildings, commercial buildings, construction sites 500 Public accommodations Hotels, hostels, apartments, resorts 300–2000 (2) Geodetector Analysis In practical applications, independent variables must be categorical. Continuous variables require discretization, as different discretization methods and interval counts can significantly influence the q -value. Therefore, for each factor, the discretization scheme that maximized its q -value was selected. Based on this principle, the Geodetector was employed to examine the relationship between the spatial distribution of historical OHCA events in Qinhuai District, Nanjing, and a set of discretized explanatory variables. The explanatory power of each factor was quantified by its q -value, calculated as follows Eq. (3): $$\:\begin{array}{c}q=1-\frac{{\sum\:}_{h=1}^{L}{N}_{h}{\sigma\:}_{h}^{2}}{N{\sigma\:}^{2}}\#\left(3\right)\end{array}$$ where \(\:\text{N}\) is the total number of grid cells, \(\:{{\sigma\:}}^{2}\:\) is the overall variance of OHCA incidence, \(\:\text{L}\) is the number of strata, \(\:{\text{N}}_{\text{h}}\) is the number of cells in stratum \(\:\text{h}\) , and \(\:{\sigma\:}{\text{ₕ}}^{2}\) is the within-stratum variance. The q -value ranges from 0 to 1, with higher values indicating stronger explanatory power. Factor stratification was performed using the Jenks natural breaks method to minimize within-class variance and maximize between-class variance, consistent with prior spatial heterogeneity studies. To assess the combined effects of two factors, the interaction detector was applied. This method evaluates whether the interaction between environmental factors \(\:{X}_{1}\) and \(\:{\text{X}}_{2}\) enhances or weakens their explanatory power by comparing the interaction q -value, \(\:q\left({X}_{1}\cap\:{X}_{2}\right),\) with the individual q -values \(\:\:q\left({X}_{1}\right)\:\) and \(\:q\left({X}_{2}\right)\:\) [21]. To evaluate the combined effects of two environmental factors, the interaction detector was applied. This method compares the interaction q -value, \(\:q\left({X}_{1}\cap\:{X}_{2}\right),\) with the individual q -values \(\:\:q\left({X}_{1}\right)\) and \(\:q\left({X}_{2}\right)\) to determine whether their joint influence enhances or weakens explanatory power. Interaction types were classified according to the criteria in Table 4 : Table 4 Criteria for determining interaction types. q -value Interaction types \(\:{q(X}_{1}\cap\:{X}_{2})\:<\:\text{m}\text{i}\text{n}\:[{q(X}_{1}),\:q\left({X}_{2}\right)\) ] Nonlinear weakening min [ \(\:{q(X}_{1})\) , \(\:q\left({X}_{2}\right)\) ] \(\:{<q(X}_{1}\cap\:{X}_{2})\:\:\text{m}\text{a}\text{x}\:[{q(X}_{1}),\:q\left({X}_{2}\right)\) ] Bi-factor enhancement \(\:{q(X}_{1}\cap\:{X}_{2})\:=\:{q(X}_{1})+\:q\left({X}_{2}\right)\) Independence \(\:{q(X}_{1}\cap\:{X}_{2})\:>\:{q(X}_{1})+\:q\left({X}_{2}\right)\) Nonlinear enhancement (3) Candidate Area Screening The study area was divided into 200m×200m grid cells, consistent with AED coverage recommendations in dense urban settings. For each grid cell \(\:j\) , a composite AED demand index \(\:{C}_{j}\) was calculated as Eq. (4): $$\:\begin{array}{c}{C}_{j}={\sum\:}_{i=1}^{N}{\omega\:}_{i}\bullet\:{X}_{i,norm}^{j}\#\left(4\right)\end{array}$$ where \(\:{\omega\:}_{i}\) is the weight of factor \(\:i\) (its q -value from Geodetector) and \(\:{X}_{i,norm}^{j}\) is the normalized value of factor \(\:i\) in grid \(\:j\) . Grids with \(\:{C}_{j}\:\) > 0.269, (the mean value) were selected to balance coverage and feasibility. Candidate grids were spatially clustered to identify contiguous high-demand zones, which were cross-checked against existing AED sites to highlight underserved areas [ 12 ]. 2.3.2. Multi-Objective Optimization Model Construction This study formulates the AED deployment problem as a multi‑objective optimization model based on the P‑center framework [ 22 , 23 ]. The model simultaneously considers spatial fairness, service quality, economic efficiency, and coverage performance. The four objectives are defined as follows: (1) Objective Functions Based on the P-center model, four objectives were defined: 1) Minimize maximum distance $$\:\begin{array}{c}min{Z}_{1}={max}_{i\in\:I,\:\:\:j\in\:J}\left\{{d}_{ij}\text{}\cdot\:{x}_{ij}\text{}\right\}\#\left(5\right)\end{array}$$ Where \(\:\:I\) is the set of OHCA demand points; \(\:J\) is the set of candidate AED locations; \(\:{d}_{ij}\) is the Euclidean distance (m) from candidate \(\:j\) to demand point \(\:i\) ; \(\:\:{x}_{ij}=1\) if demand \(\:i\) is assigned to candidate \(\:j\) , and 0 otherwise. This objective focuses on spatial equity: by minimizing the farthest service distance, the model ensures that even the most remote demand point is as close as possible to an AED, reducing disparities in access. 2) Maximize average satisfaction Satisfaction \(\:F\left(t\right)\) is defined as: $$\:\begin{array}{c}F\left(t\right)=\left\{\begin{array}{c}1+{R}_{0}\bullet\:{e}^{-{\gamma\:}t},\:\:t{\text{T}}_{i}\end{array}\right.\#\left(6\right)\end{array}$$ The objective function is: $$\:\begin{array}{c}max{Z}_{2}=\frac{1}{N}\sum\:_{i\in\:I}\sum\:_{j\in\:J}{x}_{ij}\bullet\:F\left({t}_{ij}\text{}\right)\#\left(7\right)\end{array}$$ Where \(\:t\) is the waiting time (min), \(\:{t}_{ij}\:\) is the time between \(\:i\:\) and \(\:j\) , and \(\:\:N\:\text{i}\text{s}\:\text{t}\text{h}\text{e}\:\) total number of demand points. The discontinuities at \(\:{t}_{i}\) =2 and \(\:{\text{T}}_{i}\) =6 are intentional, reflecting clinically recognized thresholds in OHCA survival probability and public satisfaction [ 24 ]. The first threshold (2 min) corresponds to the “golden response” window, while the second (6 min) represents the upper limit for effective defibrillation before survival rates drop sharply. This step-change design emphasizes the urgency of rapid AED access [ 25 ]. 3) Minimize average treatment cost $$\:\begin{array}{c}{minZ}_{3}=\frac{1\:}{N}\sum\:_{i\in\:I}\left({C}_{0}+{\text{C}}_{s}\bullet\:\sum\:_{j\in\:J}{x}_{ij}\bullet\:{t}_{ij}\right)\#\left(8\right)\end{array}$$ where \(\:{C}_{0}\) = 5100 ¥ is the basic treatment cost per case, and \(\:{C}_{s}\) 5000 ¥/min is the delay cost per minute. This formulation separates the fixed cost (e.g., standard medical intervention) from the time‑dependent cost (e.g., deterioration due to delayed defibrillation), making the economic trade‑offs transparent [ 26 , 27 ]. 4) Maximize coverage rate $$\:\begin{array}{c}{maxZ}_{4}=\frac{1}{N}\sum\:_{j\in\:J}{H}_{j}\text{}\cdot\:{y}_{j}\#\left(9\right)\end{array}$$ \(\:\) where \(\:{H}_{j}\) is the number of covered OHCA points for site \(\:j\) , and \(\:{y}_{j}\) is a binary site selection variable. Due to the unique assignment constraint (see below), each demand point is counted only once in \(\:\:{Z}_{4}\) , avoiding double counting. This objective captures the overall spatial reach of the AED network [ 23 ]. Constraints Assignment and Logic: \(\:\sum\:_{j\in\:J}{x}_{ij}=1\left(\forall\:i\in\:I,{x}_{ij}\le\:{y}_{j}\right)\) , each demand point is assigned to exactly one site. Service and Facility Limits: \(\:{t}_{ij}\bullet\:{x}_{ij}\le\:6\left(\forall\:i\in\:I,j\in\:J,\sum\:_{j\in\:J}{y}_{j}=50\right)\) , service time must not exceed 6 minutes, and exactly 50 AEDs are deployed. Variable domains: \(\:{x}_{ij},\:\:{y}_{j},{\:c}_{i}\in\:\left\{\text{0,1}\right\}\) , binary variables for assignment, site selection, and coverage. 2.3.3. Improved NSGA-II Algorithm for Model Solution To solve the proposed multi‑objective optimization model, an enhanced version of the Non‑dominated Sorting Genetic Algorithm II (NSGA‑II) was developed [ 17 ]. The improvements aim to accelerate convergence, avoid premature stagnation in local optima, and maintain a balance between solution diversity and feasibility. These strategic enhancements are implemented through the following mechanisms: Chromosome encoding: A binary (0–1) encoding scheme was adopted to represent AED site selection decisions. Each gene corresponds to a candidate location, with a value of 1 indicating selection and 0 indicating exclusion. This representation is intuitive and facilitates the integration of location‑specific constraints [ 28 ]. Tabu list integration: To mitigate premature convergence and escape local optima, a Tabu list mechanism was incorporated. Recently visited solutions are recorded and prohibited from reappearing within a fixed tenure. The Tabu tenure is dynamically adjusted according to the population size and problem scale, ensuring a balance between exploration and exploitation [ 29 ]. Fitness function: The fitness function combines a weighted sum of normalized objective values with a penalty term for constraint violations: $$\:\begin{array}{c}{f}_{i}=\:\sum\:_{k\in\:K}{z}_{i}^{k}+\:\lambda\:\:\cdot\:{l}_{0}\#\left(10\right)\end{array}$$ where \(\:{f}_{i}\) is the fitness value of the \(\:{i}^{th}\) individual; smaller values indicate better adaptability and higher priority for survival into the next generation. K = 4, which is the number of objective functions, corresponding to: \(\:{Z}_{1}\) (minimize maximum distance), \(\:{Z}_{2}\) (maximize average satisfaction), \(\:{Z}_{3}\) (minimize average treatment cost), and \(\:{Z}_{4}\) (maximize coverage rate). \(\:{z}_{i}^{k}\) is the value of the \(\:{k}^{th}\) objective function for the \(\:{i}^{th}\) individual, calculated from Eqs. (5)–(8). λ = 1000, the penalty coefficient for constraint violations, selected to strongly penalize infeasible solutions and enforce compliance with operational constraints such as the 6-minute golden rescue window. \(\:{l}_{o}\:\) is the degree of constraint violation, e.g., the total minutes exceeding the 6-minute limit or the number of AEDs exceeding the deployment budget; \(\:{l}_{o}=0\:\) for feasible solutions. This unweighted summation approach treats all objectives equally in the fitness evaluation, while the penalty term ensures that infeasible solutions are effectively discouraged during the evolutionary search [ 18 ]. 3. Results and analysis 3.1. Spatial Pattern of Existing AED Allocation The spatial distribution of existing AEDs in Qinhuai District exhibited a distinct clustering pattern. The 1-standard deviation standard deviational ellipse analysis [ 30 ] showed that 68% of AEDs were located within a northwest–southeast “ring” configuration, characterized by central concentration and peripheral sparsity (Fig. 3 ). This suggests that AED deployment has historically been concentrated in the urban core, likely reflecting higher population density, commercial activity, and public facility availability in central areas. The average nearest neighbor (ANN) analysis further confirmed significant clustering [ 31 ]. The observed mean nearest neighbor distance (206.39 m) was substantially shorter than the expected random distance (258.08 m), yielding an ANN ratio of 0.800 and a z-score of − 6025 (p < 0.001). This statistically significant clustering indicates that AED placement is non-random and influenced by socio-economic and infrastructural factors. Kernel density estimation [ 32 ] identified four high-density AED clusters in Hongwulu, Chaotiangong, Daguanglu, and Fuzimiao Streets (Fig. 4 ). These areas correspond to major commercial and cultural hubs, indicating that AED deployment has been prioritized in zones with high pedestrian traffic and public gatherings. Peripheral residential areas remain underserved, highlighting potential inequities in spatial accessibility. 3.2. Geodetector Results 3.2.1. Factor Detector The factor detector quantified the explanatory power of various socio-demographic and infrastructural variables on AED demand (Table 5 ). The results indicate a clear hierarchical influence among the factors. The highest \(\:q\) -values were observed for susceptible population density ( \(\:{a}_{2}\) , q = 0.8531) and resident population density ( \(\:{a}_{1}\) , q = 0.7941). This confirms that AED deployment is most strongly associated with areas of high population density, consistent with core public health planning principles. Notably, while residential areas remain the primary focus of AED coverage due to the high frequency of indoor cardiac events [ 33 ], our results highlight the critical role of public mobility nodes. Specifically, shopping mall density ( \(\:{c}_{5}\) , q = 0.5345) and transportation hubs ( \(\:{c}_{1}\) , q = 0.5019) exhibit substantial explanatory power. This aligns with the perspective that population mobility is a key determinant of AED demand in dense urban environments [ 34 ]. Our findings suggest that in hyper-dense districts like Qinhuai, the "Mobile Population Risk" at commercial centers is a dominant driver of AED demand, complementing traditional resident-based allocation strategies. Table 5 Factor detector results. Factor q -Value Ranking \(\:{a}_{2}\) 0.8531 1 \(\:{a}_{1}\) 0.7941 2 \(\:{c}_{5}\) 0.5345 3 \(\:{c}_{1}\) 0.5019 4 \(\:{c}_{8}\) 0.4935 5 \(\:{c}_{2}\) 0.4416 6 \(\:{c}_{6}\) 0.3853 7 \(\:{b}_{2}\) 0.3652 8 \(\:{c}_{4}\) 0.3468 9 \(\:{c}_{7}\) 0.3292 10 \(\:{c}_{3}\) 0.2851 11 \(\:{d}_{1}\) 0.1528 12 \(\:{b}_{1}\) 0.0396 13 3.2.2. Interaction Detector The interaction detector results (Fig. 5 ) reveal that all factor pairs exhibit synergistic enhancement, with the explanatory power radiating from the demographic core at the bottom-left toward urban functional variables at the top-right. The peak interaction occurs between population density and the high-risk population ( \(\:{a}_{1}\cap\:{a}_{2}=0.9621\) ), establishing the primary spatial template for AED demand at the heatmap's origin. Conversely, a saturation effect is observed as the analysis shifts toward environmental factors (e.g., \(\:{a}_{1}\cap\:{d}_{1}=0.8153\) ), where q -values plateau due to the overwhelming independent influence of the demographic core. Significant planning insights emerge from the high-intensity synergies between the high-risk population ( \(\:{a}_{2}\) ) and functional urban nodes, specifically with accommodation density ( \(\:{a}_{2}\cap\:{c}_{8}=0.9086\) ), sports facility density ( \(\:{a}_{2}\cap\:{c}_{2}=0.8940\) ), and shopping mall density ( \(\:{a}_{2}\cap\:{c}_{5}=0.8925\) ). These findings, visualized in the mid-section of the matrix, underscore that OHCA risk is most effectively predicted where vulnerable demographics intersect with public activity hotspots characterized by high foot traffic or physical exertion. Consequently, AED deployment strategies should transcend basic population metrics to prioritize these high-synergy functional intersections [ 34 ]. 3.2.3. AED Demand Index The calculated AED Demand Index (ADI) ranges from 0.033 to 0.764, with a mean value of 0.2862. High-demand grids (ADI > 0.2862) are primarily clustered within Chaotiangong, Hongwulu, and Fuzimiao Streets, representing 41.8% of the total grid cells (Fig. 6 ). These areas overlap substantially with the high-density AED clusters identified earlier, but also highlight additional underserved zones with high predicted demand [ 13 ]. Among the 561 total candidate grids, 383 (68.3%) were identified as underserved zones. This selection process reflects a rigorous, data-driven prioritization that integrates spatial clustering, socio-demographic factors, and accessibility constraints, ensuring that future installations target the urban intersections with the most acute needs [ 35 ]. 