An Integrated Framework for Multi-Objective Optimization of Night Lighting in Urban Residential Areas: Synergistic Control of Outdoor Activity Places Lighting and Indoor Light Trespass

Abstract

In the context of increasing urban night lighting, the phenomenon of light trespass in residential areas is becoming increasingly serious, affecting the night comfort and circadian rhythm of residents. Aiming at this problem, this paper takes the night lighting of activity places in old multi-story residential areas of Shijingshan, Beijing, as the research object, and proposes a research framework integrating parametric modeling, multi-objective optimization, correlation analysis, and scheme decision-making, aiming to trade off the two objectives of maximizing the night lighting of the activity places and minimizing indoor light intrusiveness. The study first establishes a parametric model based on Rhino and Grasshopper, combines the NSGA-II algorithm with multi-objective optimization simulation to obtain the Pareto optimal solution, analyzes the correlation between the design variables and the objective function by the Spearman method, and finally assists in the scheme decision-making by K-means clustering. The results showed that the streetlight heights (SH), distance between buildings and streetlights (DBS), and streetlight matrix types (SMT) were the key factors affecting lighting performance, which should be emphasized in the actual lighting design. Secondly, the Cluster2 solution set optimally performs the two objective functions. The 18th individual of Generation 15 (Gen. 15 Ind. 18) and Gen. 31 Ind. 42 are recommended, providing practical guidance for night lighting design in residential areas. The innovation of this study lies in applying multi-objective optimization and K-means clustering to optimize the night lighting environment in micro-spaces within old multi-story residential areas in cities, offering new insights for lighting design in similar scenarios.

1. Introduction

As urban lighting installations continue to develop, the intensity of artificial light at night (ALAN) has rapidly increased, and its global reach has been expanding [1]. Specifically, ALAN consists of a variety of outdoor light sources such as street lighting, perimeter building lighting, and activity place lighting. It provides many important functions in urban life, including path navigation, spatial recognition, and supporting feelings of safety and security, as well as reducing fear of crime [2,3]. The emergence of ALAN has expanded the time and scope of human activities and facilitated human production and life. However, irrational ALANs usually have serious negative impacts on humans [4]. Light trespass: numerous studies have shown that overexposure to light at night not only severely affects human circadian rhythms but also suppresses melatonin production, leading to insomnia and stressing the visual system [5,6,7,8].

Over the past 10 years, night lighting has increased globally by nearly 12% per year, far more than previously thought [9]. It is well known that excessive use of ALANs produces light pollution, which leads to sky glow, light trespass, and glare. All of the above are linked to the adverse impacts on human beings [10]. Light trespass, as one of the main forms of light pollution, is of great concern due to its high impact on residents [11]. The Illuminating Engineering Society of North America (IESNA) defines light trespass as the intrusion of artificial light sources into non-targeted areas. This includes non-essential illumination of adjacent areas and excessively bright lights in the field of view. It occurs when unwanted outdoor light enters a building’s interior space [12]. In order to quantify the impact of light trespass, the International Commission on Illumination (CIE) has published a series of international standards for combating light trespass at night, emphasizing vertical illuminance on the exterior surfaces of building windows as the core evaluation index [13]. The current Chinese norms are also based on the CIE requirements [14]. According to surveys, the impact of light trespass on human health is becoming more pronounced due to the lack of rational planning and management of outdoor lighting, with more than 80% of the world’s population today being affected by light trespass in one form or another [15,16]. Compared with developed countries, China’s night lighting problem is more obvious [17]. Beijing, for example, has become an area of severe light trespass due to its high percentage of urbanized land, concentrated population, and dense lighting facilities [18]. Especially in residential areas, the problem of light trespass in residential areas is more prominent due to the high population size and density in residential areas, and the superposition of the surrounding commercial lighting, roadway lighting, and community interior lighting. However, existing research mainly focuses on urban public spaces, with relatively few studies on indoor light trespass in residential areas [19,20].

In order to fill this research gap, this study addresses the problem of light trespass in typical multi-story residential areas in large cities, and takes the residential areas of Shijingshan in Beijing as an example, proposes a framework for a multi-objective optimization method based on the optimization of outdoor lighting and the prevention of indoor light trespass at night, and focuses on the impacts of streetlight matrix types (SMT), streetlight heights (SH), and distances between buildings and streetlights (DBS), etc., on the lighting environment. The innovation of this study lies primarily in the fact that the night light trespass areas we investigated are micro-spaces within old multi-story residential areas in cities. It also involves the integration of multi-objective optimization with K-means clustering methods within this specific scenario. Through the use of parametric modeling (Rhino + Grasshopper), performance simulation (Ladybug tools), and machine learning techniques, the optimal performance indicators of the night lighting environment are simulated and revealed, which provide scientific and effective technical support for the prevention and control of light trespass in the residential area, and at the same time, provide quantifiable program decision-making and practical guidance for the design of night lighting in the residential areas.

2. Literature Review

2.1. Progress in the Study of Night Light Trespass

Outdoor lighting is an indispensable element of the modern city, stemming primarily from the human need for safety and extended periods of activity. However, in the absence of harmonized lighting standards, night lighting is often haphazard and light-intrusive, raising new challenges for healthy environments [21]. This contradiction highlights the importance of scientific management, and existing studies have explored multi-dimensional aspects of light trespass assessment systems, detection techniques, and governance optimization.

