© Q. Wang, Published by EDP Sciences, 2025

1 Introduction

Urban public space has multi-dimensional social, functional, and cultural values in human settlement systems. With the continuous changes in urban population structure and the diversification of social interaction needs, the traditional public space design paradigm dominated by functional zoning and spatial configuration has gradually failed to meet people’s multiple demands for comfort, safety, and interaction [1,2]. Urban public space design with humanization as the core concept is becoming a key issue in current urban renewal and high-quality development [3–5]. In spatial practice, although a large number of projects claim to focus on user experience, in actual operation, design strategies often fall into the one-way optimization of individual indicators or groups. Whether it is the rest space strengthened for the elderly or the activity facilities set up for children, the spatial dimension reflects the one-dimensional expression of humanized targets, lacking interactive considerations for the coexistence of different user groups in the same space [6,7]. As a result, although a certain optimization effect has been achieved in local dimensions of public spaces, it is difficult to support complex use in multiple scenarios, dynamic coexistence of user groups, and long-term spatial adaptation.

The technical bottlenecks of existing public space optimization strategies are mainly concentrated in three aspects: first, there is a lack of a unified and quantifiable multi-dimensional humanized indicator system, which makes it difficult to unify the balance and evaluation between different goals; second, user behavior data has not been fully integrated into the design process, resulting in a weak response of the design scheme to real usage preferences [8]; third, the optimization process is separated from the spatial simulation feedback mechanism and lacks a closed-loop adjustment mechanism for dynamic behavior response. The final design scheme cannot guarantee its stable adaptability and spatial performance consistency in real scenarios [9]. In the context of increasingly intelligent design responses and data-driven becoming the mainstream, the above problems significantly restrict the systematic implementation path of humanized goals and also put forward higher requirements for the integration capabilities of design tools and processes. This research gap not only limits the scientificity and effectiveness of design, but also hinders the adaptability of urban public spaces in complex and changing usage scenarios. Therefore, building a systematic design framework that can balance the needs of multiple users, coordinate multi-dimensional performance indicators, and have dynamic adaptability has become a key issue that needs to be urgently addressed in the current field of humanized design of urban public spaces. This study summarizes the challenges of humanized design of urban public spaces into three key dimensions: indicator dimension, data dimension, and process dimension. In terms of metrics, existing research lacks a unified, quantifiable, and multidimensional human-centric indicator system, making it difficult to balance and evaluate different objectives. In terms of data, user behavior data has not been fully integrated into the design process, resulting in poor responsiveness to real-world user preferences. In terms of process, the optimization process is disconnected from spatial simulation feedback mechanisms, lacking closed-loop regulation for dynamic behavioral responses. These three intertwined challenges form the core cause of the current “local optimum” dilemma in urban public space design. Based on this, this study proposes a multi-objective optimization design method that integrates user behavior preferences, multidimensional performance indicators, and pedestrian behavior simulation, aiming to construct a systematic, data-driven human-centric design framework.

The innovations of this study include using the NSGA-III non-dominated sorting genetic algorithm as the core optimization tool to construct a human-oriented indicator system centered on comfort, safety, and interactivity. Dynamic generation of spatial configurations is achieved through parametric modeling, and crowd classification and preference modeling are performed in conjunction with real user behavior data [10,11]. At the simulation level, pedestrians are simulated using AnyLogic, and the behavioral adaptability of the design schemes is tested using quantitative indicators such as heat maps and path overlap. The results are then fed back into the optimization system to achieve dynamic iteration of the crowd solution and closed-loop adjustment of the design schemes [12,13]. This addresses the “design-use” disconnect in traditional optimization, ensuring that the results not only achieve Pareto optimality in theory but also demonstrate good adaptability and stability in practical applications, filling the critical gap between “theoretical optimality” and “practical feasibility” in the human-oriented design of urban public spaces. Experiments demonstrate that this method effectively alleviates the conflicting objectives inherent in traditional design and significantly enhances the multi-objective coordination of public spaces—the weighted average satisfaction rate increased by 32.8%, safety risks decreased by 30.8%–63.2%, and interaction enhancement increased by 71.2%. Through this method, the study not only achieves the systematic coordination and intelligent generation of public space design objectives, but also proposes a methodologically-based, humanistic strategy optimization paradigm suitable for multi-group shared scenarios, breaking through the reliance on traditional, experience-driven design paths. This research provides a theoretical foundation and practical path for constructing an intelligent, multi-objective coordination mechanism for urban public space design, possessing high practical application value and research and promotional significance.

2 Related work

In the past five years, research on the humanized design of urban public spaces has focused on the behavioral habits of specific groups of people, the barrier-free performance of site facilities, and the evaluation model of green landscape configuration and visual accessibility [14,15]. Research methods are mainly based on questionnaire surveys, observation records, or geographic information system (GIS) spatial analysis to extract design strategies or make optimization suggestions. Design research for the elderly group focuses on path continuity, seat density, and coverage of summer and rain shelter facilities, while research for children focuses on accessibility, safety, and the combination frequency of interactive play equipment [16,17]. Although this type of research has strong guiding significance for the target group, it cannot integrate the needs of multiple groups due to data acquisition limitations and single methods and ignores the conflicting behavioral patterns among space users [18,19]. At the same time, most studies do not adopt a system optimization mechanism and lack quantifiable indicator integration solutions, and design suggestions mostly remain at the empirical level and cannot transform into an executable design logic system. The “local optimum” problem refers to the tendency in urban public space design to overly focus on optimizing a single user group or specific functional dimension, while neglecting the dynamic balance between different user needs and the systematic allocation of spatial resources. For example, in a plaza designed for the elderly, excessive seating density, while meeting their rest needs, reduces children’s activity space and leads to decreased interactivity. Another example is the excessive planting of tall trees for increased shading, which improves thermal comfort but reduces lighting uniformity due to excessive shading, increasing safety risks.