3.3. Spatial Evaluation of Optimized AED Deployment The E-NSGA-II algorithm converged to a Pareto-optimal front, providing a diverse range of candidate solutions for the AED allocation problem. To determine the most effective deployment strategy from this candidate set, the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) was employed. By evaluating the relative closeness of each candidate to the ideal solution across all objective functions, a comprehensive optimal solution was identified. This scheme was selected as the final recommended deployment strategy due to its superior capability in balancing spatial equity \(\:\:\left({Z}_{1}\right)\) , social satisfaction \(\:\left({Z}_{2}\right)\) , economic efficiency ( \(\:{Z}_{3}\) ), and time-critical coverage ( \(\:{Z}_{4}\) ). The comprehensive performance metrics for the three scenarios are summarized in Table 6 . Compared to the original scheme, TOPSIS-based optimal solution achieved a transformative reduction in \(\:{Z}_{1}\) by 55.3%, effectively shortening the maximum travel distance for residents from 632.46 m to 282.84 m. This drastic improvement directly enhances the likelihood of timely defibrillation during the critical "golden window" of out-of-hospital cardiac arrest [ 36 ]. Average satisfaction ( \(\:{Z}_{2}\) ) increased to 0.997 (a 9.1% improvement), reflecting a near-perfect alignment between AED placement and user accessibility expectations [ 37 ]. Simultaneously, treatment costs ( \(\:{Z}_{3}\) ) were reduced by 21.3%, demonstrating that superior coverage can coexist with enhanced economic efficiency. Most notably, the coverage rate ( \(\:{Z}_{4}\) ) reached a comprehensive 100%, uniformly eliminating all previous time-violation points and ensuring every resident is within the recommended response radius [ 38 ]. Against the P-center model, the TOPSIS-based optimal solution demonstrated superior balanced performance. While the P-center model focuses exclusively on equity, the TOPSIS solution achieved 1.7% lower treatment costs ( \(\:{Z}_{3}\) ) and 0.9% higher satisfaction ( \(\:{Z}_{2}\) ) while maintaining the same optimal distance and coverage standards. These results demonstrate that the proposed multi-objective approach, refined through TOPSIS, significantly outperforms traditional single-objective models by maximizing cost-effectiveness and coverage equity simultaneously [ 39 ]. Table 6 Objective function values of optimal schemes. Scheme \(\:{\varvec{Z}}_{1}\) (m) \(\:{\varvec{Z}}_{2}\) \(\:{\varvec{Z}}_{3}\) (¥) \(\:{\varvec{Z}}_{4}\) TOPSIS-based optimal solution 282.84 0.997 10,998.25 1.000 P-center 282.84 0.988 11,187.03 1.000 Original 632.46 0.914 13,973.29 0.966 As illustrated in Fig. 7 , the spatial pattern of the optimal scheme closely follows the existing AED layout, which is already concentrated around hospitals, major commercial corridors, and transport hubs. Building on this foundation, the model reallocates and adds new devices primarily to high‑demand grids identified earlier, especially in peripheral residential neighborhoods, school catchment areas, and community service centers that were previously underserved. By simultaneously leveraging the existing network and strategically reinforcing weak links, this deployment pattern not only closes critical coverage gaps but also better aligns with the study’s overarching goal of enhancing both equity and efficiency in AED accessibility [ 40 ]. In the AED location optimization experiment, the E‑NSGA‑II (enhanced with a Tabu mechanism) demonstrated clear advantages over the standard NSGA‑II in both efficiency and solution quality. Under identical population and iteration settings, E‑NSGA‑II reduced computational time by 27.5%, requiring only 47.95 s to converge compared with 66.11 s for the baseline. Although the enhanced algorithm generated a slightly smaller set of non-dominated solutions (193 vs. 220), it achieved a higher Hypervolume (0.076586 vs. 0.074736) and a superior Spread index (1.0008 vs. 1.0010). These metrics indicate that the proposed algorithm provides a more comprehensive and balanced representation of the multi-objective trade‑off space, ensuring that the resulting deployment schemes are both mathematically robust and spatially representative. 4. Discussion 4.1. Driving Mechanisms and Algorithmic Response The factor detector results (Table 5 ) provide a robust quantitative basis for understanding the spatial heterogeneity of AED demand. High-risk population density ( \(\:{a}_{2}\) , \(\:q=0.8531\) ) and resident population density ( \(\:{a}_{1}\) , \(\:q=0.7941\) ) emerged as the primary anchors of the spatial template. This hierarchical influence confirms that AED deployment remains fundamentally rooted in high-density residential fabrics where the base probability of indoor OHCA events is highest [ 33 ]. The interaction detector (Fig. 5 ) further reveals a synergistic "radiating" effect. The peak interaction occurs between \(\:{a}_{1}\) and \(\:{a}_{2}\) ( \(\:{a}_{1}\cap\:{a}_{2}=0.9621\) ), establishing a robust demographic core at the heatmap’s origin. Conversely, a saturation effect is observed as the analysis shifts toward environmental factors (e.g., \(\:{a}_{1}\cap\:{d}_{1}=0.8153\) ), where \(\:q\) -values plateau due to the overwhelming independent influence of the demographic core. Significant planning insights emerge from the high-intensity synergies between the high-risk population ( \(\:{a}_{2}\) ) and functional nodes, such as accommodation ( \(\:{a}_{2}\cap\:{c}_{8}=0.9086\) ), sports facilities ( \(\:{a}_{2}\cap\:{c}_{2}=0.8940\) ), and shopping malls ( \(\:{a}_{2}\cap\:{c}_{5}=0.8925\) ). These findings underscore that OHCA risk is most effectively predicted where vulnerable demographics intersect with public activity hotspots characterized by high foot traffic or physical exertion. To effectively address these complex demand patterns, the E‑NSGA‑II algorithm demonstrated superior technical efficacy. By integrating a Tabu list mechanism and 2-opt mutation, the algorithm achieved a 27.5% reduction in computational time (47.95 s vs. 66.11 s) and successfully avoided the "clustering trap"—a common issue where solutions gravitate toward a local optimum at the expense of global equity. The resulting Pareto-optimal scheme facilitated a transformative 55.3% reduction in maximum travel distance (from 282.84 m to 632.46 m), proving that heuristic refinements are essential for translating complex geospatial drivers into mathematically efficient deployment schemes [ 41 ]. 4.2. Strategic Redundancy and Spatial Equity A key finding from our optimization results is the allocation of additional units even to certain well-served sectors in the central district. This "strategic redundancy" is not a resource waste but a calculated response to extreme demographic pressure ( \(\:{a}_{1},{a}_{2}\) ). In hyper-dense urban grids, achieving basic spatial coverage ( \(\:{Z}_{1}\) ) is insufficient to guarantee survival; the patient satisfaction ( \(\:{Z}_{2}\) ) must also account for the probability of concurrent cardiac events and the micro-scale impedance of complex street networks. The near-perfect satisfaction level (0.997) suggests that our model optimized the "perceived accessibility," ensuring that every resident is within a reliable response radius during the critical "6-minute golden window" [ 25 , 33 ]. Furthermore, the multi-objective approach balances cost-effectiveness ( \(\:{Z}_{3}\) ) with socio-economic equity. While income level ( \(\:{d}_{1}\) ) showed a lower independent explanatory power, its inclusion in the optimization ensures that "defibrillation equity" is maintained. This prevents the emergence of "survival deserts" in low-income residential blocks, where residents might otherwise face reduced survival chances due to economic disadvantage [ 42 ]. By prioritizing these underserved yet high-risk intersections, the model moves beyond simple distance-based coverage toward a more socially just distribution of emergency resources. 4.3. Policy Implications and Research Trajectories The data-driven ADI provides a granular prioritization framework for urban planners. Based on our findings, we propose a transition toward an ADI-led allocation framework, prioritizing "survival deserts" like Chaotiangong and Hongwulu Streets. This strategy should be twofold: first, leveraging urban renewal projects to "embed" AEDs into new public service centers; and second, implementing Socio-economic Equity Correction through targeted funding for low-income residential blocks ( \(\:{d}_{1}\) ), ensuring that economic disadvantage does not translate into reduced survival chances [ 42 ]. Furthermore, training programs should be concentrated at high-synergy functional nodes ( \(\:{c}_{2},{c}_{8}\) ) to translate physical proximity into effective bystander intervention. However, the transition from static optimization to real-world deployment faces ongoing challenges. The reliance on static historical data remains a primary limitation, as it fails to capture the dynamic "temporal risk" of cities where population shifts significantly between day and night. Future research trajectories should focus on integrating real-time mobile signaling data to enable dynamic AED allocation. Additionally, expanding the objective set ( \(\:{Z}_{Z}\) ) to include maintenance logistics and bystander psychology would enhance the operational sustainability of the network. Testing this framework in lower-density rural environments remains essential to confirm its generalizability and to refine penalty coefficients for diverse spatial contexts [ 43 ]. 5. Conclusion This study developed and validated a comprehensive spatial allocation framework for AEDs that integrates spatial factor detection, a patient-centric multi-objective optimization model, and an enhanced evolutionary algorithm. The framework was designed to address the dual challenge of improving AED accessibility while ensuring equitable distribution, particularly in high-risk urban environments. By combining Geodetector with a multi-objective model, the approach simultaneously quantified the spatial correlation between OHCA incidence and influencing factors, and optimized AED placement to balance efficiency, patient needs, and operational constraints. The Geodetector analysis revealed that high-risk population density ( \(\:{a}_{2},q=0.8531\) ) and resident population density ( \(\:{a}_{1},q=0.7941\) ) were the dominant drivers of AED demand. Their interaction exhibited a powerful synergistic effect, with the peak interaction occurring between these two demographic variables ( \(\:{a}_{1}\cap\:{a}_{2}=0.9621\) ), establishing a robust demographic core for the spatial risk template. Furthermore, significant synergistic explanatory power was observed when demographics intersected with functional nodes, such as accommodation ( \(\:{a}_{2}\cap\:{c}_{8}=0.9086\) ) and sports facilities ( \(\:{a}_{2}\cap\:{c}_{2}=0.8940\) ). These findings provide a robust, evidence-based foundation for identifying priority deployment areas. The multi-objective model incorporated four objectives—coverage ( \(\:{Z}_{1}\) ), patient satisfaction ( \(\:{Z}_{2}\) ), cost ( \(\:{Z}_{3}\) ), and coverage equity ( \(\:{Z}_{4}\) )—and achieved a transformative 55.3% reduction in maximum travel distance (from 632.46 m to 282.84 m) while maintaining a near-perfect satisfaction level (0.997). This demonstrates clear advantages over traditional single-objective approaches, which often neglect patient-oriented metrics and spatial equity. Algorithmic performance tests confirmed that the E-NSGA-II, enhanced with a Tabu list mechanism and 2-opt mutation, significantly outperformed the standard NSGA-II. These refinements led to a 27.5% reduction in computational time (47.95 s vs. 66.11 s) and enhanced the algorithm’s global search capability, ensuring the optimization process avoided premature convergence and successfully navigated complex urban constraints. The optimized schemes generated for Qinhuai District validated the method’s feasibility, producing deployment plans that are both operationally practical and clinically relevant. Beyond methodological contributions, the results have direct policy and planning implications. High-demand areas such as Chaotiangong and Hongwulu Streets should be prioritized for AED installation, with the ADI serving as a transparent tool for standardizing allocation. Targeted subsidies should be provided to high-risk, low-income areas to address equity gaps, and public training should be expanded to translate accessibility into actual life-saving interventions. This research offers a scalable framework extensible to other emergency medical resources. Future studies will prioritize dynamic allocation by integrating real-time mobile signaling and traffic data, while expanding the objective function to incorporate maintenance logistics and bystander usage rates. By bridging spatial analytics, patient-centered optimization, and advanced evolutionary computation, this study contributes both a methodological innovation and a practical decision-support tool for enhancing emergency medical service efficiency and improving OHCA survival rates in diverse urban settings. Declarations Conflict of Interest The authors declare that they have no conflicts of interest. Ethics Statement This study does not involve human participants or identifiable personal data and therefore did not require ethics approval. Funding This research was supported by the National Natural Science Foundation of China (Grant No. 42371444); the Open Fund of the State Key Laboratory of Remote Sensing Science (Grant No. OFSLRSS202430); the Opening Foundation of Key Laboratory (Grant No. JSHD202407); and the Jiangsu Province Capability Improvement Project through Science, Technology and Education (Grant No. ZDXYS202210). Additional support was provided by the 2023 Jiangsu Provincial Institute of Public Health Emergency Research Project, Current Status and Optimization Strategies for Automated External Defibrillator Deployment Based on GIS (Grant No. JSWSYJ‑20230105). Author Contribution Jia Wang designed the study, conducted the spatial analysis, developed the optimization models, and drafted the manuscript. Jingyi Zhou contributed to data curation, preprocessing, and statistical analysis. Shaohua Wang assisted with methodological refinement and provided technical support for spatial modeling. Min Zhang offered domain expertise in public health emergency management and contributed to the interpretation of results. Jie Shen supervised the study, guided the research framework, and critically revised the manuscript. Tianhao Zhao supported visualization, mapping, and model validation. Chenxin Xiao contributed to literature review, data verification, and manuscript editing. All authors reviewed and approved the final version of the manuscript. Acknowledgement The authors would like to express their sincere gratitude to the Aerospace Information Research Institute, Chinese Academy of Sciences, for providing technical support and data coordination. The authors also thank the Jiangsu Provincial Health Commission for facilitating access to relevant public health data and administrative resources that made this study possible. Data Availability Aggregated spatial datasets generated during this study, including the AED Demand Index and optimization outputs, are available from the corresponding author upon reasonable request. Raw population and OHCA data cannot be shared due to institutional restrictions. References Yan S, Gan Y, Jiang N, Wang R, Chen Y, Luo Z, et al. The global survival rate among adult out-of-hospital cardiac arrest patients who received cardiopulmonary resuscitation: a systematic review and meta-analysis. Crit Care. 2020;24:61. https://doi.org/10.1186/s13054-020-2773-2 . Van Nieuwenhuizen BP, Oving I, Kunst AE, Daams J, Blom MT, Tan HL, et al. Socio-economic differences in incidence, bystander cardiopulmonary resuscitation and survival from out-of-hospital cardiac arrest: A systematic review. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8600130","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":588182556,"identity":"bcb4f66e-85cd-4213-b4c9-6b4aa99d0441","order_by":0,"name":"Jia Wang","email":"","orcid":"","institution":"Key Laboratory of Virtual Geographic Environment (Nanjing Normal University), Ministry of Education","correspondingAuthor":false,"prefix":"","firstName":"Jia","middleName":"","lastName":"Wang","suffix":""},{"id":588182558,"identity":"6c183f70-e409-41d2-872a-199d09ae4ffb","order_by":1,"name":"Jingyi Zhou","email":"","orcid":"","institution":"State Key Laboratory of Remote Sensing and Digital Earth, Aerospace Information Research Institute, Chinese Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"Jingyi","middleName":"","lastName":"Zhou","suffix":""},{"id":588182559,"identity":"e1e49491-557a-45f0-9582-1a2173abe268","order_by":2,"name":"Shaohua Wang","email":"","orcid":"","institution":"State Key Laboratory of Remote Sensing and Digital Earth, Aerospace Information Research Institute, Chinese Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"Shaohua","middleName":"","lastName":"Wang","suffix":""},{"id":588182561,"identity":"d5b4b4e3-654f-4297-9dd5-f39ab8168f19","order_by":3,"name":"Min Zhang","email":"","orcid":"","institution":"National Health Commission Key Laboratory of Contraceptives Vigilance and Fertility Surveillance","correspondingAuthor":false,"prefix":"","firstName":"Min","middleName":"","lastName":"Zhang","suffix":""},{"id":588182567,"identity":"de276653-5a09-47ee-a8f7-adc23b26e75c","order_by":4,"name":"Jie Shen","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2klEQVRIiWNgGAWjYDACCRA2YJBjYDgA4jITr8WYRC1AkNgAoYnQIj+7+dgDiwKb9O2MZ49JMFRYJzawnz2AV4vBnWPpBhIGabk7G86lSTCcSU9s4MlLwK9FIsdMQsLgcO6GA2fMJBjbDic2SPAY4HfYjPxvQC3/0w3AWv4RoYXhRg4bUMuBBIiWBiK0GNxIAzks2RDoMGOLhGPpxm08OYQclvxMWuKPnbzBjTOGNz7UWMv2s58h4DAgYAbHjcQBBoYEIM1GUD0QMH4AkfwNxKgdBaNgFIyCkQgAds5CvC3/w9EAAAAASUVORK5CYII=","orcid":"","institution":"Key Laboratory of Virtual Geographic Environment (Nanjing Normal University), Ministry of Education","correspondingAuthor":true,"prefix":"","firstName":"Jie","middleName":"","lastName":"Shen","suffix":""},{"id":588182571,"identity":"701b5f16-f88e-4282-94f9-d1ee4f62df17","order_by":5,"name":"Tianhao Zhao","email":"","orcid":"","institution":"Key Laboratory of Virtual Geographic Environment (Nanjing Normal University), Ministry of Education","correspondingAuthor":false,"prefix":"","firstName":"Tianhao","middleName":"","lastName":"Zhao","suffix":""},{"id":588182574,"identity":"8fc348af-5f87-4176-8fa3-db18dd939fd8","order_by":6,"name":"Chenxin Xiao","email":"","orcid":"","institution":"Key Laboratory of Virtual Geographic Environment (Nanjing Normal University), Ministry of Education","correspondingAuthor":false,"prefix":"","firstName":"Chenxin","middleName":"","lastName":"Xiao","suffix":""}],"badges":[],"createdAt":"2026-01-14 09:38:33","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8600130/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8600130/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":102326614,"identity":"780bcd2c-2d05-4c71-966c-7cc65c343fcd","added_by":"auto","created_at":"2026-02-10 14:37:54","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":123614,"visible":true,"origin":"","legend":"\u003cp\u003eSpatial distribution of OHCA locations in Qinhuai District, Nanjing, China.\u003c/p\u003e","description":"","filename":"image1.png","url":"https://assets-eu.researchsquare.com/files/rs-8600130/v1/68bda303bcc9a4d7d97c95a2.png"},{"id":102745459,"identity":"e841f9e0-1c2d-44e2-b940-35d7a16d378e","added_by":"auto","created_at":"2026-02-16 08:50:51","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":679660,"visible":true,"origin":"","legend":"\u003cp\u003eTechnical roadmap for multi-objective optimization allocation of urban AEDs.\u003c/p\u003e","description":"","filename":"image2.png","url":"https://assets-eu.researchsquare.com/files/rs-8600130/v1/9446faf29427aa47046677fd.png"},{"id":102326616,"identity":"fabfbe8c-1daf-421c-90d3-ca1b3e3b2c50","added_by":"auto","created_at":"2026-02-10 14:37:54","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":135562,"visible":true,"origin":"","legend":"\u003cp\u003eStandard deviational ellipse of AED in Qinhuai district.\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-8600130/v1/5d0a29616c8279d8381964cf.png"},{"id":102326620,"identity":"80e5a46d-c606-485d-8322-1f49b4ebab1d","added_by":"auto","created_at":"2026-02-10 14:37:54","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":171678,"visible":true,"origin":"","legend":"\u003cp\u003eKernel density estimation of the spatial distribution of existing AEDs in Qinhuai district.\u003c/p\u003e","description":"","filename":"image4.png","url":"https://assets-eu.researchsquare.com/files/rs-8600130/v1/7e09b07035ccde4e4ee09feb.png"},{"id":105727607,"identity":"0eae999e-890c-4048-8833-b64a3bb3f331","added_by":"auto","created_at":"2026-03-30 10:54:48","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":53423,"visible":true,"origin":"","legend":"\u003cp\u003eSynergistic interaction effects of multiple factors on AED demand priority.\u003c/p\u003e","description":"","filename":"image5.png","url":"https://assets-eu.researchsquare.com/files/rs-8600130/v1/2bb409780c09ea4d70078516.png"},{"id":102326619,"identity":"98922785-c8be-423e-8ae4-1511241af8d7","added_by":"auto","created_at":"2026-02-10 14:37:54","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":46612,"visible":true,"origin":"","legend":"\u003cp\u003eAED Demand Index in Qinhuai District.\u003c/p\u003e","description":"","filename":"image6.png","url":"https://assets-eu.researchsquare.com/files/rs-8600130/v1/0d1d3f69921700f9fa74b36f.png"},{"id":102404235,"identity":"4ddd1f37-1744-46e8-b1cc-3282f57700ad","added_by":"auto","created_at":"2026-02-11 11:03:37","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":96094,"visible":true,"origin":"","legend":"\u003cp\u003eOptimal AED allocation in Qinhuai district.\u003c/p\u003e","description":"","filename":"image7.png","url":"https://assets-eu.researchsquare.com/files/rs-8600130/v1/dcd73c62fa5a45c282e7dbb8.png"},{"id":105752230,"identity":"ea5075ed-0f54-4b36-8af9-51f00123a623","added_by":"auto","created_at":"2026-03-30 15:56:10","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3006184,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8600130/v1/e01b6013-d55c-4d7b-9960-941f27802ccf.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A GIS‑Based Multi‑Objective Optimization Strategy for Urban Automated External Defibrillator Deployment","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eOut‑of‑hospital cardiac arrest (OHCA) is a major global public health challenge and a leading cause of premature mortality. Defined as the abrupt cessation of cardiac mechanical activity, OHCA often occurs without warning, and without immediate intervention, irreversible brain injury or death can occur within minutes. Globally, millions of OHCA cases occur annually, yet survival‑to‑discharge rates in most countries remain below 10% despite advances in emergency medical services (EMS) and resuscitation science [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. In resource-limited countries, the chain of survival for OHCA faces significant barriers. Public awareness and training in cardiopulmonary resuscitation (CPR) remain low, often hindered by cultural norms and legal concerns, resulting in minimal bystander intervention. EMS are frequently underdeveloped, with delayed response times or, in some regions, no formal system at all [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn China, the situation is equally concerning. The Report on Cardiovascular Health and Diseases in China 2023 indicates a continuous rise in cardiovascular disease prevalence, with coronary heart disease mortality increasing steadily since 2012 [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. In China, the OHCA treated by emergency medical services is approximately 97.1 per 100,000 population. Although public awareness of CPR has improved, the survival-to-discharge rate remains critically low at 1.2%, with bystander CPR performed in only 17% of cases [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. These figures highlight persistent gaps in emergency response infrastructure, public training, and post-resuscitation care. Nationwide registry data from the BASIC‑OHCA study, covering 32 monitoring sites and approximately 9% of the Chinese population, further estimate over one million OHCA cases annually, with 76.85% occurring at home, a mean patient age of 65.8 years, and survival‑to‑discharge of only 1.15% [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. In contrast, countries with mature public‑access defibrillation systems, such as Japan and the United States, report bystander CPR rates exceeding 40% and survival rates above 8\u0026ndash;10% for shockable rhythms[\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], underscoring a substantial performance gap. To address these spatial disparities in OHCA outcomes, it is essential to examine the deployment and accessibility of life-saving interventions such as Automated External Defibrillators (AEDs).\u003c/p\u003e \u003cp\u003eDespite the proven life‑saving value of AEDs, their deployment in Chinese cities faces systemic challenges. National policy frameworks for AED allocation were introduced relatively late and financial constraints\u0026mdash;including the costs of equipment procurement, routine maintenance, and public training\u0026mdash;have hindered comprehensive implementation [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. On a per‑capita basis, AED density in mainland China remains far below that of developed countries: fewer than 100 units per 100,000 population nationally, compared with approximately 700 units in the Netherlands, 550 units in Japan, and 300 units in the United States [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Spatially, large Chinese cities often exhibit a \u0026ldquo;dense‑in‑central‑areas, sparse‑in‑peripheries\u0026rdquo; clustered distribution pattern, leaving high‑OHCA‑risk peripheral areas underserved. For example, a spatial analysis of Nanjing\u0026rsquo;s central districts found that the average observed nearest‑neighbor distance between AEDs was 195.99 m\u0026mdash;significantly shorter than the expected random distance of 258.47 m\u0026mdash;indicating clustering in central zones but potential service blind spots in outlying areas [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Moreover, many current deployment strategies rely on heuristic placement strategies\u0026mdash;such as prioritizing transportation hubs or commercial complexes\u0026mdash;rather than data‑driven spatial correlation analyses between OHCA incidence and influencing factors (e.g., population density, EMS accessibility), limiting both the rationality and equity of AED placement [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. Building on this analytical framework, AED deployment can be formulated as a multi-objective spatial optimization problem, enabling data-driven strategies that better align with clinical and operational needs.\u003c/p\u003e \u003cp\u003eAED deployment can be modeled as a multi-objective spatial optimization problem, with the ultimate goal of meeting public rescue needs in the event of cardiac arrest. In an urban context, the analysis process typically consists of three stages: candidate area selection, multi‑objective optimization model construction, and model solution. Traditional multi‑objective optimization approaches often assign weights to each objective function and combine them into a single aggregated objective. However, weight selection can significantly affect results, limiting generalizability and practical applicability [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. The Genetic Algorithm (GA) [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e], with its strong global search capability and adaptability, has been widely applied in optimization problems and can effectively address these limitations. As multi-objective optimization tasks become increasingly prevalent, researchers have developed evolutionary algorithms to address trade-offs among competing objectives. Notable examples include the Multi-Objective Genetic Algorithm (MOGA) and the Non‑Dominated Sorting Genetic Algorithm (NSGA) [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. Among them, the NSGA‑II algorithm [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e] enhances convergence and solution diversity through fast non‑dominated sorting and crowding‑distance calculation. While NSGA‑II performs well for problems with two or three objectives, its efficiency declines in high‑dimensional objective spaces. To overcome this, the NSGA‑III algorithm was proposed. By introducing a reference‑point mechanism, NSGA‑III can generate a uniformly distributed Pareto‑optimal solution set in high‑dimensional spaces, demonstrating superior performance in complex, real‑world multi‑objective optimization scenarios [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eTo validate the proposed framework, a case study was conducted in Qinhuai District of Nanjing. In this study, Qinhuai District of Nanjing was selected as the case area. Standard deviational ellipse and other spatial analytical techniques were employed to examine existing issues in the spatial allocation of AEDs. Based on a systematic review and synthesis of relevant AED policy guidelines, the key influencing factors for urban AED deployment were identified and quantitatively defined. The Geodetector method was then applied to determine the weights of these factors, enabling the calculation of an AED urban spatial allocation demand index. Subsequently, a time-loss function was incorporated into a location\u0026ndash;allocation framework to quantify the objective function of the AED deployment model. Constraints were formulated in accordance with the OHCA chain of survival to ensure clinical and operational relevance, resulting in the construction of a multi-objective AED allocation model. Accordingly, we propose an improved NSGA-II algorithm that integrates a tabu-list-based evolutionary mechanism to enhance solution diversity, improve local search, and prevent premature convergence. Based on this approach, the optimized AED deployment scheme was obtained. This research offers both theoretical contributions and actionable strategies for improving AED deployment in urban environments.