Early research developed the Outdoor Lighting Performance System, which laid the methodological foundation for light trespass assessment by quantifying light trespass, glare index, sky glow intensity, and other metrics [22]. With the breakthrough of satellite remote sensing technology, the research scale of light trespass has been expanded. Among them, relevant studies have improved the detection and analysis accuracy of large-scale light trespass through night light remote sensing data and high-resolution satellite technology [23]. In addition, another study accurately characterized the heterogeneity of light trespass in the urban area of Nanjing, China, through field illuminance measurements and Luojia imagery [24]. Along with the enhancement of detection capability, relevant researchers have begun to systematically analyze the impact mechanism of light trespass. For example, studies have shown that excessive ALAN not only reduces the visibility of the sky but also affects human health by suppressing melatonin secretion and significantly affects the circadian rhythm of plants and animals [25]. At the same time, to address the impact of the above light trespass, relevant research has optimized the streetlight layouts through GIS spatial analysis, so as to reduce the impact of light trespass [26]. Furthermore, there are studies that incorporate remote sensing of night lighting into urban management systems, effectively improving the synergistic optimization of lighting efficiency and ecological protection [27]. However, single technical methods have certain limitations. For example, while multi-source remote sensing data can improve the timeliness of detection, bottlenecks such as sensor calibration and algorithm standardization need to be addressed [28].

In summary, there are some limitations in the existing studies. On one hand, most studies are limited to a single technology and fail to synergize multiple technologies to form a more comprehensive optimization system; on the other hand, for urban residential areas, outdoor lighting is necessary to satisfy the night activities of residents, and the prevention of indoor light trespass is the key to ensuring the quality of sleep and the comfort of residents, which are closely related. Still, there is a lack of research on the synergistic optimization of the two. Therefore, this study provides an effective solution to improve the quality of night lighting in urban residential areas by establishing a multi-platform assessment framework to synergistically optimize the two objectives of outdoor night lighting and indoor light trespass.

2.2. Multi-Objective Optimization (MOO) Methods in Lighting Research

In the night lighting design of urban residential areas, how to trade off between outdoor lighting and indoor light trespass at night is a multi-objective optimization problem with typical conflict characteristics. Therefore, constructing a reasonable multi-objective optimization model is of great significance for night architectural lighting research.

Relevant studies have pointed out that the Multi-Objective Optimization Algorithm based on evolutionary algorithms is widely used in the fields of construction, urban planning, transportation, and energy due to its stable robustness and global nature [29]. The advantage is the ability to weigh multiple conflicting goals and generate Pareto solution sets to provide designers with a variety of solutions [30]. Secondly, MOO not only has the ability to deal with multi-objective problems, but also can be easily integrated with performance simulation platforms, thus providing significant advantages in the study of the built environment and urban design [31]. In the field of night lighting, related research has gradually shifted from simple energy consumption analysis to multi-dimensional consideration of light trespass and visual comfort. At present, the MOO method has not yet been applied in the study of night lighting and light trespass in residential areas. It still needs to be explored how to balance the lighting demand of public areas and indoor light trespass, as well as how to set the optimization target. In the field of roadway lighting, a study applied MOO to roadway lighting design. For the first time, it included lighting quality in the optimization objective and constructed a model with luminance uniformity, glare prevention, and energy consumption as the objectives [32]. Another study examined the design of lighting for rural roads and ecological reserves, using MOO to weigh the issues of visibility, energy efficiency, and light interference, resulting in a conceptual model of “eco-lighting” [33]. In addition, relevant researchers in construction lighting research constructed a multi-objective mixed-integer planning model, designed to meet the basic lighting needs of the construction site under the premise of constraints on the layout and operation of the lamps and lanterns, to balance light trespass and the cost of installation, for the rational design of night lighting at the site to provide data support [34]. Although MOO has demonstrated significant applicability in the design of night lighting environments, there are limitations in the decision-making phase of the scheme, such as the large set of Pareto optimal solutions, which affects the efficiency of the final decision-making process [30]. Especially in lighting environments, evaluation criteria often include social, cultural, and aesthetic indicators that are difficult to quantify, further reducing the precision of program selection [31].

In summary, MOO provides a powerful tool for night lighting design. However, in this study, an assisted decision-making mechanism needs to be introduced to trade off between outdoor night lighting and indoor light trespass problems, and to ensure the efficiency and accuracy of program screening.

2.3. Decision Support for Optimization Schemes

In multi-objective optimization problems, algorithms such as NSGA-II and multi-objective particle swarm optimization usually produce a large set of non-dominated solutions, making it difficult for decision makers to quickly filter out representative solutions [29,35,36]. For this reason, researchers usually use machine learning algorithms such as clustering and neural networks to post-process the solution set, which improves the interpretability and screening efficiency of the scheme [37].

Earlier studies have mainly used fuzzy C-means, hierarchical clustering, and Gaussian mixture models to reveal clustering trends in the solution set and identify representative values [35,38]. However, traditional clustering methods usually have some limitations. Studies have shown that most methods require the decision maker to artificially preset the number of clusters, which may lead to overfitting and significantly affect the clustering quality of the solution set [39,40]. Moreover, although fuzzy clustering can characterize the similarity between solution sets, it is susceptible to local optimal solutions [38]. Therefore, effective assisted decision-making tools are particularly important for the efficient and accurate screening of solution sets. In recent years, the K-means clustering method has been widely used in multi-objective optimization problems. Compared with traditional methods, the K-means method is computationally efficient, adaptable, and able to effectively capture the localized dense regions in the solution set and identify representative solutions, which significantly improves the screening efficiency of decision makers. By integrating K-means and gravitational search algorithms, the researchers have achieved fast structured grouping of solution sets and optimal solution localization [41]. Another study has greatly enhanced the ability of K-means to extract solution set distributions by combining it with a genetic algorithm [42]. In addition, K-means clustering has been used as a decision support tool in multi-objective particle swarm optimization to achieve automatic filtering of globally representative solutions in the solution set, while demonstrating significant generalization capabilities [43].