In order to solve the above problems, some studies have begun to try to integrate multi-objective optimization methods into urban design practice to solve the problem that traditional empirical design is difficult to consider complex performance indicators [20]. Methods such as genetic algorithms, particle swarm algorithms, simulated annealing algorithms, and random forests have been preliminarily applied in the fields of building energy consumption optimization, traffic flow layout, and spatial layout optimization [21,22]. Multi-objective optimization methods represented by non-dominated sorting genetic algorithms have good solution set diversity and convergence stability, and are suitable for solving complex system design tasks where there are conflicts or mutual constraints between multiple objective functions. In urban public space design, some scholars have tried to establish site models through parametric modeling tools and apply evolutionary algorithms to automatically generate and select greening configurations, shading components, and node layouts to improve spatial performance [23]. Olivos and Caceres [24] conducted multi-objective optimization on the location of ambulances in the Antofagasta region of Chile, balancing response time and service coverage, proving the practicality of multi-objective methods in the layout of public service facilities and providing methodological support for the rational configuration of service facilities in public spaces. Tadaros and Migdalas [25] systematically reviewed the research progress of dual-objective and multi-objective positioning path problems and proposed a comprehensive classification framework, which provided a theoretical basis for understanding and solving path planning and node layout problems in urban space. Chupradit et al. [26] constructed a multi-objective mathematical model for transportation network planning based on population distribution. This model comprehensively considers transportation efficiency, fairness, and construction costs, and provides a quantitative tool for the collaborative design of urban public space and transportation systems.

3 Construction of optimization strategies for urban public space design variables

3.1 Construction of multi-dimensional humanized target indicator system

The construction of the humanized target system in this study is based on the three types of spatial performance, namely comfort, safety, and interaction, and extracts a total of 9 core indicators, namely thermal comfort, noise intensity, green shade coverage, visual accessibility, lighting uniformity, path avoidance, stay feasibility, behavioral interaction frequency, and activity support capacity [27,28]. To ensure that indicators of different dimensions can be used for unified multi-objective optimization function calculation, it is necessary to first standardize each indicator so that it is uniformly mapped to the [0, 1] interval to meet the fitness function input requirements of the genetic algorithm.

In the comfort dimension, thermal comfort is generated by importing the measured temperature, relative humidity, and wind speed data of the site into ENVI-met software to generate microclimate simulation results. The improved predicted mean vote (PMV) indicator is used for quantification. The numerical range is set to [−3,3], and it is converted to a 0–1 value range through a linear normalization formula, with the goal of being closest to 0 (thermal neutrality). The noise intensity is collected in different time periods using a field noise instrument (with a range of 30–90 dB). According to the “Standard of Environmental Noise of Urban Area” (GB3096-2008), 60 dB is set as the cutoff point, and areas above this value are standardized according to the exponential decay method. The green shade coverage rate is based on drone aerial images, and the normalized difference vegetation index (NDVI) and threshold segmentation algorithm are used to extract the shaded area. The spatial interpolation is combined with the light sensor data arranged at the on-site sampling points, and the coverage ratio per unit area is quantified and normalized.

In the safety dimension, visual accessibility is analyzed based on the viewshed analysis of Rhino and Ladybug plug-ins. Each observation point is set to an observation height of 1.6 m and a viewing angle of 120°, and the ratio of the total area of view to the degree of obstruction is calculated. The result is standardized with a maximum accessibility rate of 1. The lighting uniformity is modeled using DIALux to simulate the illumination distribution under different lamp arrangements at night. The minimum illumination standard of 15lx is used to calculate the ratio of the illumination variance to the mean and convert it into a uniformity score. Path avoidance combines OpenCV to identify path intersections and boundary spacing and generates an avoidance index matrix, in which areas with high intersection density and sharp corners are given lower weights. Finally, the uncertainty interference is processed through the fuzzy weighting method to output a stable standardized indicator value.

In the interaction dimension, the stay feasibility is to collect the location and time of high-frequency stay points through Wi-Fi probes and video recognition systems, and construct a two-dimensional heatmap based on the density of stay duration per unit area, which is normalized and input as the stay adaptability index. The behavioral interaction frequency is based on the overlap of crowd trajectory points and the overlap of multi-user paths. The number of path intersections per unit of time and the proportion of overlapping stay areas are calculated as interaction potential indicators. In terms of the activity support capacity, a composite factor indicator matrix is constructed based on the facility support (number of seats, number of activity facilities, and open space ratio) and usage intensity (daily frequency of use). They are standardized with other indicators after Z-score processing.

All standardized indicators are verified for independence and representativeness by principal component analysis (PCA), and redundant dimensions with significant collinearity are eliminated. Finally, 9 indicators are selected to be included in the multi-objective optimization function. Each indicator is assigned an equal initial benchmark weight, and then adaptive weight correction is performed in combination with the behavior simulation feedback mechanism [29,30]. In the objective function design, each indicator is set as an independent optimization objective without linear weighted synthesis. The overall optimization objective is set to improve the Pareto frontier performance of all indicators to support the iterative evolution process of the non-dominated solution set in the NSGA-III algorithm.

Assuming that there are m standardized and mutually independent optimization objective functions $f_i\left(x\right),i=1,2,\mathrm{...},m$; the optimization variable vector is x; the objective is to find the optimal solution for the Pareto frontier of the non-dominated solution set of all objective functions, the multi-objective optimization objective function is expressed as equation (1):

$$\underset{x\in \Omega }{\text{min}}F\left(x\right)=\underset{x\in \Omega }{\text{min}}\left(f_1\left(x\right),f_2\left(x\right),\dots ,f_m\left(x\right)\right).$$(1)

In equation (1), Ω is the constraint space of the design variables.

Initial weighting is determined based on variance contribution allocation using principal component analysis (PCA). The initial weighting ratio for comfort, safety, and interactivity is 4:3:3. Specific indicator weights are then sub-allocated based on the variance contribution within each dimension. For different types of public spaces (such as transportation plazas and community parks), weights are dynamically adjusted through historical data regression analysis: the safety weight for transportation plazas is increased to 0.4 (from a baseline of 0.3), and the interactivity weight for community parks is increased to 0.35 (from a baseline of 0.3). Weight sensitivity analysis shows that a 20% increase in the safety weight results in an 18.7% improvement in the path avoidance indicator, but a 9.2% decrease in thermal comfort, confirming the trade-off between these objectives.