\u003c/p\u003e"},{"header":"2. Data and Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n\u003ch2\u003e2.1. Study Area\u003c/h2\u003e\n\u003cp\u003eThis study focuses on Qinhuai District, located in Nanjing, Jiangsu Province, China. Geographically, Nanjing spans 31.23\u0026deg;\u0026ndash;32.62\u0026deg;N, 118.37\u0026deg;\u0026ndash;119.23\u0026deg;E, situated in the southwestern part of Jiangsu. Qinhuai lies at the core of Nanjing\u0026rsquo;s urban area and serves as the city\u0026rsquo;s political, economic, cultural, and historical center (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e\n\u003cp\u003eQinhuai has a high population density, with approximately 800,000 permanent residents and a substantial floating population. The district is characterized by intense human activity, including frequent commercial, cultural, and tourism events, which contribute to elevated public health risks and increased demand for emergency response services. Rapid urbanization has driven significant economic growth, positioning Qinhuai as one of the city\u0026rsquo;s most economically active regions. Its infrastructure includes multiple metro lines, wide road coverage, and a dense network of public facilities such as hospitals, schools, shopping centers, and cultural venues.\u003c/p\u003e\n\u003cp\u003eAccording to local registry data, Qinhuai reports approximately 380 cases of OHCA annually, with a majority occurring in residential and commercial zones. As shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e, OHCA incidents are spatially concentrated in densely populated urban blocks, particularly near transportation hubs, commercial centers, and residential clusters. These patterns reflect elevated public health risks and highlight the urgency of improving emergency response capabilities. In response to this demand, an increasing number of public places have installed AEDs. Although Qinhuai hosts a high concentration of medical institutions, traffic congestion and spatial heterogeneity in facility distribution pose challenges to timely emergency access. Scientifically optimizing AED deployment to improve response efficiency has become a pressing public safety concern, and Qinhuai\u0026mdash;characterized by its strategic location, population density, economic vitality, and robust public infrastructure\u0026mdash;offers substantial potential for such research.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\n\u003ch2\u003e2.2. Data\u003c/h2\u003e\n\u003cp\u003eThe datasets used in this study were obtained from a diverse range of institutions and platforms, encompassing spatial, demographic, and transportation-related information essential for optimizing emergency medical services. A summary of dataset formats and sources is provided in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e. The specific datasets are described below.\u003c/p\u003e\n\u003cp\u003e(1) OHCA Data\u003c/p\u003e\n\u003cp\u003eOHCA records were obtained from the Jiangsu Provincial Health Development Research Center. Each record includes the geographic coordinates, timestamp, and age of the individual involved, covering incidents that occurred within Nanjing.\u003c/p\u003e\n\u003cp\u003e(2)\u0026nbsp;AED Data\u003c/p\u003e\n\u003cp\u003eAED deployment data were also provided by the same institution. This dataset contains the locations of all installed AEDs across the city, reflecting the current spatial coverage and distribution of emergency defibrillation resources.\u003c/p\u003e\n\u003cp\u003e(3)\u0026nbsp;Road Network Data\u003c/p\u003e\n\u003cp\u003eRoad network data were sourced from OpenStreetMap (OSM), covering Nanjing and its surrounding areas. The dataset includes geometric attributes (e.g., road length, connectivity) and classification types (e.g., highways, arterial roads, secondary roads), which were used to evaluate road density and accessibility.\u003c/p\u003e\n\u003cp\u003e(4)\u0026nbsp;Public Facility Data\u003c/p\u003e\n\u003cp\u003ePoint-of-interest (POI) data for public facilities were retrieved from the Gaode (Amap) Developer Platform. This dataset includes major urban amenities such as transportation hubs (e.g., metro stations, bus stops, railway stations), public buildings (e.g., schools, hospitals, shopping centers), and recreational venues (e.g., cinemas, museums).\u003c/p\u003e\n\u003cp\u003e(5)\u0026nbsp;Population Data\u003c/p\u003e\n\u003cp\u003ePopulation estimates were obtained from the WorldPop project, which integrates remote sensing and statistical modeling to produce high-resolution global population rasters. For this study, 100 m-resolution data for different age groups in Nanjing were used to assess population exposure and vulnerability.\u003c/p\u003e\n\u003cp\u003e(6)\u0026nbsp;GDP Data\u003c/p\u003e\n\u003cp\u003eGross Domestic Product (GDP) data were acquired from the Resource and Environment Science Data Platform. These data reflect the economic development level of each region and serve as an important reference for assessing AED deployment needs and prioritization.\u003c/p\u003e\n\u003cp\u003eTo enable spatial analysis, the study area was divided into 200 m \u0026times; 200 m grid cells. Population-related factors\u0026mdash;including resident and susceptible population densities\u0026mdash;were calculated as population-to-area ratios. Road network density was computed as the total road length per unit area, while medical accessibility was evaluated using an origin\u0026ndash;destination (OD) cost matrix [\u003cspan class=\"CitationRef\"\u003e19\u003c/span\u003e]. Kernel density analysis was applied to public places, with service radii assigned according to facility type (e.g., 1000 m for metro stations) [\u003cspan class=\"CitationRef\"\u003e20\u003c/span\u003e]. GDP values were normalized to a [0, 1] range to ensure comparability and integration into the analytical model.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv class=\"colspec\" align=\"char\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003ctable id=\"Tab1\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eDescription of datasets used in the study, including format and source.\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eData Name\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eTime\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eFormat\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eData Source\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eHistorical OHCA Incident Data\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2023\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e.xlsx\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eJiangsu Institute of Health Development\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eAED Device Data in Nanjing\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2024\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e.xlsx\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eJiangsu Institute of Health Development\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ePopulation Data\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2020\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e.tif\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eWorldPop website\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eRoad Network Data\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2023\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e.shp\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eOpenStreetMap website\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ePublic Facility Data\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2023\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e.shp\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eAmap Open Platform\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eGDP Data\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2023\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e.xlsx\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eResource and Environment Science Data Platform\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\n\u003ch2\u003e2.3. Methods\u003c/h2\u003e\n\u003cp\u003eBased on a multi-objective optimization framework, this study conducts research on the optimal allocation of urban AEDs (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e). Firstly, it establishes an empirical foundation by integrating multi-dimensional data such as OHCA records and urban infrastructure indicators. Secondly, it applies techniques including Geodetector and demand index modeling to quantify spatial heterogeneity and identify high-priority AED deployment areas. Subsequently, a multi-objective optimization model is constructed, with objective functions and constraints designed to \"maximize service satisfaction and coverage while minimizing treatment costs\". Finally, the improved NSGA-II algorithm is used for model solution, generating diverse and high-quality deployment schemes to effectively resolve the complex trade-off issues in AED allocation.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003cdiv id=\"Sec6\" class=\"Section3\"\u003e\n\u003ch2\u003e2.3.1. Analysis of AED Influencing Factors and Candidate Areas\u003c/h2\u003e\n(1) Factor Selection and Quantification\u003cbr /\u003e\n\u003cp\u003eBased on a comprehensive review of national and municipal guidelines, as well as relevant literature, four primary categories of influencing factors were identified. These categories reflect the spatial characteristics of Qinhuai District and the current AED distribution pattern, and include: population-related factors (A), transportation-related factors (B), public facility-related factors (C), and economic factors (D). A total of 13 variables were selected across these four categories to represent the key drivers of AED deployment demand (Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e).\u003c/p\u003e\n\u003col\u003e\n\u003cli\u003e\n\u003cp\u003ePopulation factors reflect potential demand intensity, including the resident population density (RPD) and the susceptible population density (SPD), which refers to individuals aged 55\u0026ndash;80 who are most vulnerable to OHCA according to epidemiological studies.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eTraffic factors represent accessibility constraints, where Road network density (RND) measures total road length per unit area, with higher values indicating better access.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003ePublic venue factors capture spatial clustering of high‑footfall locations (e.g., transportation hubs, sports facilities, schools, shopping malls, cultural venues, offices, accommodations) that increase the likelihood of public cardiac arrest events. The service radii of these facilities were determined according to their functional characteristics (Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e), which served as the basis for subsequent spatial analysis.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eEconomic factors (GDP per unit area) serve as a proxy for urban development level, which may influence both AED deployment capacity and public activity patterns.\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ol\u003e\n\u003cp\u003ePositive factors (where higher values indicate greater AED demand potential) were normalized using Eq.\u0026nbsp;(1), and negative factors (where lower values indicate better conditions, e.g., shorter travel time to hospitals) were normalized using Eq.\u0026nbsp;(2):\u003c/p\u003e\n\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equa\" class=\"mathdisplay\"\u003e$$\\:\\begin{array}{c}{X}_{norm}=\\frac{\\left(X-\\:{X}_{min}\\right)}{\\left({X}_{max}-\\:{X}_{\\text{m}\\text{i}\\text{n}}\\right)}\\:\\#\\left(1\\right)\\end{array}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equb\" class=\"mathdisplay\"\u003e$$\\:\\begin{array}{c}{X}_{norm}=\\frac{\\left({X}_{max}-\\:X\\right)}{\\left({X}_{max}-{X}_{\\text{m}\\text{i}\\text{n}}\\right)}\\#\\left(2\\right)\\end{array}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:X\\)\u003c/span\u003e\u003c/span\u003e is the original value, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{X}_{norm}\\)\u003c/span\u003e\u003c/span\u003e is the normalized value, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{{X}_{max}}{{X}_{min}}\\)\u003c/span\u003e\u003c/span\u003e are the minimum/maximum values of the factor, respectively. All spatial datasets were projected to a common coordinate system (CGCS2000) and resampled to a 200 m resolution to ensure spatial alignment before normalization.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003ctable id=\"Tab2\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eAED allocation influencing factors and their quantification.\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eCategory\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eFactor\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eCode\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eQuantification Method\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003ePopulation\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eResident population density\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{a}_{1}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ePeople per km\u0026sup2; (WorldPop data)\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eHigh-risk population (55\u0026ndash;80y) density\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{a}_{2}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ePeople per km\u0026sup2; (WorldPop data)\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eTraffic\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eRoad network density\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{b}_{1}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eTotal road length per km\u0026sup2; (OSM data)\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eMedical facility accessibility\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{b}_{2}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eAverage travel time to nearest hospital (min)\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"8\" align=\"left\"\u003e\n\u003cp\u003ePublic Venues\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eTransportation hub density\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{c}_{1}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eKernel density (stations, airports)\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eSports facility density\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{c}_{2}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eKernel density (gyms, stadiums)\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eElderly care facility density\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{c}_{3}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eKernel density (nursing homes)\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eSchool density\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{c}_{4}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eKernel density (primary/secondary schools)\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eShopping mall density\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{c}_{5}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eKernel density (shopping centers)\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eCultural venue density\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{c}_{6}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eKernel density (museums, theaters)\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eOffice density\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{c}_{7}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eKernel density (office buildings)\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eAccommodation density\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{c}_{8}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eKernel density (hotels, resorts)\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eEconomic\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eGDP per unit area\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{d}_{1}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eGDP per km\u0026sup2; (resource and environmental platform)\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003ctfoot\u003e\n\u003ctr\u003e\n\u003ctd colspan=\"4\"\u003e\u003cem\u003eNote: Eq.