Based on the above research background, K-means clustering is not only suitable for fast classification of high-dimensional solution sets but also can be used as an effective decision-making tool in multi-objective optimization problems. However, the method is also affected by the number of artificially preset clusters. Future research could further combine this clustering method with intelligent optimization mechanisms to achieve synergistic optimization of clustering efficiency and accuracy.

3. Research Methods

3.1. Research Framework

This study proposes a cross-platform collaborative optimization framework integrating parametric modeling, multi-objective optimization, and Spearman correlation analysis, aiming to trade off the maximization of outdoor night lighting with the minimization of indoor light trespass. The framework mainly consists of four core components: field research and parameter setting, performance simulation and multi-objective optimization, correlation analysis, and decision support (Figure 1).

3.2. Field Research Studies

This study takes multi-story houses in the residential areas of Shijingshan in Beijing as an example, mainly because one of the core orientations of Shijingshan is eco-livability, compared to other highly commercialized central districts. This characteristic makes the area a good place to study the effects of night light trespass on human comfort [44]. Moreover, the source of light trespass in high-rise residential buildings is more complex and susceptible to factors such as distant billboards and electronic screens. In contrast, multi-storey residential buildings are widely spaced to avoid the reflection of light from the surrounding buildings. They are mainly affected by the surrounding streetlights, thus greatly reducing the interference of external variables on the experimental results. Since 1997, Beijing has carried out a large-scale urban night lighting program, which has resulted in an unprecedented development of lighting facilities and a gradual increase in the ambient brightness of activity places in residential areas [45]. Nevertheless, Beijing has a high density of buildings, population, and lighting facilities. This dense layout pattern has led to serious light trespass in residential areas, greatly affecting the night comfort of residents. More notably, the city has been designated a seriously light-polluted area by Science Advances [18]. This further highlights the urgency of the night lighting problem in that city. Taking the residential areas of Shijingshan in Beijing as the research object, this study aims to explore the coupling relationship between outdoor night lighting and indoor light trespass. In the field research phase, the research team conducted field research on all 196 residential activity places in the Shijingshan area one by one, and collected data related to activity place illuminance, streetlight height, streetlight arrangement, etc. (Figure 2).

After the preliminary statistics of 196 activity places in residential areas were analyzed, it was found that the area of activity places was concentrated between 8 and 10,000 m²; in terms of shape, they could be mainly classified into rectangular, triangular, square, and irregular polygonal places. On this basis, we found that there are discrete values in the data through box-and-line diagram analysis. To ensure an accurate grasp of the real night lighting situation in the residential areas of Shijingshan, the study eliminated some of the outliers and selected data samples located within the range of 25~75%. The final data sample included activity places with an area greater than 112 m² or less than 468 m². Secondly, in order to be able to truly reflect the overall characteristics of the activity places in the Shijingshan residential area, the unrepresentative heterogeneous places were further excluded, and finally, 38 regular activity places, including rectangular and square places, were selected. In order to achieve accurate simulation and optimization of these activity places, the study used parametric modeling with five streetlight matrices commonly found in the research sample as prototypes.

3.3. Parameter Selection and Objective Function Construction

3.3.1. Design Variables

In the selected samples, based on the actual dimensions of the activity places and the arrangement density of streetlights, the study first divides the streetlight matrix of the activity places into five types: 2 × 2, 2 × 3, 2 × 4, 3 × 3, and 3 × 4 (Figure 3). Meanwhile, in order to improve the reliability and validity of the simulation, we further provided accurate boundary constraints. Combined with the research results of existing literature, the study introduces four more types of design variables: Streetlight Height (SH), Streetlight Span (SS), Streetlight Depth (SD), and Distance Between Buildings and Streetlights (DBS) (

Table 1. Design variables and their distribution.

Design Variable	Abbreviation	Range	Unit	Probability	Basis	Basisline
Streetlight Matrix Type	SMT	0, 1, 2, 3, 4	-	Discrete	Field survey, n = 38	-
Distance between Buildings and Streetlights	DBS	3~15	m	Continuous		8
Streetlight Height	SH	2~5	m	Continuous		2.5
Streetlight Span	SS	13~70	m	Continuous		10
Streetlight Depth	SD	6~25	m	Continuous		10

NOTE: n represents the number of research locations. The numbers 0, 1, 2, 3, and 4 refer to L0, L1, L2, L3, and L4, respectively.

). Relevant studies have shown that SH directly affects the coverage of lighting and the distribution of luminous flux, and the difference in the projection angle of streetlights of different heights will cause different degrees of lighting effects on the surrounding environment, so they are included in the design variables of this study [46,47]; the spacing of streetlights affects the uniformity of illumination. Too much spacing may result in areas of contrasting light and darkness in the event space, affecting the safety of residents at night. Too little spacing may result in light stacking and thus increase the risk of light trespass [48,49]. DBS is of significant importance in the light trespass problem, as it directly determines the path of the light and the degree of attenuation of the light as it travels. When the distance is close, the spill light is more likely to penetrate into the interior space with less attenuation, and the risk of light trespass in the interior is usually higher [50].

By introducing these five variables, a more comprehensive and diversified parametric model can be constructed, providing richer input parameters for the subsequent performance simulation and multi-objective optimization stages.