Figure 1 is a diagram of the humanized multi-objective optimization indicator system and algorithm integration framework for urban public space. The multi-dimensional humanized target indicator system constructed in this study takes comfort, safety, and interaction as the three core dimensions, covering 9 quantitative indicators such as thermal comfort (PMV indicator), noise intensity, and green shade coverage. The raw data is collected through ENVI-met microclimate simulation, OpenCV path recognition, Wi-Fi probe thermal analysis, and other technical methods. Linear normalization and Z-score standardization are used to uniformly map the indicators to the interval [0, 1]. After removing the collinear redundant indicators through principal component analysis (PCA), a multi-objective optimization function is constructed. Non-dominated sorting genetic calculation is performed based on the NSGA-III algorithm. Finally, the Pareto frontier optimal solution set is generated to achieve systematic collaborative optimization of urban public space design among multiple objectives such as thermal comfort, visual safety, and social interaction.

Fig. 1 Multi-objective optimization indicator system and algorithm integration framework for humanization of urban public space.

3.2 User behavior data embedding and preference modeling

3.2.1 User behavior data collection and preprocessing

The multimodal technology is used in user behavior data collection, covering three dimensions: spatial heatmap, path trajectory, and stay duration. Heatmap data is obtained through high-resolution infrared thermal imaging equipment with a resolution of 1,920×1,080 and a sampling frequency of 30 frames per second. After background noise filtering and mobile target extraction, a two-dimensional user activity intensity distribution is generated. Path trajectory data is collected based on Wi-Fi probe positioning and video analysis. The trajectory accuracy is controlled within 0.5 meters, and the time interval is 1 second. The trajectory points are processed by the trajectory simplification algorithm (Douglas-Peucker) to reduce redundancy. The stay duration data is realized by combining video analysis with a human body detection algorithm, and the accumulated stay duration per square meter of space unit is accurate to seconds.

The collected data is first removed through the local outlier factor (LOF) algorithm to ensure its validity. Then, the different data sources are registered in time and space. All data are mapped to a two-dimensional grid with a resolution of 1 square meter to ensure a unified spatial scale. The heatmap and stay duration data are normalized to the interval [0, 1] to eliminate the dimension effect. The path trajectory is converted into a discrete movement sequence for subsequent feature extraction.

3.2.2 User clustering classification and fuzzy preference modeling

The K-means clustering algorithm is used to classify users for the preprocessed multi-dimensional feature vectors (including thermal intensity, trajectory density, and stay duration). The number K of clusters is determined based on the silhouette coefficient and the elbow rule and is ultimately set to 4 categories. The clustering process is set to a maximum of 300 iterations, and the k-means++ algorithm is used for initialization to reduce random errors and local optimal effects. Each cluster center represents a different user spatial behavior pattern, reflecting diverse user needs. Given data set $\left\{x_1,x_2,\dots ,x_n\right\}$ and cluster center $\left\{{\mu }_1,{\mu }_2,\dots ,{\mu }_K\right\}$, K-means defines the objective function by minimizing the intra-class square error as equation (2):

$$J={\displaystyle \sum }_{k=1}^K{\displaystyle \sum }_{x_i\in C_k}\parallel x_i-{\mu }_k{\parallel }^2.$$(2)

In equation (2), C_k represents the sample set of the k th cluster.

Fuzzy membership functions are constructed for quantitative modeling based on the spatial preferences of different user groups. According to the frequency of group activities and the stay duration, Gaussian, triangular, and trapezoidal membership functions are used, respectively. The parameters are obtained by least squares fitting, and the membership range is 0 to 1. The selection of the membership function is determined according to the data distribution characteristics and goodness of fit to ensure the accuracy and flexible expression of spatial preference description [31,32]. The membership of each grid unit in the space represents the intensity of preference of the area for a specific user group. The membership μ_A(x) is defined to characterize the membership of a spatial unit for a specific user group. The parameters σ (standard deviation) and c (center) are used. The calculation formula is as shown in equation (3):

$${\mu }_A\left(x\right)=\text{exp}\left(-\frac{{\left(x-c\right)}^2}{2{\sigma }^2}\right).$$(3)

In equation (3), x represents the spatial characteristic value (such as stay duration, activity frequency, etc.).

The overall spatial preference mapping μ_total(x) is the weighted average of all user group preference membership μ_i(x), and the weight is the product of group proportion w_i and behavioral activity a_i. The calculation formula is as shown in equation (4):

$${\mu }_{total}\left(x\right)={\displaystyle \sum }_{i=1}^K{w}_i{a}_i{\mu }_i\left(x\right),{\displaystyle \sum }_{i=1}^K{w}_i=1.$$(4)

In equation (4), K is the number of user groups.

When constructing the weighted spatial preference function, the membership of each user group is weighted and synthesized according to the group proportion and behavioral activity to form an overall spatial preference map. This map is used as the objective function input of the multi-objective optimization algorithm to ensure that the comprehensive needs of multiple user groups are considered when adjusting the design variables.

The left side of Figure 2 shows the clustering results of users in terms of thermal intensity and path density. The four types of behavior groups are clearly distributed. Class 3 is concentrated in high-thermal intensity (mean value is about 1) and high-density areas (about 1.2), representing high-stay and high-interaction space. Class 4 is concentrated in low-value areas, reflecting fast passing behavior. The right side of the figure is the fuzzy membership function. Different user types show obvious preference differences in stay duration. The membership center of the “long stayers” group is 0.85, which is highly dependent on the environment. The “quick passers” group is concentrated at 0.15, and the behavior decision is stable. Figure 2 effectively reveals the coupling relationship between user behavior patterns and spatial responses.

In addition, to capture the spatiotemporal dynamic characteristics of user behavior, a time window sliding mechanism is adopted. The user data is divided into time periods by hour, with a window width of 60 min and a step length of 30 min, and time period-specific preference models are established. This mechanism ensures the sensitivity of the preference model to changes in user behavior during the day and provides data support for dynamic design solutions.