\u0026nbsp;(1) applies to positive factors (\u003c/em\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{a}}_{2}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{a}}_{2}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{b}}_{1}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{c}}_{1}\\)\u003c/span\u003e\u003c/span\u003e\u003cem\u003e\u0026ndash;\u003c/em\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{c}}_{8}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{d}}_{1}\\)\u003c/span\u003e\u003c/span\u003e\u003cem\u003e); Eq.\u0026nbsp;(2) applies only to negative factor\u003c/em\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{b}}_{2}\\)\u003c/span\u003e\u003c/span\u003e \u003cem\u003e(medical accessibility, lower values indicate better access).\u003c/em\u003e\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tfoot\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003ctable id=\"Tab3\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003ePublic venues, typical subcategories, and their service radius.\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eMajor category\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eTypical subcategories\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eService radius (m)\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eTransportation hubs\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ePorts, airports, railway/high-speed rail stations, metro stations, passenger terminals, bus stops, cruise terminals\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e500\u0026ndash;5000\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eSports and fitness venues\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eStadiums, ball game facilities, gyms, and swimming pools\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e500\u0026ndash;1000\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eElderly care institutions\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eNursing homes, elder care centers, senior activity centers\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e500\u0026ndash;1000\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eSchools\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eUniversities, high schools, middle schools, primary schools, and kindergartens\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e300\u0026ndash;1000\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eLarge shopping centers\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eMetropolitan shopping centers, general malls\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e500\u0026ndash;1000\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eCultural and recreational venues\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eExhibition halls, museums, art galleries, libraries, theaters, concert halls, religious sites, bookstores\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e300\u0026ndash;1000\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eOffice facilities\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eOffice buildings, commercial buildings, construction sites\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e500\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ePublic accommodations\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eHotels, hostels, apartments, resorts\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e300\u0026ndash;2000\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv class=\"Section3\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv class=\"Section3\"\u003e(2) Geodetector Analysis\u003cbr /\u003e\n\u003cp\u003eIn practical applications, independent variables must be categorical. Continuous variables require discretization, as different discretization methods and interval counts can significantly influence the \u003cem\u003eq\u003c/em\u003e-value. Therefore, for each factor, the discretization scheme that maximized its \u003cem\u003eq\u003c/em\u003e-value was selected.\u003c/p\u003e\n\u003cp\u003eBased on this principle, the Geodetector was employed to examine the relationship between the spatial distribution of historical OHCA events in Qinhuai District, Nanjing, and a set of discretized explanatory variables. The explanatory power of each factor was quantified by its \u003cem\u003eq\u003c/em\u003e-value, calculated as follows Eq.\u0026nbsp;(3):\u003c/p\u003e\n\u003cdiv id=\"Equc\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equc\" class=\"mathdisplay\"\u003e$$\\:\\begin{array}{c}q=1-\\frac{{\\sum\\:}_{h=1}^{L}{N}_{h}{\\sigma\\:}_{h}^{2}}{N{\\sigma\\:}^{2}}\\#\\left(3\\right)\\end{array}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{N}\\)\u003c/span\u003e\u003c/span\u003e is the total number of grid cells, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{{\\sigma\\:}}^{2}\\:\\)\u003c/span\u003e\u003c/span\u003eis the overall variance of OHCA incidence, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{L}\\)\u003c/span\u003e\u003c/span\u003e is the number of strata, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{N}}_{\\text{h}}\\)\u003c/span\u003e\u003c/span\u003e is the number of cells in stratum \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{h}\\)\u003c/span\u003e\u003c/span\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\sigma\\:}{\\text{ₕ}}^{2}\\)\u003c/span\u003e\u003c/span\u003e is the within-stratum variance. The \u003cem\u003eq\u003c/em\u003e-value ranges from 0 to 1, with higher values indicating stronger explanatory power. Factor stratification was performed using the Jenks natural breaks method to minimize within-class variance and maximize between-class variance, consistent with prior spatial heterogeneity studies.\u003c/p\u003e\n\u003cp\u003eTo assess the combined effects of two factors, the interaction detector was applied. This method evaluates whether the interaction between environmental factors \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{X}_{1}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{X}}_{2}\\)\u003c/span\u003e\u003c/span\u003e enhances or weakens their explanatory power by comparing the interaction \u003cem\u003eq\u003c/em\u003e-value, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:q\\left({X}_{1}\\cap\\:{X}_{2}\\right),\\)\u003c/span\u003e\u003c/span\u003e with the individual \u003cem\u003eq\u003c/em\u003e-values\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\:q\\left({X}_{1}\\right)\\:\\)\u003c/span\u003e\u003c/span\u003eand \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:q\\left({X}_{2}\\right)\\:\\)\u003c/span\u003e\u003c/span\u003e[21].\u003c/p\u003e\n\u003cp\u003eTo evaluate the combined effects of two environmental factors, the interaction detector was applied. This method compares the interaction \u003cem\u003eq\u003c/em\u003e-value, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:q\\left({X}_{1}\\cap\\:{X}_{2}\\right),\\)\u003c/span\u003e\u003c/span\u003e with the individual \u003cem\u003eq\u003c/em\u003e-values\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\:q\\left({X}_{1}\\right)\\)\u003c/span\u003e\u003c/span\u003eand \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:q\\left({X}_{2}\\right)\\)\u003c/span\u003e\u003c/span\u003e to determine whether their joint influence enhances or weakens explanatory power. Interaction types were classified according to the criteria in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e:\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003ctable id=\"Tab4\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eCriteria for determining interaction types.\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eq\u003c/em\u003e-value\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eInteraction types\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{q(X}_{1}\\cap\\:{X}_{2})\\:\u0026lt;\\:\\text{m}\\text{i}\\text{n}\\:[{q(X}_{1}),\\:q\\left({X}_{2}\\right)\\)\u003c/span\u003e\u003c/span\u003e]\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eNonlinear weakening\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003emin [\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{q(X}_{1})\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:q\\left({X}_{2}\\right)\\)\u003c/span\u003e\u003c/span\u003e] \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\u0026lt;q(X}_{1}\\cap\\:{X}_{2})\\:\u0026lt;\\)\u003c/span\u003e\u003c/span\u003e max [\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{q(X}_{1})\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:q\\left({X}_{2}\\right)\\)\u003c/span\u003e\u003c/span\u003e]\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eUni-factor nonlinear weakening\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{q(X}_{1}\\cap\\:{X}_{2})\\:\u0026gt;\\:\\text{m}\\text{a}\\text{x}\\:[{q(X}_{1}),\\:q\\left({X}_{2}\\right)\\)\u003c/span\u003e\u003c/span\u003e]\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eBi-factor enhancement\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{q(X}_{1}\\cap\\:{X}_{2})\\:=\\:{q(X}_{1})+\\:q\\left({X}_{2}\\right)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eIndependence\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{q(X}_{1}\\cap\\:{X}_{2})\\:\u0026gt;\\:{q(X}_{1})+\\:q\\left({X}_{2}\\right)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eNonlinear enhancement\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv class=\"Section3\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv class=\"Section3\"\u003e(3) Candidate Area Screening\u003cbr /\u003e\n\u003cp\u003eThe study area was divided into 200m\u0026times;200m grid cells, consistent with AED coverage recommendations in dense urban settings. For each grid cell \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:j\\)\u003c/span\u003e\u003c/span\u003e, a composite AED demand index \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{C}_{j}\\)\u003c/span\u003e\u003c/span\u003e was calculated as Eq.\u0026nbsp;(4):\u003c/p\u003e\n\u003cdiv id=\"Equd\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equd\" class=\"mathdisplay\"\u003e$$\\:\\begin{array}{c}{C}_{j}={\\sum\\:}_{i=1}^{N}{\\omega\\:}_{i}\\bullet\\:{X}_{i,norm}^{j}\\#\\left(4\\right)\\end{array}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\omega\\:}_{i}\\)\u003c/span\u003e\u003c/span\u003e is the weight of factor \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:i\\)\u003c/span\u003e\u003c/span\u003e (its \u003cem\u003eq\u003c/em\u003e-value from Geodetector) and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{X}_{i,norm}^{j}\\)\u003c/span\u003e\u003c/span\u003eis the normalized value of factor \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:i\\)\u003c/span\u003e\u003c/span\u003e in grid \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:j\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003eGrids with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{C}_{j}\\:\\)\u003c/span\u003e\u003c/span\u003e\u0026gt; 0.269, (the mean value) were selected to balance coverage and feasibility. Candidate grids were spatially clustered to identify contiguous high-demand zones, which were cross-checked against existing AED sites to highlight underserved areas [\u003cspan class=\"CitationRef\"\u003e12\u003c/span\u003e].\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec7\" class=\"Section3\"\u003e\n\u003ch2\u003e2.3.2. Multi-Objective Optimization Model Construction\u003c/h2\u003e\n\u003cp\u003eThis study formulates the AED deployment problem as a multi‑objective optimization model based on the P‑center framework [\u003cspan class=\"CitationRef\"\u003e22\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e23\u003c/span\u003e]. The model simultaneously considers spatial fairness, service quality, economic efficiency, and coverage performance. The four objectives are defined as follows:\u003c/p\u003e\n\u003cp\u003e(1) Objective Functions\u003c/p\u003e\n\u003cp\u003eBased on the P-center model, four objectives were defined:\u003c/p\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003ch3\u003e1) Minimize maximum distance\u003c/h3\u003e\n\u003cdiv id=\"Eque\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Eque\" class=\"mathdisplay\"\u003e$$\\:\\begin{array}{c}min{Z}_{1}={max}_{i\\in\\:I,\\:\\:\\:j\\in\\:J}\\left\\{{d}_{ij}\\text{}\\cdot\\:{x}_{ij}\\text{}\\right\\}\\#\\left(5\\right)\\end{array}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eWhere\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\:I\\)\u003c/span\u003e\u003c/span\u003e is the set of OHCA demand points; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:J\\)\u003c/span\u003e\u003c/span\u003e is the set of candidate AED locations; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{d}_{ij}\\)\u003c/span\u003e\u003c/span\u003e is the Euclidean distance (m) from candidate \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:j\\)\u003c/span\u003e\u003c/span\u003e to demand point \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:i\\)\u003c/span\u003e\u003c/span\u003e;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\:{x}_{ij}=1\\)\u003c/span\u003e\u003c/span\u003e if demand \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:i\\)\u003c/span\u003e\u003c/span\u003e is assigned to candidate \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:j\\)\u003c/span\u003e\u003c/span\u003e, and 0 otherwise. This objective focuses on spatial equity: by minimizing the farthest service distance, the model ensures that even the most remote demand point is as close as possible to an AED, reducing disparities in access.