3.3.2. Performance Objective Function

In order to achieve a balance between outdoor night lighting and light trespass, the study adopts a multi-objective optimization method based on NSGA-II. The algorithm mainly weighs conflicting objectives by simulating the natural selection mechanism, and finally generates the Pareto optimal solution set with the following function formula (1). On the basis of this formula, this study constructs two performance objective functions for minimizing the vertical illuminance of the building window and maximizing the horizontal illuminance on the ground of the activity places, whose mathematical expressions are given in Equations (2) and (3) as follows:

$$\begin{gathered} \mathrm{m}\mathrm{i}\mathrm{n}\mathrm{f}\left(\mathrm{x}\right)={\left[{\mathrm{f}}_1\left(\mathrm{x}\right),{\mathrm{f}}_2\left(\mathrm{x}\right),\dots {\mathrm{f}}_{\mathrm{n}}\left(\mathrm{x}\right)\right]}^T \\ \mathrm{s}.\mathrm{t}.{\mathrm{g}}_{\mathrm{i}}\left(\mathrm{x}\right)=(0,i=\mathrm{1,2}\dots ,h,x\in R) \end{gathered}$$

(1)

$$-\mathrm{M}\mathrm{a}\mathrm{x}{\mathrm{f}}_{{\mathrm{E}}_{\mathrm{h},\mathrm{a}\mathrm{v}}}={\mathrm{g}}_{\mathrm{i}}({\mathrm{x}}_1,{\mathrm{x}}_2,\dots ,{\mathrm{x}}_{\mathrm{k}})$$

(2)

$$\mathrm{M}\mathrm{i}\mathrm{n}{\mathrm{f}}_{{\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{v}}}={\mathrm{g}}_{\mathrm{i}}({\mathrm{x}}_1,{\mathrm{x}}_2,\dots ,{\mathrm{x}}_{\mathrm{k}})$$

(3)

All of the above objective functions use the design variables enumerated in this study as input parameters, where $\mathrm{f}\left(\mathrm{x}\right)$ denotes the objective function and ${\mathrm{x}}_{\mathrm{k}}$ represents the k-dimensional design variables. In this study, it mainly refers to five adjustable variables, namely SS, SD, SMT, SH, and DBS. Moreover, each objective function is limited by a specific constraint ${\mathrm{g}}_{\mathrm{i}}\left(\mathrm{x}\right)$. Given that the Wallacei X v2.7 platform defaults to minimization as the optimization direction, this study inverts ${\mathrm{f}}_{{\mathrm{E}}_{\mathrm{h},\mathrm{a}\mathrm{v}}}$ and inputs it into the optimization model, while ${\mathrm{f}}_{{\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{v}}}$ is kept as the default.

3.4. Evaluation Indicators for Night Lighting

3.4.1. Horizontal Illuminance on the Ground of the Activity Place (${\mathrm{E}}_{\mathrm{h},\mathrm{a}\mathrm{v}}$)

${\mathrm{E}}_{\mathrm{h},\mathrm{a}\mathrm{v}}$ refers to the intensity of light received at the horizontal ground of an activity place, and is a key parameter for measuring the quality of lighting at an activity place. ${\mathrm{E}}_{\mathrm{h},\mathrm{a}\mathrm{v}}$ is closely related to the visibility, safety, and accessibility of residents at night. Secondly, it also affects the visual level of the surrounding environment and the overall environmental satisfaction. Relevant standards show that the activity plaza has ${\mathrm{E}}_{\mathrm{h},\mathrm{m}\mathrm{i}\mathrm{n}}$ for 10 lx, ${\mathrm{E}}_{\mathrm{h},\mathrm{a}\mathrm{v}}$ for 30 lx [51]. In addition, at ${\mathrm{E}}_{\mathrm{h},\mathrm{a}\mathrm{v}}$ of 5 lx, the satisfaction level of residents is 60%; at ${\mathrm{E}}_{\mathrm{h},\mathrm{a}\mathrm{v}}$ of 10 lx and 15 lx, the satisfaction level is about 65% and 80%, respectively [14]. In this study, by using the Radiance kernel integrated into Honeybee v0.0.069, the horizontal illuminance is measured accurately at the sampling points inside the activity places, and the average value is taken as the quantitative result of this index. The calculation formula is as follows (4):

$${\mathrm{E}}_{\mathrm{h},\mathrm{a}\mathrm{v}}={\displaystyle \frac{\mathrm{I}·\cos \mathsf{\theta }}{{\mathrm{d}}^2}}$$

(4)

3.4.2. Vertical Illumination of Building Windows (${\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{v}}$)

${\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{v}}$ refers to the light intensity formed on the window surface by the luminous flux produced by outdoor lighting facilities, which reflects the potential interference of outdoor light sources on indoor space. In the relevant lighting standards, the provisions for urban residential window illuminance are divided into two categories: before lights out, shall not be greater than 10 lx; after curfew, shall not be greater than 2 lx [52]. Excessive ${\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{v}}$ can cause severe light trespass, which can disrupt residents’ circadian rhythms and affect sleep quality [8]. In this study, when monitoring ${\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{v}}$, the detection points are mainly set at the windows of the main functional areas of the building, with an interval of 1 m and a range of 3~20 m. The specific calculations are shown in (5):

$${\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{v}}={\displaystyle \frac{\mathrm{I}·\sin \mathsf{\theta }}{{\mathrm{d}}^2}}$$

(5)

In the above two formulas, E represents the illuminance in lx; I represents the light intensity of the light source in a particular direction in cd; θ refers to the angle between the light ray and the normal to the illuminance test surface in °; d represents the distance between the light source and the testing point in m.