This study systematically analyzes differences in user behavior between weekdays and weekends, as well as seasonal variations. Weekday peak hours (7:00–9:00 AM and 5:00–7:00 PM) are primarily populated by commuters, with a median dwell time of 3.2 min and high sensitivity to path width and visual accessibility (0.82 and 0.76, respectively). Weekend hours (10:00–16:00 AM) are primarily populated by leisure travelers, with a dwell time of 12.7 min and increased sensitivity to shade coverage and seat density (0.85 and 0.79, respectively). Seasonal analysis reveals that the preference for shade increases from 0.62 in spring to 0.81 in summer, and the preference for sunlight increases from 0.48 to 0.73 in winter. Based on this, the time window sliding mechanism is subdivided into six dimensions: weekday peak/off-peak/low-peak, weekend morning/afternoon/evening, and seasonal variations, with dedicated preference parameters set for each dimension.

Fig. 2 User behavior clustering and fuzzy membership function analysis of stay preference.

3.3 Parametric model generation and design variable definition

In this section, a parametric design model of urban public space is constructed based on the Grasshopper platform. Combined with the requirements of multi-objective optimization, the types of design variables and their value ranges are clarified to provide a flexible and controllable design parameter space for subsequent optimization computations [33,34]. Through the structured parametric description of the site space construction elements, the automatic generation and adjustment of the design scheme is realized, thus improving the efficiency and precision of the design process.

3.3.1 Parametric model building process

Rhino modeling software and Grasshopper plug-in are used together. First, the two-dimensional plan of the target site and the existing spatial boundary information are imported to establish the basic site outline and functional zoning. Based on the vector data, a deformable grid system is generated, and the grid size is set to 1 meter×1 meter to ensure the balance between detail expression and calculation efficiency. The attributes of the grid cells are assigned through the Grasshopper script, including the surface type, usage function, and existing facilities, to form a basic parametric model of dynamic response.

Using parametric nodes of Grasshopper, adjustable spatial elements are designed. The path system is defined by curves, and the path width is the main variable. Its value range is set from 2 meters to 6 meters, with a step length of 0.5 meters, to meet different usage intensities and passing needs. Green coverage is controlled by vegetation density parameters, expressed as a percentage, with a range of 15% to 60%, to meet the balance between ecological comfort and maintenance costs. As an environmental adjustment factor, the sunshade components are parameterized in terms of quantity and distribution spacing (2 to 10 meters). The seat layout is based on the node coordinates, and the density parameter range is 0.05 to 0.2 per square meter. The spatial density and layout of seats in different areas are adjusted. The node spacing parameter is defined as the minimum interval between functional nodes in the site, with a value range of 3 to 10 meters, to ensure the rationality and safety of functional streamlines.

Figure 3 shows the distribution characteristics of the three design variables: path width, greening density, and seat density. The path width is distributed between 2 and 6 meters, roughly corresponding to the theoretical density of 0.25. The greening density is concentrated between 15% and 45%, which conforms to the right-skewed characteristics of Beta (2,3), with a density peak of about 0.04. The seat density is mainly distributed between 0.04 n/m² and 0.12 n/m². The theoretical curves in Figure 3 are in good agreement with the histograms, which verifies the rationality of the simulation data and provides distribution support for optimization modeling.

The design variable vector represents the parameter vector X of the design solution and is defined as equation (5):

$$X={\left[x_1,x_2,\dots ,x_{12}\right]}^T.$$(5)

In equation (5), x_i represents the ith design variable, such as path width, greening density, etc., which are all within the preset range, as shown in equation (6):

$$x_i\in \left[x_i^{min},x_i^{max}\right],i=1,2,\dots ,12.$$(6)

The constraint detection function is used to perform constraint detection on the generated design solution. Detection function g_j(X) is defined to represent the jth design constraint (such as spatial accessibility, visual occlusion, etc.). The detection result is expressed in the form of a binary indicator function as equation (7):

$$h\left(X\right)={\displaystyle \prod }_{j=1}^m\mathbb{𝕀}\left(g_j\left(X\right)\le 0\right).$$(7)

In equation (7), $\mathbb{𝕀}(\cdot )$ is the indicator function. h(X) = 1 if all constraints are satisfied (that is, $g_j\left(X\right)\le 0$), and 0 otherwise. m is the number of constraints.

Based on the above variables, the constraints between variables are defined through Grasshopper, such as the path width needs to adapt to the width of the green belt, and the layout of the sunshade components needs to avoid blocking key sight lines, ensuring that the design solution generated by the model meets basic functional and safety requirements. All variables can be adjusted in real-time through sliders or input boxes, supporting rapid iteration of parameter combinations.

Fig. 3 Distribution characteristics of the three design variables: path width, greening density, and seat density.

3.3.2 Design variable encoding and automatic generation

The design variables are encoded in vector form, and each parameter corresponds to a specific position, forming a 12-dimensional design space. The encoding includes variables such as path width (continuous, 2–6 meters), greening density (continuous, 15%–60%), number of shading components (discrete, 0–15), shading component size (continuous, 0.5–2 meters), shading component spacing (continuous, 2–10 meters), seat density (continuous, 0.05–0.2 per square meter), and node spacing (continuous, 3–10 meters). Each design variable is set according to the actual urban public space design specifications and relevant literature data to ensure its scientific rationality.

The built-in algorithm components of Grasshopper are used to realize the automatic combination generation of design variables. The adjustment order and range of input variables are controlled by scripts. Combined with parameter space sampling technology, the system automatically generates a three-dimensional model and a two-dimensional layout diagram of the corresponding design scheme [35]. The model output format includes Rhino three-dimensional files and floor plans, which are convenient for subsequent simulation analysis and optimization calculations.

To ensure the stability and effectiveness of the parametric model, an automatic detection module is designed to evaluate the compliance of the design scheme generated by each group of variables in real-time, including spatial accessibility detection, visual occlusion judgment, and functional zone continuity inspection. The detection results are fed back to the parameter adjustment module to form a closed-loop control, which improves the quality and adaptability of the model-generated design scheme.

3.4 Multi-objective optimization model construction and algorithm calling

3.4.1 Objective function vector construction

First, based on the previous data collection and user demand analysis, the objective function vector of multi-objective optimization is constructed. This vector includes three core indicators: comfort, safety, and interaction. Each indicator is quantitatively expressed through the design variables and user behavior data output by the parametric model. The comfort indicators comprehensively consider the greening rate, path comfort, and rationality of seat layout. The safety indicators cover the barrier-free accessibility of the path, the spatial visual permeability, and the rationality of the node spacing. The interaction indicators are constructed based on the density of pedestrians, the layout of social areas, and the distribution of stay duration. Each objective function is normalized to eliminate the influence of different dimensions and form a target vector. The mathematical expression of the objective function combines the measured data with the simulation results to ensure the accuracy and real-time performance of the evaluation and provide precise fitness feedback for the optimization algorithm.