\u003c/p\u003e\n\u003ch3\u003e2) Maximize average satisfaction\u003c/h3\u003e\n\u003cp\u003eSatisfaction \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:F\\left(t\\right)\\)\u003c/span\u003e\u003c/span\u003e is defined as:\u003c/p\u003e\n\u003cdiv id=\"Equf\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equf\" class=\"mathdisplay\"\u003e$$\\:\\begin{array}{c}F\\left(t\\right)=\\left\\{\\begin{array}{c}1+{R}_{0}\\bullet\\:{e}^{-{\\gamma\\:}t},\\:\\:t\u0026lt;{t}_{i}\\\\\\:\\frac{{\\text{T}}_{i}-t}{{\\text{T}}_{i}-{t}_{i}}+{R}_{0}{\\bullet\\:e}^{-{\\gamma\\:}t},\\:\\:{t}_{i}\\le\\:t\\le\\:{\\text{T}}_{i}\\\\\\:{{R}_{0}\\bullet\\:e}^{-{\\gamma\\:}t},\\:\\:t\u0026gt;{\\text{T}}_{i}\\end{array}\\right.\\#\\left(6\\right)\\end{array}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eThe objective function is:\u003c/p\u003e\n\u003cdiv id=\"Equg\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equg\" class=\"mathdisplay\"\u003e$$\\:\\begin{array}{c}max{Z}_{2}=\\frac{1}{N}\\sum\\:_{i\\in\\:I}\\sum\\:_{j\\in\\:J}{x}_{ij}\\bullet\\:F\\left({t}_{ij}\\text{}\\right)\\#\\left(7\\right)\\end{array}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:t\\)\u003c/span\u003e\u003c/span\u003e is the waiting time (min), \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{t}_{ij}\\:\\)\u003c/span\u003e\u003c/span\u003eis the time between \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:i\\:\\)\u003c/span\u003e\u003c/span\u003eand \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:j\\)\u003c/span\u003e\u003c/span\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\:N\\:\\text{i}\\text{s}\\:\\text{t}\\text{h}\\text{e}\\:\\)\u003c/span\u003e\u003c/span\u003etotal number of demand points. The discontinuities at \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{t}_{i}\\)\u003c/span\u003e\u003c/span\u003e=2 and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{T}}_{i}\\)\u003c/span\u003e\u003c/span\u003e=6 are intentional, reflecting clinically recognized thresholds in OHCA survival probability and public satisfaction [\u003cspan class=\"CitationRef\"\u003e24\u003c/span\u003e]. The first threshold (2 min) corresponds to the \u0026ldquo;golden response\u0026rdquo; window, while the second (6 min) represents the upper limit for effective defibrillation before survival rates drop sharply. This step-change design emphasizes the urgency of rapid AED access [\u003cspan class=\"CitationRef\"\u003e25\u003c/span\u003e].\u003c/p\u003e\n\u003ch3\u003e3) Minimize average treatment cost\u003c/h3\u003e\n\u003cdiv id=\"Equh\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equh\" class=\"mathdisplay\"\u003e$$\\:\\begin{array}{c}{minZ}_{3}=\\frac{1\\:}{N}\\sum\\:_{i\\in\\:I}\\left({C}_{0}+{\\text{C}}_{s}\\bullet\\:\\sum\\:_{j\\in\\:J}{x}_{ij}\\bullet\\:{t}_{ij}\\right)\\#\\left(8\\right)\\end{array}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{C}_{0}\\)\u003c/span\u003e\u003c/span\u003e = 5100 \u0026yen; is the basic treatment cost per case, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{C}_{s}\\)\u003c/span\u003e\u003c/span\u003e 5000 \u0026yen;/min is the delay cost per minute. This formulation separates the fixed cost (e.g., standard medical intervention) from the time‑dependent cost (e.g., deterioration due to delayed defibrillation), making the economic trade‑offs transparent [\u003cspan class=\"CitationRef\"\u003e26\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e27\u003c/span\u003e].\u003c/p\u003e\n\u003ch3\u003e4) Maximize coverage rate\u003c/h3\u003e\n\u003cdiv id=\"Equi\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equi\" class=\"mathdisplay\"\u003e$$\\:\\begin{array}{c}{maxZ}_{4}=\\frac{1}{N}\\sum\\:_{j\\in\\:J}{H}_{j}\\text{}\\cdot\\:{y}_{j}\\#\\left(9\\right)\\end{array}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:\\)\u003c/span\u003e \u003c/span\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{H}_{j}\\)\u003c/span\u003e\u003c/span\u003e is the number of covered OHCA points for site \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:j\\)\u003c/span\u003e\u003c/span\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{y}_{j}\\)\u003c/span\u003e\u003c/span\u003e is a binary site selection variable. Due to the unique assignment constraint (see below), each demand point is counted only once in\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\:{Z}_{4}\\)\u003c/span\u003e\u003c/span\u003e, avoiding double counting. This objective captures the overall spatial reach of the AED network [\u003cspan class=\"CitationRef\"\u003e23\u003c/span\u003e].\u003c/p\u003e\n\u003col\u003e\n\u003cli\u003e\n\u003cp\u003eConstraints\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eAssignment and Logic: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sum\\:_{j\\in\\:J}{x}_{ij}=1\\left(\\forall\\:i\\in\\:I,{x}_{ij}\\le\\:{y}_{j}\\right)\\)\u003c/span\u003e\u003c/span\u003e, each demand point is assigned to exactly one site.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eService and Facility Limits: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{t}_{ij}\\bullet\\:{x}_{ij}\\le\\:6\\left(\\forall\\:i\\in\\:I,j\\in\\:J,\\sum\\:_{j\\in\\:J}{y}_{j}=50\\right)\\)\u003c/span\u003e\u003c/span\u003e, service time must not exceed 6 minutes, and exactly 50 AEDs are deployed.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eVariable domains: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{ij},\\:\\:{y}_{j},{\\:c}_{i}\\in\\:\\left\\{\\text{0,1}\\right\\}\\)\u003c/span\u003e\u003c/span\u003e, binary variables for assignment, site selection, and coverage.\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ol\u003e\n\u003cdiv id=\"Sec12\" class=\"Section3\"\u003e\n\u003cdiv class=\"Heading\"\u003e2.3.3. Improved NSGA-II Algorithm for Model Solution\u003c/div\u003e\n\u003cp\u003eTo solve the proposed multi‑objective optimization model, an enhanced version of the Non‑dominated Sorting Genetic Algorithm II (NSGA‑II) was developed [\u003cspan class=\"CitationRef\"\u003e17\u003c/span\u003e]. The improvements aim to accelerate convergence, avoid premature stagnation in local optima, and maintain a balance between solution diversity and feasibility. These strategic enhancements are implemented through the following mechanisms:\u003c/p\u003e\n\u003col\u003e\n\u003cli\u003e\n\u003cp\u003eChromosome encoding: A binary (0\u0026ndash;1) encoding scheme was adopted to represent AED site selection decisions. Each gene corresponds to a candidate location, with a value of 1 indicating selection and 0 indicating exclusion. This representation is intuitive and facilitates the integration of location‑specific constraints [\u003cspan class=\"CitationRef\"\u003e28\u003c/span\u003e].\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eTabu list integration: To mitigate premature convergence and escape local optima, a Tabu list mechanism was incorporated. Recently visited solutions are recorded and prohibited from reappearing within a fixed tenure. The Tabu tenure is dynamically adjusted according to the population size and problem scale, ensuring a balance between exploration and exploitation [\u003cspan class=\"CitationRef\"\u003e29\u003c/span\u003e].\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eFitness function: The fitness function combines a weighted sum of normalized objective values with a penalty term for constraint violations:\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ol\u003e\n\u003cdiv id=\"Equj\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equj\" class=\"mathdisplay\"\u003e$$\\:\\begin{array}{c}{f}_{i}=\\:\\sum\\:_{k\\in\\:K}{z}_{i}^{k}+\\:\\lambda\\:\\:\\cdot\\:{l}_{0}\\#\\left(10\\right)\\end{array}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{f}_{i}\\)\u003c/span\u003e\u003c/span\u003e is the fitness value of the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{i}^{th}\\)\u003c/span\u003e\u003c/span\u003e individual; smaller values indicate better adaptability and higher priority for survival into the next generation. K\u0026thinsp;=\u0026thinsp;4, which is the number of objective functions, corresponding to:\u003c/p\u003e\n\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:{Z}_{1}\\)\u003c/span\u003e \u003c/span\u003e (minimize maximum distance), \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Z}_{2}\\)\u003c/span\u003e\u003c/span\u003e (maximize average satisfaction), \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Z}_{3}\\)\u003c/span\u003e\u003c/span\u003e (minimize average treatment cost), and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Z}_{4}\\)\u003c/span\u003e\u003c/span\u003e (maximize coverage rate).\u003c/p\u003e\n\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:{z}_{i}^{k}\\)\u003c/span\u003e \u003c/span\u003e is the value of the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{k}^{th}\\)\u003c/span\u003e\u003c/span\u003e objective function for the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{i}^{th}\\)\u003c/span\u003e\u003c/span\u003e individual, calculated from Eqs.\u0026nbsp;(5)\u0026ndash;(8).\u003c/p\u003e\n\u003cp\u003e\u0026lambda;\u0026thinsp;=\u0026thinsp;1000, the penalty coefficient for constraint violations, selected to strongly penalize infeasible solutions and enforce compliance with operational constraints such as the 6-minute golden rescue window.\u003c/p\u003e\n\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:{l}_{o}\\:\\)\u003c/span\u003e \u003c/span\u003eis the degree of constraint violation, e.g., the total minutes exceeding the 6-minute limit or the number of AEDs exceeding the deployment budget; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{l}_{o}=0\\:\\)\u003c/span\u003e\u003c/span\u003efor feasible solutions.\u003c/p\u003e\n\u003cp\u003eThis unweighted summation approach treats all objectives equally in the fitness evaluation, while the penalty term ensures that infeasible solutions are effectively discouraged during the evolutionary search [\u003cspan class=\"CitationRef\"\u003e18\u003c/span\u003e].\u003c/p\u003e\n\u003c/div\u003e"},{"header":"3. Results and analysis","content":"\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e3.1. Spatial Pattern of Existing AED Allocation\u003c/h2\u003e \u003cp\u003eThe spatial distribution of existing AEDs in Qinhuai District exhibited a distinct clustering pattern. The 1-standard deviation standard deviational ellipse analysis [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e] showed that 68% of AEDs were located within a northwest\u0026ndash;southeast \u0026ldquo;ring\u0026rdquo; configuration, characterized by central concentration and peripheral sparsity (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). This suggests that AED deployment has historically been concentrated in the urban core, likely reflecting higher population density, commercial activity, and public facility availability in central areas.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe average nearest neighbor (ANN) analysis further confirmed significant clustering [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. The observed mean nearest neighbor distance (206.39 m) was substantially shorter than the expected random distance (258.08 m), yielding an ANN ratio of 0.800 and a z-score of \u0026minus;\u0026thinsp;6025 (p\u0026thinsp;\u0026lt;\u0026thinsp;0.001). This statistically significant clustering indicates that AED placement is non-random and influenced by socio-economic and infrastructural factors.\u003c/p\u003e \u003cp\u003eKernel density estimation [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e] identified four high-density AED clusters in Hongwulu, Chaotiangong, Daguanglu, and Fuzimiao Streets (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). These areas correspond to major commercial and cultural hubs, indicating that AED deployment has been prioritized in zones with high pedestrian traffic and public gatherings. Peripheral residential areas remain underserved, highlighting potential inequities in spatial accessibility.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003e3.2. Geodetector Results\u003c/h2\u003e \u003cdiv id=\"Sec16\" class=\"Section3\"\u003e \u003ch2\u003e3.2.1. Factor Detector\u003c/h2\u003e \u003cp\u003eThe factor detector quantified the explanatory power of various socio-demographic and infrastructural variables on AED demand (Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e). The results indicate a clear hierarchical influence among the factors. The highest \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:q\\)\u003c/span\u003e\u003c/span\u003e-values were observed for susceptible population density (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{a}_{2}\\)\u003c/span\u003e\u003c/span\u003e, q\u0026thinsp;=\u0026thinsp;0.8531) and resident population density (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{a}_{1}\\)\u003c/span\u003e\u003c/span\u003e, q\u0026thinsp;=\u0026thinsp;0.7941). This confirms that AED deployment is most strongly associated with areas of high population density, consistent with core public health planning principles.\u003c/p\u003e \u003cp\u003eNotably, while residential areas remain the primary focus of AED coverage due to the high frequency of indoor cardiac events [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e], our results highlight the critical role of public mobility nodes. Specifically, shopping mall density (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{c}_{5}\\)\u003c/span\u003e\u003c/span\u003e, q\u0026thinsp;=\u0026thinsp;0.5345) and transportation hubs (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{c}_{1}\\)\u003c/span\u003e\u003c/span\u003e, q\u0026thinsp;=\u0026thinsp;0.5019) exhibit substantial explanatory power. This aligns with the perspective that population mobility is a key determinant of AED demand in dense urban environments [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]. Our findings suggest that in hyper-dense districts like Qinhuai, the \"Mobile Population Risk\" at commercial centers is a dominant driver of AED demand, complementing traditional resident-based allocation strategies.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eFactor detector results.