3.5. Parametric Simulation Model and Simulation Optimization

3.5.1. Parametric Simulation Modeling

Based on the above research samples and design variables, the study constructs a parametric model of the activity places through Rhino v7.33 and Grasshopper v1.0.0007. Secondly, the Honeybee plug-in is used to identify and interface with the above parameteric model. It further sets the night lighting parameters, such as calculation grid accuracy, streetlight illuminance, and sky model in its environment, and finalizes the lighting model. Among them, the calculation grids of activity places and building surfaces are divided with a precision of 1 m × 1 m to improve the accuracy of illuminance calculation; the sky model is selected as a uniform CIE sky model based on the climatic characteristics of the Beijing region to ensure that the illumination conditions in the simulated environment are in line with the actual illumination conditions.

3.5.2. MOO Simulation

After the model is built, the simulation is carried out using Ladybug tools v0.0.66. The Ladybug v0.0.66 component is used to initialize the simulation environment, and then Honeybee is used to construct the 3D geometric model, define the light source type, and call the Radiance lighting simulation kernel to accurately calculate the lighting metrics for each scenario, repeating the process until all individual variables have been simulated, and then using TT Toolbox v2.0.7 to construct a dataset that contains both the design variables and the target. Through Wallacei’s internal NSGA-II algorithm, it automatically filters the dataset for individuals with balanced performance and that are not dominated by each other, and finally generates the optimal Pareto front solution set, realizing the complete process from parametric modeling-simulation analysis-optimization solution set extraction. The integrated NSGA-II algorithm can quickly evolve non-dominated solution sets among multiple conflicting objectives with high flexibility and good constraints, and finally achieve the trade-off and optimization among multiple objectives [53]. The specific parameter settings for the NSGA-II algorithm are shown below (

Table 2. NSGA-II algorithm parameter settings.

Parameters	Values
Crossover Probability	0.9
Mutation Probability	1/0.9
Crossover Distribution Index	20
Mutation Distribution Index	20
Random Seed	1
Generation Count	40
Generation Size	50
Fitness Objectives	2
Genes Values	6

).

3.6. Analysis of the Correlation Between the Objective Function and the Design Variables

3.6.1. Theoretical Basis of Spearman Correlation Analysis

In order to further explore the correlation between the objective function and the design variables, this study introduces the Spearman correlation analysis method to statistically analyze the solution set. This method is a non-parametric statistical method that measures the linear or non-linear monotonic relationship between two variables by calculating the correlation coefficient, where the index takes the value range of [−1, 1]. A positive value characterizes the facilitating effect between the variables, while a negative value represents the inhibitory effect. In addition, the closer the absolute value is to 1, the stronger the correlation [54]. Compared to the Pearson correlation coefficient, the Spearman correlation analysis is not limited by the distribution state of the data and is more robust to outliers.

3.6.2. Operational Steps

In the specific implementation process, the optimized solution set is first preprocessed to ensure the data integrity of the seven input parameters SS, SH, SD, SMT, DBS, ${\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{v}}$, and ${\mathrm{E}}_{\mathrm{h},\mathrm{a}\mathrm{v}}$, and then the Correlation Plot v1.31 plug-in based on the Origin 2024 platform is used to perform correlation analysis on the 2000 solution sets obtained from the multi-objective optimization to visualize the results, and the 7 × 7 correlation heat map is automatically calculated after running the plug-in. The statistical analysis results provide a scientific basis for the subsequent screening of design variables, lighting performance trade-offs, and decision support.

3.7. Programmatic Decision Support

In the process of multi-objective optimization, NSGA-II usually generates a series of Pareto-optimal solution sets, which represent the optimal equilibrium between different objectives but are large in size and complex in structure. As a result, designers often have difficulty quickly filtering the more advantageous solutions based on experience and are unable to intuitively grasp the diversity of the solution sets and their representativeness.

To alleviate this problem, this study introduces the K-means clustering algorithm to classify the solution set in a structured way and improve the efficiency of data screening. K-means clustering is an unsupervised machine learning method that is able to classify the high-latitude solution set into a number of neighboring subclasses. The algorithm has the advantages of high computational efficiency, simple implementation, and suitability for large-scale datasets, etc. By setting the appropriate number of clustering clusters, it automatically identifies similar optimization solutions and performs cluster compression to realize the transformation from a large number of optimal solutions to a small number of typical solutions [55]. The center solution of each class is the representative solution of the solution set of the class, which can help the design to quickly identify the structured features and performance parameters of different classes of solution sets. In addition, the K-means clustering algorithm is able to identify boundary solutions that are biased towards a certain optimization objective, which provides support for the subsequent construction of design parameters. It is worth noting that in this study, although the Pareto optimal solution sets have been obtained in the multi-objective optimization process, they are limited and concentrated, and there may be situations such as local convergence or local optimality, which ignores the potential other high-quality regions, leading to difficulties in accurately revealing the diversity of the solution set space and the performance distribution characteristics. Therefore, the feasible solutions are finally selected for clustering analysis, while the appropriate number of clusters K is determined based on the elbow diagram and contour coefficients, so as to ensure the accuracy of the results (Figure 4).

4. Results and Discussions

4.1. Feasible Solutions and Pareto Optimal Solution Sets for Multi-Objective Optimization

This section focuses on the results generated by the multi-objective optimization, where the study generates a total of 2000 feasible solution sets and 12 Pareto optimal solution sets after 40 generations of simulation iterations. In order to deeply understand the mechanism between the design parameters and the objective function, the feasible and optimal solutions are superimposed, analyzed, and plotted as a parallel coordinate plot (PCP) (Figure 5).