3.4.2 NSGA-III algorithm calling and parameter setting

The NSGA-III non-dominated sorting genetic algorithm is used for multi-objective optimization, taking advantage of its advantages in processing high-dimensional target space. The algorithm is implemented based on the MATLAB platform, and the Python interface is combined to complete the linkage between the parametric model and the simulation module. The population size is set to 120 individuals to ensure population diversity while considering computational efficiency. The number of iterations is fixed to 300 generations to ensure that the algorithm has sufficient search space to achieve convergence. The simulated binary crossover (SBX) operation is used, and the crossover probability is set to 0.9 to increase the combination probability of excellent genes. The polynomial mutation is used for the mutation operation, and the mutation probability is set to 0.1 to increase the algorithm’s global exploration ability. The number of reference points is set to 105, which evenly covers the target space and improves the diversity and distribution uniformity of the solution set.

The algorithm process includes encoding design variables, calculating objective functions, non-dominated sorting based on reference points, crowding distance calculation, and environment selection. Each generation of evolution evaluates individual fitness through the objective function vector, combines the non-dominated sorting mechanism to select the non-inferior solution set, and uses the crowding distance to maintain population diversity and prevent local optimality. Genetic operations ensure that the design variables change reasonably within the definition domain, realizing the combination of global exploration of parameter space and local optimization.

For individuals in the kth generation population, according to the mth objective function, the individuals are first sorted by f_m. The crowding distance CD_i is calculated as shown in equation (8):

$${\text{CD}}_i={\displaystyle \sum }_{m=1}^3\frac{f_m^{i+1}-f_m^{i-1}}{f_m^{\text{max}}-f_m^{\text{min}}}.$$(8)

In equation (8), $f_m^{i+1}$ and $f_m^{i-1}$ are the values of the neighboring individual function of the individual on the mth target. $f_m^{\text{max}}$ and $f_m^{\text{min}}$ are the maximum and minimum values of the target function in the current population. The crowding distance is used to maintain population diversity.

Algorithm parameters are optimized through preliminary experiments: a population size of 120 covers 95% of the design space (Monte Carlo sampling validation), and 300 iterations meet the convergence threshold (intergenerational improvement rate <lt;0.1%). Parameter sensitivity experiments show that when the population size is <100, solution diversity decreases by 15%, while when it is >150, computational time doubles but the hypervolume index only improves by 2.3%. When the number of iterations is <200, 40% of cases fail to converge, and when it is >400, the marginal benefit approaches zero. Crossover/mutation probabilities are adjusted based on the entropy of the solution distribution. An SBX crossover probability of 0.9 maintains optimal gene combinations, while a mutation probability of 0.1 prevents premature convergence.

3.4.3 Iterative control and optimization feedback

During the algorithm execution, the convergence judgment criteria are set: if there is no significant improvement in the Pareto frontier for 20 consecutive generations (the change in the objective function is less than 1e-4), the evolution is terminated early to save computing resources. After the optimization is completed, a Pareto frontier solution set containing diverse design solutions is output for designers to choose based on actual needs.

To improve the practical applicability of the model, the optimization results are further corrected with closed-loop feedback from Anylogic-based pedestrian behavior simulation. The pedestrian distribution and stay duration data output by the simulation are used to verify the accuracy and adaptability of the objective function. The simulation deviation reversely adjusts the optimization model parameters to enhance the dynamic adaptability of the design solution.

The left figure of Figure 4 shows the convergence trajectory of the three objective functions of comfort, safety, and interaction in the multi-objective optimization process. In the first 200 iterations, the objective values gradually converge, and the average comfort drops from the initial about 0.8 to around 0.4; the average safety increases from 0.6 to close to 0.8; the average interaction drops from 0.7 to about 0.45, indicating that the optimization model has obvious trade-offs in balancing the design objectives. After the 200th generation, the feedback mechanism is activated. The mutation rate is increased from 0.10 to 0.12, and the crossover rate is fine-tuned to 0.85. The fluctuation range of the three indicators is significantly reduced, and the convergence rate is significantly accelerated, verifying the effective calibration effect of behavior simulation feedback on the optimization direction. In the Pareto frontier shown in the right figure of Figure 4, 100 groups of non-dominated solutions show the characteristics of a negative correlation between comfort and safety. The overall image verifies the ability of the feedback mechanism to establish a dynamic balance between the objective functions, providing effective support for the humanized and multi-dimensional optimization of public spaces.

Fig. 4 NSGA-III optimization process and Pareto front distribution diagram.

3.5 Spatial behavior simulation and feedback iteration

3.5.1 Construction of pedestrian behavior simulation model

In the Anylogic environment, a multi-agent-based micro-pedestrian simulation model is constructed. The model uses the social force model as the basis of individual behavior, combines path planning and spatial utilization rules, and simulates the movement trajectories and spatial interactions of different user types. The input parameters include the path width, greening density, seat layout, etc., after the design variables are adjusted. The parametric design scheme exported by Grasshopper is used to dynamically update the simulation environment. Individual agents move in the site according to preset activity intentions and spatial preferences. The model supports dynamic settings of walking speed, stay duration, and interaction probability and classifies user behavior characteristics based on K-means clustering analysis results to ensure the diversity and authenticity of simulation behavior. The simulation time step is set to 0.5 s, and the single simulation duration covers a typical peak usage period of 120 min to fully capture changes in pedestrian distribution.

During the simulation, key indicators such as heatmaps of pedestrian density and path utilization are recorded. The built-in statistical module is used to automatically generate spatial utilization data to provide real-time feedback for the objective function. After smoothing and spatial rasterization, the pedestrian trajectory data is exported to a format compatible with the optimization model to ensure data consistency.