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFactor\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eq\u003c/em\u003e-Value\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRanking\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{a}_{2}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.8531\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{a}_{1}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.7941\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{c}_{5}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.5345\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{c}_{1}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.5019\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{c}_{8}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.4935\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{c}_{2}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.4416\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{c}_{6}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.3853\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{b}_{2}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.3652\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{c}_{4}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.3468\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{c}_{7}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.3292\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{c}_{3}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.2851\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{d}_{1}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.1528\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{b}_{1}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.0396\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section3\"\u003e \u003ch2\u003e3.2.2. Interaction Detector\u003c/h2\u003e \u003cp\u003eThe interaction detector results (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e) reveal that all factor pairs exhibit synergistic enhancement, with the explanatory power radiating from the demographic core at the bottom-left toward urban functional variables at the top-right. The peak interaction occurs between population density and the high-risk population (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{a}_{1}\\cap\\:{a}_{2}=0.9621\\)\u003c/span\u003e\u003c/span\u003e), establishing the primary spatial template for AED demand at the heatmap's origin. Conversely, a saturation effect is observed as the analysis shifts toward environmental factors (e.g., \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{a}_{1}\\cap\\:{d}_{1}=0.8153\\)\u003c/span\u003e\u003c/span\u003e), where \u003cem\u003eq\u003c/em\u003e-values plateau due to the overwhelming independent influence of the demographic core.\u003c/p\u003e \u003cp\u003eSignificant planning insights emerge from the high-intensity synergies between the high-risk population (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{a}_{2}\\)\u003c/span\u003e\u003c/span\u003e) and functional urban nodes, specifically with accommodation density (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{a}_{2}\\cap\\:{c}_{8}=0.9086\\)\u003c/span\u003e\u003c/span\u003e), sports facility density (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{a}_{2}\\cap\\:{c}_{2}=0.8940\\)\u003c/span\u003e\u003c/span\u003e), and shopping mall density (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{a}_{2}\\cap\\:{c}_{5}=0.8925\\)\u003c/span\u003e\u003c/span\u003e). These findings, visualized in the mid-section of the matrix, underscore that OHCA risk is most effectively predicted where vulnerable demographics intersect with public activity hotspots characterized by high foot traffic or physical exertion. Consequently, AED deployment strategies should transcend basic population metrics to prioritize these high-synergy functional intersections [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section3\"\u003e \u003ch2\u003e3.2.3. AED Demand Index\u003c/h2\u003e \u003cp\u003eThe calculated AED Demand Index (ADI) ranges from 0.033 to 0.764, with a mean value of 0.2862. High-demand grids (ADI\u0026thinsp;\u0026gt;\u0026thinsp;0.2862) are primarily clustered within Chaotiangong, Hongwulu, and Fuzimiao Streets, representing 41.8% of the total grid cells (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e). These areas overlap substantially with the high-density AED clusters identified earlier, but also highlight additional underserved zones with high predicted demand [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eAmong the 561 total candidate grids, 383 (68.3%) were identified as underserved zones. This selection process reflects a rigorous, data-driven prioritization that integrates spatial clustering, socio-demographic factors, and accessibility constraints, ensuring that future installations target the urban intersections with the most acute needs [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec19\" class=\"Section2\"\u003e \u003ch2\u003e3.3. Spatial Evaluation of Optimized AED Deployment\u003c/h2\u003e \u003cp\u003eThe E-NSGA-II algorithm converged to a Pareto-optimal front, providing a diverse range of candidate solutions for the AED allocation problem. To determine the most effective deployment strategy from this candidate set, the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) was employed. By evaluating the relative closeness of each candidate to the ideal solution across all objective functions, a comprehensive optimal solution was identified. This scheme was selected as the final recommended deployment strategy due to its superior capability in balancing spatial equity\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\:\\left({Z}_{1}\\right)\\)\u003c/span\u003e\u003c/span\u003e, social satisfaction \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left({Z}_{2}\\right)\\)\u003c/span\u003e\u003c/span\u003e, economic efficiency (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Z}_{3}\\)\u003c/span\u003e\u003c/span\u003e), and time-critical coverage (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Z}_{4}\\)\u003c/span\u003e\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe comprehensive performance metrics for the three scenarios are summarized in Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. Compared to the original scheme, TOPSIS-based optimal solution achieved a transformative reduction in \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Z}_{1}\\)\u003c/span\u003e\u003c/span\u003e by 55.3%, effectively shortening the maximum travel distance for residents from 632.46 m to 282.84 m. This drastic improvement directly enhances the likelihood of timely defibrillation during the critical \"golden window\" of out-of-hospital cardiac arrest [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. Average satisfaction (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Z}_{2}\\)\u003c/span\u003e\u003c/span\u003e) increased to 0.997 (a 9.1% improvement), reflecting a near-perfect alignment between AED placement and user accessibility expectations [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]. Simultaneously, treatment costs (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Z}_{3}\\)\u003c/span\u003e\u003c/span\u003e) were reduced by 21.3%, demonstrating that superior coverage can coexist with enhanced economic efficiency. Most notably, the coverage rate (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Z}_{4}\\)\u003c/span\u003e\u003c/span\u003e) reached a comprehensive 100%, uniformly eliminating all previous time-violation points and ensuring every resident is within the recommended response radius [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e]. Against the P-center model, the TOPSIS-based optimal solution demonstrated superior balanced performance. While the P-center model focuses exclusively on equity, the TOPSIS solution achieved 1.7% lower treatment costs (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Z}_{3}\\)\u003c/span\u003e\u003c/span\u003e) and 0.9% higher satisfaction (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Z}_{2}\\)\u003c/span\u003e\u003c/span\u003e) while maintaining the same optimal distance and coverage standards. These results demonstrate that the proposed multi-objective approach, refined through TOPSIS, significantly outperforms traditional single-objective models by maximizing cost-effectiveness and coverage equity simultaneously [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eObjective function values of optimal schemes.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eScheme\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{Z}}_{1}\\)\u003c/span\u003e\u003c/span\u003e\u0026nbsp;(m)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{Z}}_{2}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{Z}}_{3}\\)\u003c/span\u003e\u003c/span\u003e (\u0026yen;)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{Z}}_{4}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTOPSIS-based optimal solution\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e282.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.997\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e10,998.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eP-center\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e282.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.988\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e11,187.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOriginal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e632.46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.914\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e13,973.29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.966\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eAs illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e, the spatial pattern of the optimal scheme closely follows the existing AED layout, which is already concentrated around hospitals, major commercial corridors, and transport hubs. Building on this foundation, the model reallocates and adds new devices primarily to high‑demand grids identified earlier, especially in peripheral residential neighborhoods, school catchment areas, and community service centers that were previously underserved. By simultaneously leveraging the existing network and strategically reinforcing weak links, this deployment pattern not only closes critical coverage gaps but also better aligns with the study\u0026rsquo;s overarching goal of enhancing both equity and efficiency in AED accessibility [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn the AED location optimization experiment, the E‑NSGA‑II (enhanced with a Tabu mechanism) demonstrated clear advantages over the standard NSGA‑II in both efficiency and solution quality. Under identical population and iteration settings, E‑NSGA‑II reduced computational time by 27.5%, requiring only 47.95 s to converge compared with 66.11 s for the baseline. Although the enhanced algorithm generated a slightly smaller set of non-dominated solutions (193 vs. 220), it achieved a higher Hypervolume (0.076586 vs. 0.074736) and a superior Spread index (1.0008 vs. 1.0010). These metrics indicate that the proposed algorithm provides a more comprehensive and balanced representation of the multi-objective trade‑off space, ensuring that the resulting deployment schemes are both mathematically robust and spatially representative.\u003c/p\u003e \u003c/div\u003e"},{"header":"4. Discussion","content":"\u003cdiv id=\"Sec21\" class=\"Section2\"\u003e \u003ch2\u003e4.1. Driving Mechanisms and Algorithmic Response\u003c/h2\u003e \u003cp\u003eThe factor detector results (Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e) provide a robust quantitative basis for understanding the spatial heterogeneity of AED demand. High-risk population density (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{a}_{2}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:q=0.8531\\)\u003c/span\u003e\u003c/span\u003e) and resident population density (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{a}_{1}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:q=0.7941\\)\u003c/span\u003e\u003c/span\u003e) emerged as the primary anchors of the spatial template. This hierarchical influence confirms that AED deployment remains fundamentally rooted in high-density residential fabrics where the base probability of indoor OHCA events is highest [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe interaction detector (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e) further reveals a synergistic \"radiating\" effect. The peak interaction occurs between \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{a}_{1}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{a}_{2}\\)\u003c/span\u003e\u003c/span\u003e (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{a}_{1}\\cap\\:{a}_{2}=0.9621\\)\u003c/span\u003e\u003c/span\u003e), establishing a robust demographic core at the heatmap\u0026rsquo;s origin. Conversely, a saturation effect is observed as the analysis shifts toward environmental factors (e.g., \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{a}_{1}\\cap\\:{d}_{1}=0.8153\\)\u003c/span\u003e\u003c/span\u003e), where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:q\\)\u003c/span\u003e\u003c/span\u003e-values plateau due to the overwhelming independent influence of the demographic core. Significant planning insights emerge from the high-intensity synergies between the high-risk population (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{a}_{2}\\)\u003c/span\u003e\u003c/span\u003e) and functional nodes, such as accommodation (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{a}_{2}\\cap\\:{c}_{8}=0.9086\\)\u003c/span\u003e\u003c/span\u003e), sports facilities (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{a}_{2}\\cap\\:{c}_{2}=0.8940\\)\u003c/span\u003e\u003c/span\u003e), and shopping malls (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{a}_{2}\\cap\\:{c}_{5}=0.8925\\)\u003c/span\u003e\u003c/span\u003e). These findings underscore that OHCA risk is most effectively predicted where vulnerable demographics intersect with public activity hotspots characterized by high foot traffic or physical exertion.\u003c/p\u003e \u003cp\u003eTo effectively address these complex demand patterns, the E‑NSGA‑II algorithm demonstrated superior technical efficacy. By integrating a Tabu list mechanism and 2-opt mutation, the algorithm achieved a 27.5% reduction in computational time (47.95 s vs. 66.11 s) and successfully avoided the \"clustering trap\"\u0026mdash;a common issue where solutions gravitate toward a local optimum at the expense of global equity. The resulting Pareto-optimal scheme facilitated a transformative 55.3% reduction in maximum travel distance (from 282.84 m to 632.46 m), proving that heuristic refinements are essential for translating complex geospatial drivers into mathematically efficient deployment schemes [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec22\" class=\"Section2\"\u003e \u003ch2\u003e4.2. Strategic Redundancy and Spatial Equity\u003c/h2\u003e \u003cp\u003eA key finding from our optimization results is the allocation of additional units even to certain well-served sectors in the central district. This \"strategic redundancy\" is not a resource waste but a calculated response to extreme demographic pressure (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{a}_{1},{a}_{2}\\)\u003c/span\u003e\u003c/span\u003e). In hyper-dense urban grids, achieving basic spatial coverage (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Z}_{1}\\)\u003c/span\u003e\u003c/span\u003e) is insufficient to guarantee survival; the patient satisfaction (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Z}_{2}\\)\u003c/span\u003e\u003c/span\u003e) must also account for the probability of concurrent cardiac events and the micro-scale impedance of complex street networks. The near-perfect satisfaction level (0.997) suggests that our model optimized the \"perceived accessibility,\" ensuring that every resident is within a reliable response radius during the critical \"6-minute golden window\" [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eFurthermore, the multi-objective approach balances cost-effectiveness (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Z}_{3}\\)\u003c/span\u003e\u003c/span\u003e) with socio-economic equity. While income level (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{d}_{1}\\)\u003c/span\u003e\u003c/span\u003e) showed a lower independent explanatory power, its inclusion in the optimization ensures that \"defibrillation equity\" is maintained. This prevents the emergence of \"survival deserts\" in low-income residential blocks, where residents might otherwise face reduced survival chances due to economic disadvantage [\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e]. By prioritizing these underserved yet high-risk intersections, the model moves beyond simple distance-based coverage toward a more socially just distribution of emergency resources.