In terms of the overall distribution of the PCP, the feasible solutions are more widely distributed (Figure 5b). For example, ${\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{v}}$ ranges from 0 to 23 lx; ${\mathrm{E}}_{\mathrm{h},\mathrm{a}\mathrm{v}}$ extends from 1.9 lx to 34 lx, reflecting the complexity and diversity of the feasible solution space. While the Pareto optimal solution, as the non-dominated solution set obtained after multi-objective optimization, shows more obvious aggregation characteristics in the figure (Figure 5a), ${\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{v}}$ and ${\mathrm{E}}_{\mathrm{h},\mathrm{a}\mathrm{v}}$ are mainly concentrated in the intervals of 0~11 lx and 11~34 lx, respectively, and there are only 12 solutions. Further analysis reveals that there are a large number of inferior solutions within the feasible solutions, although some of the solutions achieve a higher level of ${\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{v}}$ or lower ${\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{v}}$, the performance of the other objective deteriorates. For example, Gen.9 Ind.32 has a higher ${\mathrm{E}}_{\mathrm{h},\mathrm{a}\mathrm{v}}$ but also has a level of ${\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{v}}$ of 13.154 lx, which is beyond the reasonable range bounded by the specification; Gen.13 Ind.19 has a lower ${\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{v}}$ but its ${\mathrm{E}}_{\mathrm{h},\mathrm{a}\mathrm{v}}$ is only 5.461 lx, which does not meet the night lighting demand of the activity place. The Pareto optimal solution set in the PCP shows a better combination of objective functions, i.e., most of the values of ${\mathrm{E}}_{\mathrm{h},\mathrm{a}\mathrm{v}}$ are in the range of 15~30 lx, while ${\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{v}}$ is also basically controlled within 10 lx and mainly concentrated in 0~2 lx. This difference in spatial distribution indicates that the Pareto optimal solution is selected from a large feasible solution space, and it has the advantage of maximizing outdoor night lighting while preventing and controlling the night illumination of activity places. Thus, the optimal Pareto solution achieves a better balance between maximizing outdoor night illumination and preventing light trespass.

As can be seen from the PCP plot of the Pareto optimal solution (Figure 5a), there is a tendency of isotropic change between the two objective functions, indicating that there is no obvious conflict between them. This result is consistent with the conclusions of the existing literature, which verify the isotropic change between outdoor lighting and indoor light trespass and the necessity of control by setting different vertical illuminance in different lighting environment areas [56]. Secondly, the SS and SD variables have a wide and uniform range of variations, indicating that their influence on the objective function is less significant in the optimization stage. The SH and DBS variables are more densely distributed in the optimal solution set and show an obvious coupling relationship with the objective function, which indicates that they have a strong sensitivity to changes in the objective function and can significantly affect the quality of the solution set. This is consistent with the conclusions of other lighting studies. Previous studies on urban street and campus lighting have revealed that the installation height and spacing of streetlights affect the formation of light spots, and when streetlights are close to the building, they form a small area of light spots with high illumination and luminance; when the height of the streetlights is increased, the illumination range is enlarged, but it reduces the light intensity per unit area [57,58]. It is worth noting that only three types of SMT variables, L0, L1, and L2, are left in the set of optimal solutions, suggesting that these three fixture scheduling types are able to balance the two objective functions well.

4.2. Characterization of the Global Optimal Solution

Based on the PCP analysis, this section visualizes the distribution characteristics, advantages, and formation logic of the optimal solutions in the feasible solution space through the 2D scatter plot view (Figure 6). In the 2D scatter plot, the feasible solutions form a dense region with a large number of inefficient points; in contrast, the Pareto optimal solution set is mainly concentrated in the region with high ${\mathrm{E}}_{\mathrm{h},\mathrm{a}\mathrm{v}}$ and low ${\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{v}}$ forming a Pareto curve from the bottom left to the top right, which clearly shows the evolution trend of the optimal solutions. All solutions satisfy the condition that it is impossible to raise ${\mathrm{E}}_{\mathrm{h},\mathrm{a}\mathrm{v}}$ without increasing ${\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{v}}$ or to lower ${\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{v}}$ without decreasing ${\mathrm{E}}_{\mathrm{h},\mathrm{a}\mathrm{v}}$. This echoes the characteristics of the optimal solution set, focusing on the performance boundaries exhibited in the PCP, which further validates the efficiency of the NSGA-II algorithm. This is consistent with previous studies, which identified an optimal balance of daytime light maximization and radiation minimization at the Pareto boundary, confirming that the MOO method is able to effectively balance multiple performance metrics [59], and provides theoretical support for this paper’s trade-off between night outdoor lighting and the prevention of indoor light trespass at activity places.

Secondly, there is a certain distance between the Pareto frontier solution and the dense feasible solution, indicating that NSGA-II has a good ability in controlling the diversity and stepwise nature of the solution set. This is consistent with the findings of previous studies, which pointed out that the traditional NSGA-II algorithm is able to maintain the diversity of the non-dominated solution set, but attention should be paid to the disadvantage that the crowding-distance strategy it employs tends to lead to an uneven distribution of the solution set [60]. In addition, the points in the vicinity of the Pareto curve indicate that, while many solutions are good at meeting the illuminance levels and controlling the disruptive effects of light trespass in night activity places, only a few are optimal. In a multi-objective optimization design study of a library building, the researchers found that the density of points near the “best solution” region indicates that, while different building configurations can reduce building energy consumption and discomfort time, only a few configurations can meet the high human demands for building cooling and heating energy and comfort time [61].

Overall, the figure not only reveals the synergy between the two optimization objective values, but also verifies the practicality of the optimization model proposed in this study for urban night lighting. This is achieved by quantitatively analyzing the spatial density and distribution characteristics of the solution set.