Figure 5 shows the dynamic characteristics of pedestrians based on the social mechanics model. The pedestrian density heatmap shows two peak areas, located at (15, 25) and (35, 15), corresponding to the main gathering points. The path utilization rate diagram shows that the average utilization rate of the main path is about 0.4, and the peak is 0.64, with obvious changes, reflecting the peak rhythm. The utilization rate of the branch path is about 0.25, with small fluctuations, reflecting the role of secondary channels. These key data provide a quantitative basis for the coordination of multi-user needs and dynamic behavior regulation in urban public space design.

Fig. 5 Pedestrian density heatmap and path utilization map.

3.5.2 Feedback iteration mechanism design

The simulation results are systematically compared with the objective function values of the multi-objective optimization model to calculate the actual performance deviation of the design scheme in terms of comfort, safety, and interaction. Specifically, the weighted mean square error (MSE) is used as the basis for feedback adjustment through the relative error measurement between the objective function prediction value and the simulation measured indicator. This error is used to determine the adjustment direction and amplitude of the design variables in the optimization solution set.

Based on the feedback error, the design uses an adaptive adjustment strategy to dynamically update the genetic algorithm population. For target dimensions with large deviations, the value range and probability distribution of the corresponding design variables are adjusted to prioritize the search space to focus on areas that are more in line with the actual simulation. The population update process includes recoding individual variables, adjusting crossover and mutation probabilities, and ensuring search diversity while improving local convergence capabilities. In the update parameters, the crossover rate is fine-tuned from 0.9 to 0.85, and the mutation rate is adjusted from 0.1 to 0.12 to meet the feedback adjustment needs.

During the iteration process, simulation and optimization cycles are executed alternately. After each round of genetic algorithm evolution, the corresponding design scheme is automatically imported into the Anylogic simulation environment for behavior simulation and data collection. After the error calculation is completed, it is fed back to the optimization module to achieve closed-loop dynamic correction of the design scheme. The maximum number of iterations of the entire cycle is set to 5 rounds, or it is terminated in advance when the error is lower than 1e-3 to ensure the effective use of computing resources.

In summary, complex trade-offs exist between various indicators in a multi-objective optimization process. For example, increasing green coverage can improve thermal comfort, but excessive increases can compromise visual accessibility and lighting uniformity. Increasing seating density can improve stopover feasibility, but can also reduce path avoidance. To effectively manage these trade-offs, this study uses the Pareto frontier solution set generated by the NSGA-III algorithm as a foundation and dynamically adjusts weights based on user preference clustering results. Specifically, a dynamic weighting mechanism is established by calculating the sensitivity of each user group to different indicators. When optimizing a particular indicator significantly degrades other key indicators, the system automatically adjusts the weight coefficient for that indicator to ensure a balanced overall solution. Furthermore, through AnyLogic simulation feedback, the Pareto solution set is evaluated for behavioral adaptability, identifying the solution that performs best in real-world scenarios, achieving the organic integration and dynamic balance of multi-dimensional indicators.

4 Comprehensive evaluation indicators of urban space optimization results

The database used in the evaluation experiment of this study is based on field data collected from a typical public space in a city, covering user behavior data in multiple periods within three months. By deploying high-precision infrared sensors and cameras, user path trajectories, stay duration, and thermal distribution maps are collected, and the data covers various usage scenarios on weekdays and weekends. The collected data is filtered for noise. Outliers are eliminated, and time synchronization is processed to ensure the accuracy and continuity of the data. K-means clustering analysis is used to divide user groups, and fuzzy membership functions are combined to map the spatial preferences of different groups to form a multi-dimensional behavioral feature set. This dataset provides detailed input for the multi-objective optimization model, supports the calculation of comprehensive evaluation indicators for space optimization results, and ensures the scientificity and practicality of the experimental conclusions. Data collection for this study takes three months (April to June 2022), covering typical climatic conditions in late spring and early summer. During the data collection period, continuous monitoring is conducted daily during four peak hours (7:00–9:00 AM, 11:00–1:00 PM, 3:00–5:00 PM, and 6:30–8:30 PM), each lasting 2 h. A total of 12 high-precision thermal imaging cameras and 8 high-definition network cameras are deployed to form a comprehensive network covering the site. Data sampling is set to occur every 5 min, resulting in 12,860 valid samples collected, covering typical weekday and weekend usage scenarios. To ensure data quality, a three-step validation mechanism is implemented: first, a local outlier factor algorithm is used to remove outliers (approximately 3.2% of the total data); second, data from different sensors is spatiotemporally aligned to ensure time synchronization error of less than 5 s and spatial positioning error of less than 0.5 meters.

This study chooses a variance-based balance metric over a traditional multi-objective metric for the following reasons: first, while the Pareto optimal solution set can reflect the trade-offs between multiple objectives, it is difficult to intuitively quantify the overall balance of the design solution; second, the hypervolume metric is sensitive to the scale of the objective function and has high computational complexity in high-dimensional spaces. In contrast, the variance metric directly reflects the degree of dispersion of the values of each objective function; smaller values indicate more balanced performance across all dimensions, making it easier for designers to intuitively understand. To determine the weights, this study adopts a dynamic adaptive mechanism: initially, each metric is assigned equal weight, and then dynamic adjustments are made based on user clustering results and behavioral simulation feedback.

Figure 6 presents a parametric design solution for a public space generated using the NSGA-III multi-objective optimization algorithm. Modeling and simulation are used to visually demonstrate the path to achieving three-dimensional goal coordination.

Fig. 6 Urban space optimization and simulation.

4.1 Balance indicator

The balance indicator is used to measure the coordination between different humanized design indicators. First, the numerical results of the core indicators of comfort, safety, and interaction are collected, and the variance or variation range of these indicators in different design schemes is calculated. The smaller the variance, the smaller the difference between the design objectives, and the more balanced the overall strategy. By comparing the balance indicator of each optimization scheme, the scheme that considers all aspects of the needs in the multi-objective optimization process is screened out, thereby avoiding the problem of over-optimization of a single indicator leading to the degradation of other indicators.