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec23\" class=\"Section2\"\u003e \u003ch2\u003e4.3. Policy Implications and Research Trajectories\u003c/h2\u003e \u003cp\u003eThe data-driven ADI provides a granular prioritization framework for urban planners. Based on our findings, we propose a transition toward an ADI-led allocation framework, prioritizing \"survival deserts\" like Chaotiangong and Hongwulu Streets. This strategy should be twofold: first, leveraging urban renewal projects to \"embed\" AEDs into new public service centers; and second, implementing Socio-economic Equity Correction through targeted funding for low-income residential blocks (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{d}_{1}\\)\u003c/span\u003e\u003c/span\u003e), ensuring that economic disadvantage does not translate into reduced survival chances [\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e]. Furthermore, training programs should be concentrated at high-synergy functional nodes (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{c}_{2},{c}_{8}\\)\u003c/span\u003e\u003c/span\u003e) to translate physical proximity into effective bystander intervention.\u003c/p\u003e \u003cp\u003eHowever, the transition from static optimization to real-world deployment faces ongoing challenges. The reliance on static historical data remains a primary limitation, as it fails to capture the dynamic \"temporal risk\" of cities where population shifts significantly between day and night. Future research trajectories should focus on integrating real-time mobile signaling data to enable dynamic AED allocation. Additionally, expanding the objective set (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Z}_{Z}\\)\u003c/span\u003e\u003c/span\u003e) to include maintenance logistics and bystander psychology would enhance the operational sustainability of the network. Testing this framework in lower-density rural environments remains essential to confirm its generalizability and to refine penalty coefficients for diverse spatial contexts [\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003eThis study developed and validated a comprehensive spatial allocation framework for AEDs that integrates spatial factor detection, a patient-centric multi-objective optimization model, and an enhanced evolutionary algorithm. The framework was designed to address the dual challenge of improving AED accessibility while ensuring equitable distribution, particularly in high-risk urban environments. By combining Geodetector with a multi-objective model, the approach simultaneously quantified the spatial correlation between OHCA incidence and influencing factors, and optimized AED placement to balance efficiency, patient needs, and operational constraints.\u003c/p\u003e \u003cp\u003eThe Geodetector analysis revealed that high-risk population density (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{a}_{2},q=0.8531\\)\u003c/span\u003e\u003c/span\u003e) and resident population density (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{a}_{1},q=0.7941\\)\u003c/span\u003e\u003c/span\u003e) were the dominant drivers of AED demand. Their interaction exhibited a powerful synergistic effect, with the peak interaction occurring between these two demographic variables (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{a}_{1}\\cap\\:{a}_{2}=0.9621\\)\u003c/span\u003e\u003c/span\u003e), establishing a robust demographic core for the spatial risk template. Furthermore, significant synergistic explanatory power was observed when demographics intersected with functional nodes, such as accommodation (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{a}_{2}\\cap\\:{c}_{8}=0.9086\\)\u003c/span\u003e\u003c/span\u003e) and sports facilities (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{a}_{2}\\cap\\:{c}_{2}=0.8940\\)\u003c/span\u003e\u003c/span\u003e). These findings provide a robust, evidence-based foundation for identifying priority deployment areas.\u003c/p\u003e \u003cp\u003eThe multi-objective model incorporated four objectives\u0026mdash;coverage (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Z}_{1}\\)\u003c/span\u003e\u003c/span\u003e), patient satisfaction (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Z}_{2}\\)\u003c/span\u003e\u003c/span\u003e), cost (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Z}_{3}\\)\u003c/span\u003e\u003c/span\u003e), and coverage equity (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Z}_{4}\\)\u003c/span\u003e\u003c/span\u003e)\u0026mdash;and achieved a transformative 55.3% reduction in maximum travel distance (from 632.46 m to 282.84 m) while maintaining a near-perfect satisfaction level (0.997). This demonstrates clear advantages over traditional single-objective approaches, which often neglect patient-oriented metrics and spatial equity.\u003c/p\u003e \u003cp\u003eAlgorithmic performance tests confirmed that the E-NSGA-II, enhanced with a Tabu list mechanism and 2-opt mutation, significantly outperformed the standard NSGA-II. These refinements led to a 27.5% reduction in computational time (47.95 s vs. 66.11 s) and enhanced the algorithm\u0026rsquo;s global search capability, ensuring the optimization process avoided premature convergence and successfully navigated complex urban constraints. The optimized schemes generated for Qinhuai District validated the method\u0026rsquo;s feasibility, producing deployment plans that are both operationally practical and clinically relevant.\u003c/p\u003e \u003cp\u003eBeyond methodological contributions, the results have direct policy and planning implications. High-demand areas such as Chaotiangong and Hongwulu Streets should be prioritized for AED installation, with the ADI serving as a transparent tool for standardizing allocation. Targeted subsidies should be provided to high-risk, low-income areas to address equity gaps, and public training should be expanded to translate accessibility into actual life-saving interventions.\u003c/p\u003e \u003cp\u003eThis research offers a scalable framework extensible to other emergency medical resources. Future studies will prioritize dynamic allocation by integrating real-time mobile signaling and traffic data, while expanding the objective function to incorporate maintenance logistics and bystander usage rates. By bridging spatial analytics, patient-centered optimization, and advanced evolutionary computation, this study contributes both a methodological innovation and a practical decision-support tool for enhancing emergency medical service efficiency and improving OHCA survival rates in diverse urban settings.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eConflict of Interest\u003c/h2\u003e \u003cp\u003eThe authors declare that they have no conflicts of interest.\u003c/p\u003e \u003c/p\u003e\u003cp\u003e \u003ch2\u003eEthics Statement\u003c/h2\u003e \u003cp\u003eThis study does not involve human participants or identifiable personal data and therefore did not require ethics approval.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eFunding\u003c/h2\u003e \u003cp\u003eThis research was supported by the National Natural Science Foundation of China (Grant No. 42371444); the Open Fund of the State Key Laboratory of Remote Sensing Science (Grant No. OFSLRSS202430); the Opening Foundation of Key Laboratory (Grant No. JSHD202407); and the Jiangsu Province Capability Improvement Project through Science, Technology and Education (Grant No. ZDXYS202210). Additional support was provided by the 2023 Jiangsu Provincial Institute of Public Health Emergency Research Project, Current Status and Optimization Strategies for Automated External Defibrillator Deployment Based on GIS (Grant No. JSWSYJ‑20230105).\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eJia Wang designed the study, conducted the spatial analysis, developed the optimization models, and drafted the manuscript. Jingyi Zhou contributed to data curation, preprocessing, and statistical analysis. Shaohua Wang assisted with methodological refinement and provided technical support for spatial modeling. Min Zhang offered domain expertise in public health emergency management and contributed to the interpretation of results. Jie Shen supervised the study, guided the research framework, and critically revised the manuscript. Tianhao Zhao supported visualization, mapping, and model validation. Chenxin Xiao contributed to literature review, data verification, and manuscript editing. All authors reviewed and approved the final version of the manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eThe authors would like to express their sincere gratitude to the Aerospace Information Research Institute, Chinese Academy of Sciences, for providing technical support and data coordination. The authors also thank the Jiangsu Provincial Health Commission for facilitating access to relevant public health data and administrative resources that made this study possible.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eAggregated spatial datasets generated during this study, including the AED Demand Index and optimization outputs, are available from the corresponding author upon reasonable request. 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Socioecon Plann Sci. 2022;84:101416. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.seps.2022.101416\u003c/span\u003e\u003cspan address=\"10.1016/j.seps.2022.101416\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"international-journal-of-health-geographics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"ijhg","sideBox":"Learn more about [International Journal of Health Geographics](http://ij-healthgeographics.biomedcentral.com/)","snPcode":"12942","submissionUrl":"https://submission.nature.com/new-submission/12942/3","title":"International Journal of Health Geographics","twitterHandle":"@IJHGeo","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"BMC/SO AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Automated External Defibrillators (AEDs), spatial accessibility, Geodetector, multi-objective optimization, NSGA-II, emergency response planning, health equity","lastPublishedDoi":"10.21203/rs.3.rs-8600130/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8600130/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003ch2\u003eBackground\u003c/h2\u003e \u003cp\u003eOut-of-hospital cardiac arrest (OHCA) remains a critical urban health challenge due to persistently low survival rates and uneven access to automated external defibrillators (AEDs). Existing deployment strategies often rely on heuristic decisions, limiting their ability to address spatial disparities in emergency response. This study aims to develop a spatially informed, data-driven framework to optimize AED placement and improve urban emergency response capacity.\u003c/p\u003e\u003ch2\u003eMethods\u003c/h2\u003e \u003cp\u003eUsing Qinhuai District in Nanjing as a case study, we applied Geodetector to identify the spatial determinants of OHCA risk. High-risk population density and its interaction with resident density emerged as dominant factors, informing the construction of a high-resolution AED Demand Index for candidate site selection. We then formulated a multi-objective optimization model to balance service coverage, perceived accessibility, and cost-effectiveness. The model was solved using an enhanced NSGA-II algorithm incorporating tabu search and 2-opt mutation.\u003c/p\u003e\u003ch2\u003eResults\u003c/h2\u003e \u003cp\u003eThe optimized layouts demonstrated substantial improvements over existing AED configurations. The maximum service distance decreased by 55.3%, and overall satisfaction reached a near-optimal level of 0.997. The enhanced algorithm also achieved notable computational gains compared with standard approaches.\u003c/p\u003e\u003ch2\u003eConclusions\u003c/h2\u003e \u003cp\u003eThe proposed GIS-based optimization framework provides a scalable and evidence-based tool for improving AED deployment in dense urban environments. By integrating spatial risk detection with multi-objective optimization, this approach supports urban planners in reducing spatial inequities and strengthening emergency response systems.\u003c/p\u003e","manuscriptTitle":"A GIS‑Based Multi‑Objective Optimization Strategy for Urban Automated External Defibrillator Deployment","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-10 14:37:46","doi":"10.21203/rs.3.rs-8600130/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-04-30T19:55:59+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-04-17T08:14:05+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-03-20T14:56:48+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"309643137450516282142797747349965964790","date":"2026-03-10T13:58:09+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"170029019153395811912776144410167848109","date":"2026-03-06T17:59:31+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"287047722828346927994357517638151383259","date":"2026-03-06T04:58:38+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-02-05T15:40:00+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-01-15T03:25:36+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-01-15T03:24:40+00:00","index":"","fulltext":""},{"type":"submitted","content":"International Journal of Health Geographics","date":"2026-01-14T09:27:29+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"international-journal-of-health-geographics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"ijhg","sideBox":"Learn more about [International Journal of Health Geographics](http://ij-healthgeographics.biomedcentral.com/)","snPcode":"12942","submissionUrl":"https://submission.nature.com/new-submission/12942/3","title":"International Journal of Health Geographics","twitterHandle":"@IJHGeo","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"BMC/SO AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"9a0d98fe-2cc7-4082-8862-6ec760691d01","owner":[],"postedDate":"February 10th, 2026","published":true,"recentEditorialEvents":[{"type":"decision","content":"Revision requested","date":"2026-04-30T19:55:59+00:00","index":"","fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"in-revision","subjectAreas":[],"tags":[],"updatedAt":"2026-04-30T20:08:38+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-10 14:37:46","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8600130","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8600130","identity":"rs-8600130","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}