4.3. Results of Spearman Correlation Analysis

To further reveal the correlation between the two optimization objectives and the design variables, this study used Spearman’s rank correlation analysis to quantify them (Figure 7). The results of the study show that there is a weak but significant positive correlation between ${\mathrm{E}}_{\mathrm{h},\mathrm{a}\mathrm{v}}$ and ${\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{v}}$, reflecting a certain synergistic trend between the two in terms of evaluation dimensions. This trend suggests that as the ground illuminance of an activity place increases, it is usually accompanied by an increase in window illuminance, but the two variables are not perfectly synchronized, suggesting that they may be influenced by other factors. In studies evaluating night lighting, regression analyses have shown that building height, percentage of vegetation, and building coverage all affect light levels [62].

Among the key design variables, ${\mathrm{E}}_{\mathrm{h},\mathrm{a}\mathrm{v}}$ showed a positive correlation only with SMT and SH, while ${\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{v}}$ showed a positive correlation with SMT, SH, and SS. Among them, ${\mathrm{E}}_{\mathrm{h},\mathrm{a}\mathrm{v}}$ shows a strong and significant positive correlation with SH, indicating that under the current design conditions, SH has a significant impact on ${\mathrm{E}}_{\mathrm{h},\mathrm{a}\mathrm{v}}$. Appropriately raising SH can help to raise the illumination level of the ground, which may be due to the fact that SH expands the light coverage and homogeneity, and is more capable of raising the illumination level of the surroundings, especially in the absence of shading. In previous studies of lighting levels in urban streets, it was shown that raising SH appropriately helps to improve the uniformity of illumination of the surrounding environment, light shines further away from the area with a smaller angle of incidence, and areas with strong contrasts between light and dark are avoided [63]. Moreover, another study showed that increasing the installation height is one of the effective means of controlling glare, i.e., when the light source is located higher, less light enters the driver’s field of vision, which effectively reduces the uncomfortable glare environment, thus verifying that the streetlight height has a significant impact on ground illuminance in night activity places [64]. However, ${\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{v}}$ is less correlated with this variable, suggesting that SH has little effect on the window surface illuminance. This is probably because the window illuminance is more susceptible to DBS, and when the distance is greater, the light is already substantially attenuated by the time it reaches the window. This is in line with the findings of previous studies, where researchers showed that increasing DBS resulted in a significant decrease in the average illuminance of the building surface, revealing that changing the mounting height of the luminaire had a negligible effect on the illuminance values [57].

${\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{v}}$ showed a medium-strength positive correlation with SMT, indicating that this variable can significantly affect the magnitude of ${\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{v}}$, and revealing that the propagation path of light in space is modulated by SMT. In contrast, SMT has a lesser effect on the ground illuminance. In other studies, a significant effect of the streetlight matrix on ground illuminance was revealed, i.e., streetlights arranged bilaterally created a significantly higher level of illuminance than a unilateral arrangement [65], this is contrary to the findings of this paper and may be due to the fact that the streetlight matrix specifications for residential activity places are much smaller than the streetlight row specifications for urban streets. Secondly, ${\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{v}}$ and DBS show a strong significant negative correlation, indicating that the closer the luminaire is to the building, the higher the illuminance on the window surface, and the greater the intrusion suffered by the residents, which reveals that DBS should be reasonably controlled in the actual lighting design. Whereas ${\mathrm{E}}_{\mathrm{h},\mathrm{a}\mathrm{v}}$ shows a lower correlation with this variable. The inverse square law and existing studies also confirm that the light level decreases gradually with the increase in distance [57]. Furthermore, the horizontal and vertical distances of the streetlights likewise have a limited effect on ${\mathrm{E}}_{\mathrm{h},\mathrm{a}\mathrm{v}}$ and ${\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{v}}$. It is worth noting that the correlation between the design variables also reveals the relative independence of the design dimensions. From the figure, we can learn that the correlation between the variables is generally weak, indicating that there is basically no coupling between the variables, which is conducive to the realization of the joint regulation of multi-dimensionality in lighting design. In previous studies, it has been pointed out that the effect of SH on light coverage, uniformity, and illuminance level is dynamic, and a higher installation height allows for greater pole spacing, expanding the coverage of the lamps and lanterns, and the uniformity of different arrangements has significant differences. In addition, it is also pointed out that the lighting effect does not monotonically increase with the height, but is also closely related to the arrangement and pole spacing [66,67]. This also verifies that the multi-objective optimization function is jointly influenced by the variables and is reflected in the correlation analysis.

In summary, the Spearman correlation analysis reveals the role of the relationship between design variables and lighting indicators. In the actual lighting design, ${\mathrm{E}}_{\mathrm{h},\mathrm{a}\mathrm{v}}$ should prioritize the setting of SH, while ${\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{v}}$ should focus on DBS and SMT. The results of this analysis provide an important reference for subsequent decision support and parameter sensitivity ranking.

4.4. K-Means Cluster Analysis

4.4.1. Selection of Clustered Data

In order to ensure the accuracy of the decision-making scheme, the study first classifies the solution sets into five types according to SMT, initially screens the solution sets with balanced lighting performance, and then visualizes and analyzes them through the “kernel density map + box line diagram” (Figure 8 and Figure 9). The results show that the ${\mathrm{E}}_{\mathrm{h},\mathrm{a}\mathrm{v}}$ of all five types are mainly concentrated in the range of 10~20 lx, but the median of L2 and L3 is larger than that of the other types, which demonstrates better horizontal illuminance on the ground of the activity places, and the interquartile range of the two types is smaller than the other three types, which indicates that the data are more concentrated and the performance is more stable. The kernel density plot then shows that L3 has a significantly larger ${\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{v}}$ than L2 in the high-density area, and there are a large number of medium-density areas greater than 10 lx. Further analysis shows that the ${\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{v}}$ value of L0 is focused in the range of 1.486~4.241 lx, the distribution is more concentrated, and the spacing between the median and the second quartile is significantly lower than that of the other four types, which is able to satisfy the specification and improve the indoor comfort at night. Secondly, the kernel density map also shows that the ${\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{v}}$ of L0 is strictly controlled in the range of 0~10 lx, and the high-density area is concentrated in the range of 0~3 lx, which indicates that this type can generally form a lower ${\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{v}}$.