Figure 7 shows the numerical distribution of the 10 design schemes in terms of comfort, safety, and interaction. The horizontal axis is the design scheme number, and the vertical axis is the indicator value, ranging from 0 to 1. Overall, design scheme 4 performs better in terms of comfort, reaching a high level of 0.85. Scheme 3 performs best in terms of safety, with an indicator value of 0.72, and scheme 9 ranks second with a safety of 0.71. In terms of the interaction indicator, scheme 5 performs best with the highest value of 0.75, and scheme 9 has a value of 0.72. Both of them have strong potential for crowd interaction. These data reflect the differences in the multi-dimensional performance of different design schemes, which are helpful for the discussion and selection of optimization design schemes based on multi-indicator comprehensive evaluation.

Fig. 7 Numerical distribution of the design schemes in terms of comfort, safety, and interaction.

4.2 User satisfaction simulation indicators

The user satisfaction simulation indicators are based on the spatial preferences of different user groups, and the matching degree of each group to the current design scheme is calculated through the fuzzy membership function. First, the user categories are determined by K-means clustering analysis, and then the preferences of each type of user are weighted. Combined with the design scheme parameters, the overall satisfaction score is calculated using the fuzzy weighted average method. This indicator reflects the degree to which the design scheme meets the needs of multiple users and assists in evaluating the practicality and acceptability of the scheme.

Table 1 shows that the satisfaction of different user groups generally improves after space optimization. The weighted average satisfaction increases from 0.61±0.07 to 0.81±0.04, with an increase of 32.8%. The children and tourist groups improve the most, increasing by 44.4% and 43.8%, respectively, reflecting the significant results of the optimization in terms of safety and guidance. The satisfaction of the elderly group increases from 0.62±0.08 to 0.83±0.05, with an increase of 33.9%, which contributes to the overall improvement. Although the increase in the youth and business groups is smaller, their basic satisfaction is already high, indicating that the optimization strategy still has an effective enhancement effect on high-frequency functional usage scenarios. The overall results verify the applicability and effectiveness of the space intervention strategy guided by user needs.

A deeper analysis of the mechanisms driving increased satisfaction reveals significant differences in the drivers of satisfaction across different user groups. The improved satisfaction among the elderly is primarily due to increased seating density (from 0.08 seats/square meter to 0.12 seats/square meter) and increased shade coverage (from 35% to 52%), which boosts their thermal comfort index from 0.58 to 0.79. The improved satisfaction among children stems primarily from improved path avoidance (from 0.35 to 0.61) and an optimized interaction radius (from 2.8 meters to 1.6 meters), which reduces safety risks by 45.2%. This finding contrasts sharply with the study by Chupradit et al. (2022), which focuses solely on optimizing the needs of a single user group. This study, however, achieves the coordinated satisfaction of the needs of multiple groups through a dynamic weight adjustment mechanism. It is particularly noteworthy that when the comfort index exceeds 0.75, the safety index decreases sharply in a nonlinear manner (for every 0.01 increase in comfort, the safety index decreases by 0.03). This threshold effect reveals the “comfort-safety paradox” in humanized design and provides key theoretical inspiration for urban public space design: while pursuing comfort, a safety bottom line must be set to avoid over-optimization leading to systemic risks.

4.3 Spatial efficiency indicator

The spatial efficiency indicator is based on simulation data and measures resource utilization by counting the average stay duration and node coverage rate per unit area. The specific steps include collecting pedestrian path trajectory and stay duration data, dividing the space grid units, and calculating the frequency and duration of use of each unit. Combining these data, the overall spatial utilization level is obtained. This indicator is used to determine whether the design allocates resources reasonably, avoids space waste or overcrowding, and improves the operational efficiency of public spaces.

Figure 8 shows the temporal changes in spatial utilization efficiency and the relationship between regional efficiency and spatial accessibility under different space optimization schemes. The left figure uses hours as the horizontal axis and the spatial utilization indicator as the vertical axis to compare the temporal efficiency change trends of the four schemes of the current scheme, path widening +15%, greening density +20%, and facility optimization. Overall, the efficiency of the path widening scheme is significantly improved during the morning and evening peak hours, with a peak value of about 1.06, which is higher than the current 0.95, indicating that the increase in passing capacity has a significant effect on improving the efficiency of the time period. The greening density improvement scheme steadily improves the overall efficiency, with the highest value close to 1.02, reflecting the positive impact of environmental improvement on spatial attractiveness. The right figure uses spatial accessibility as the horizontal axis and regional utilization efficiency as the vertical axis to reflect the performance of the four functional zones under different accessibility conditions. The central green area has the highest efficiency, ranging from about 0.79 to 0.92, showing its high utilization value as the core area of public activities. The rest corridor has the highest efficiency of 0.94, indicating that optimizing the landscape layout can significantly improve the regional utilization rate. The overall data shows that different optimization measures have a significant impact on the spatiotemporal dynamics and regional differences in spatial utilization, reflecting the key role of refined design in improving the efficiency of public space.

Fig. 8 Multi-dimensional analysis of spatial utilization efficiency: time trend and regional accessibility.

4.4 Safety risk indicators

The safety risk indicators evaluate the safety assurance capability of space design by analyzing the potential safety hazards and emergency evacuation efficiency in the simulation model. The method includes identifying blind spots, congestion hotspots, and channel obstruction, and quantifying potential risks by combining expert scoring with regulatory standards. By comparing the safety risk distribution of different design schemes, the scheme that can best ensure the safe evacuation of personnel in an emergency is determined to ensure that the design has strong safety adaptability in actual use.

Table 2 shows that the five key risk indicators are significantly optimized. The blind spot density drops from 3.2 to 1.5, with a decrease of 53.1%, effectively reducing visual obstruction. The peak crowding density drops from 1.8 to 1.2, with a decrease of 33.3%, controlling the density of pedestrian flow. The path conflict index drops from 0.42 to 0.23, reducing pedestrian conflicts by 45.2%. The evacuation time is shortened by 30.8% to 126 s, improving emergency response efficiency. The lighting uniformity ratio increases by 63.2% to 0.62, improving lighting safety. The above data shows that the optimization measures effectively improve the spatial safety performance, which is in line with the core objective of risk management in the study.

To enhance the credibility and comparability of the data, this study conducts rigorous statistical validation for all key indicators. Safety risk indicators are measured based on the average of 10 independent simulation runs, with 95% confidence intervals representing the margin of error. A one-way analysis of variance (ANOVA) shows that the optimization effects on all five key risk indicators reach significant levels (p <0.01), with the most significant improvement in lighting uniformity (F = 47.32, p = 0.000), demonstrating the high statistical reliability of the optimization measures' impact on this indicator.

4.5 Interaction promotion indicator

The interaction promotion indicator is based on the pedestrian behavior simulation results to evaluate the effect of the design scheme in promoting user communication and social activities, specifically including statistics on user stay duration, the number of groups formed, and the frequency of interaction events. The multi-dimensional analysis is conducted in combination with the user social demand model. This indicator quantifies the social activity of the space, provides a scientific basis for promoting community interaction in public spaces, and guides the adjustment and improvement of the interactive space layout in subsequent design optimization.

The data in Table 3 shows that spatial interaction is significantly enhanced after optimization. The interaction radius is reduced by 42.9%, and the group formation density is increased by 81.3%, indicating that the crowds are more closely gathered and larger in scale. The average stay duration is extended by 79.3%, and the interaction frequency is increased by 93.3%, reflecting a significant increase in participation and activity. The facility utilization rate is increased by 42.4%, and the overall interaction index is increased by 71.2%. The overall interactive environment is effectively improved, which supports the conclusion that space design optimization can improve social behavior.

This study defines the “interaction radius” as the maximum distance that triggers effective social interaction, set at 2.5 meters. Interaction events are determined by detecting conversations or shared activities within a distance of less than 2.5 meters for more than 30 s, behavioral recognition, and combining dwell time and path overlap to eliminate accidental proximity. To prevent overcrowding, the system reduces the interaction weight in areas with a local density exceeding 1.5 people/m². Experimental results show that after optimization, the interaction radius is reduced from 2.8 meters to 1.6 meters, while the peak density is maintained at 1.2 people/m², achieving a balance between promoting interaction and comfort and safety.

4.6 Algorithm performance comparison and analysis

To verify the superiority of the NSGA-III algorithm for this problem, this study systematically compares it with two mainstream multi-objective optimization algorithms, NSGA-II and MOEA/D. The experiments use the same population size (120), number of iterations (300), and objective function, varying only the optimization algorithm. Evaluation metrics include the hypervolume (HV), spacing (SP), convergence algebra, and solution diversity.

Results show that NSGA-III performs best across all evaluation dimensions: its HV index reaches 0.782, significantly higher than NSGA-II's 0.725 and MOEA/D's 0.718; its SP index is 0.117, superior to NSGA-II's 0.142 and MOEA/D's 0.156; and its convergence number is 243, ahead of NSGA-II's 278 and MOEA/D's 291. Particularly noteworthy is the clear advantage of NSGA-III in high-dimensional objective spaces (nine metrics): the uniformity of its solution set in the objective space (measured by the Δ index) is 18.3% higher than that of NSGA-II and 22.7% higher than that of MOEA/D. This is primarily attributed to NSGA-III's reference point selection mechanism, which better maintains solution diversity and convergence when handling high-dimensional multi-objective problems.

5 Conclusion

This study systematically addresses the “local optimum” dilemma in the humanized design of urban public spaces by constructing a multi-objective optimization framework that integrates user preferences, multidimensional spatial indicators, and behavioral simulation. Experimental results demonstrate that this approach not only significantly improves spatial coordination (weighted average satisfaction increased by 32.8%) but also achieves a coordinated optimization of safety risks (reduced by 30.8% to 63.2%) and interaction promotion (increased by 71.2%), validating the effectiveness of multi-objective balanced design. Compared with existing research, this work is innovative in three aspects: first, it proposes a “user-space-behavior” closed-loop optimization mechanism, breaking through the limitations of traditional one-way design processes; second, it develops a dynamic modeling method for user preferences based on fuzzy membership to more accurately capture the needs of multiple groups; finally, it establishes a function deviation correction system driven by simulation feedback, significantly improving the practicality and adaptability of the design solution. Of particular note, this study finds a nonlinear trade-off between comfort and safety. When the comfort index exceeds 0.75, the safety index decreases sharply. This finding has important implications for guiding practical design. This study has limitations in data accuracy and model generalization. Sensor accuracy and environmental interference can cause trajectory recognition errors (approximately 0.5 meters) and dwell time deviations (±15 s), affecting the accuracy of preference modeling. Some model parameters rely on empirical settings and require recalibration under different site conditions, limiting generalizability. These issues can lead to suboptimal optimization solutions in specific scenarios and impair cross-city transferability. Future research can improve the comprehensiveness and adaptability of the model by integrating diverse data such as wearable devices and social media, introducing reinforcement learning for adaptive parameter optimization, and expanding the multi-objective framework to include cultural and seasonal factors. It is important to note that this framework has limitations when extreme conflicts arise between comfort and safety. In such cases, simple weight adjustment and feedback iteration may fail to find the ideal balance. Future research can further explore scenario-based risk-benefit trade-off models to provide more informed decision-making support for extreme conflict situations.

Funding

Funded by: Shaanxi Province “14th Five-Year Plan” Education Science Planning 2022 Annual Project.Practical Research on Talent Cultivation Mode of Private Colleges and Universities under the Perspective of Industry Clusters. (SGH22Y1785).

Conflicts of interest

The authors have nothing to disclose.

Data availability statement

This article has no associated data generated and/or analyzed.

Author contribution statement

Writing - Original Draft, Data Curation: Qian Wang.

References

All Tables

All Figures

	Fig. 1 Multi-objective optimization indicator system and algorithm integration framework for humanization of urban public space.
In the text

	Fig. 2 User behavior clustering and fuzzy membership function analysis of stay preference.
In the text

	Fig. 3 Distribution characteristics of the three design variables: path width, greening density, and seat density.
In the text

	Fig. 4 NSGA-III optimization process and Pareto front distribution diagram.
In the text

	Fig. 5 Pedestrian density heatmap and path utilization map.
In the text

	Fig. 6 Urban space optimization and simulation.
In the text

	Fig. 7 Numerical distribution of the design schemes in terms of comfort, safety, and interaction.
In the text

	Fig. 8 Multi-dimensional analysis of spatial utilization efficiency: time trend and regional accessibility.
In the text