In the above analysis, a certain number of highly dispersion values were found, which may be due to ground reflectance. In previous studies, researchers have shown that ground reflectance and ground configuration affect the risk of light pollution in low-floor buildings, with higher ground reflectance and brighter building surfaces resulting in a greater risk of light pollution [68]. In order to ensure the accuracy of the clustering results, the study eliminated the discrete values of the data samples and finally selected the L2 with good performance of ${\mathrm{E}}_{\mathrm{h},\mathrm{a}\mathrm{v}}$ and the L0 solution set with excellent performance in ${\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{v}}$ for the K-means clustering analysis, with a total of 814 samples.

4.4.2. K-Means Clustering-Driven Screening for Programmatic Decision Making

Firstly, the 814 solution sets are normalized to eliminate differences in the quantiles. Secondly, based on the Python v3.12.10 platform, the clustering effect under different cluster classes was compared using contour coefficients, and the final optimal number of clusters was three. Subsequently, the clustering iteration was carried out until the convergence state (Figure 10). The results show that K-means better fits the distribution characteristics and diversity of the data samples, in which Cluster1 and Cluster2 contain different numbers of Pareto optimal solutions.

In terms of the objective space, Cluster1 and Cluster2 are overall more concentrated, and the overall samples are more densely distributed near the Pareto front, which represents a more balanced performance in terms of the core objectives, and may be a more worthwhile region to prioritize in the actual night lighting design. Secondly, the two optimization objective intervals of Cluster2 are highly similar to the Pareto optimal solution intervals generated by the previous multi-objective optimization, which implies that Cluster2 may be an efficient interval for generating the optimal solution set, i.e., it is easier to adjust the design variables within this range to obtain a lighting design solution that satisfies the residents. Compared with the first two clusters, the data samples in Cluster3 are more dispersed, the fluctuation of ${\mathrm{E}}_{\mathrm{h},\mathrm{a}\mathrm{v}}$ is twice as large as that of the other two clusters, and the spatial characteristics of ${\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{v}}$ are not clearly characterized. In addition, it is farther away from the Pareto frontier, indicating that the overall feasible solution quality of this category is not high enough to generate the Pareto optimal solution in the subsequent optimization.

Combined with the clustering results, it can be seen that the existing Pareto optimal solution set originates from the non-inferior solutions among the feasible solutions, and the study further narrows the optimal solution interval obtained from the above multi-objective optimization through clustering, which greatly improves the efficiency of scheme decision-making [69].

In this study, to determine the optimal number of clusters for the data, clustering results under different K values were evaluated. The findings indicate that the SSE (sum of squared errors) consistently decreases as the number of clusters increases, but the rate of decline noticeably slows around K = 3. This suggests the potential presence of an elbow point, where further increasing the number of clusters yields limited improvement in internal compactness. Concurrently, the Silhouette coefficient reached its maximum value (0.406) at K = 3, while the Davies–Bouldin index attained its minimum value. This indicates optimal intra-cluster compactness and inter-cluster separation at this point. Furthermore, as K exceeded 3, the Silhouette coefficient progressively decreased with the increasing number of clusters (

Table 3. Evaluation indices under different numbers of clusters.

K	SSE	Silhouette	Davies–Bouldin
2	956.024	0.395	1.041
3	593.027	0.406	0.851
4	478.320	0.365	0.927
5	386.303	0.365	0.871
6	321.908	0.343	0.859
7	283.797	0.343	0.863
8	247.050	0.346	0.874
9	219.304	0.332	0.892
10	199.204	0.335	0.886

, Figure 11).

To further ensure the accuracy of the clustering results, the study plotted the sample data within the above three clusters as box-and-line plots for quantitative analysis (Figure 12). The results show that the mean value of ${\mathrm{E}}_{\mathrm{h},\mathrm{a}\mathrm{v}}$ for Cluster2 and Cluster3 is significantly higher than that of Cluster1, indicating that the lighting environments of these two categories can effectively enhance residents’ satisfaction with the night lighting environment, while the risk of falls for vulnerable groups, such as the elderly and children, is greatly reduced. Comparatively, ${\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{v}}$ performs better in Cluster1 and Cluster2, indicating that these two clusters of lighting environments can effectively prevent and control indoor light trespass at night. On the other hand, 50% of ${\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{v}}$ in Cluster3 are higher than 10 lx, which does not meet the specification requirements and can significantly cause indoor light trespass, affecting the comfort of residents’ night life. In summary, the performance of Cluster2 in ${\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{v}}$ and ${\mathrm{E}}_{\mathrm{h},\mathrm{a}\mathrm{v}}$ is more balanced and stable.

Based on the multi-objective optimization and clustering synergistic analysis, this study finally selected two representative solutions from Cluster2 (Figure 13,

Table 4. Final representative solution.

Program Model	${\mathbf{E}}_{\mathbf{h},\mathbf{a}\mathbf{v}}$ (lx)	${\mathbf{E}}_{\mathbf{v},\mathbf{a}\mathbf{v}}$ (lx)	SMT	DBS (m)	SH (m)	SS (m)	SD (m)
Gen.15 Ind.18	24.701	0.541	L0	14	5	41	16
Gen.31 Ind.42	25.644	0.939		10	4.9	35	18

NOTE: The recommended DBS value is 10–14 m, exceeding the specification value of 4 m; the recommended value for E_(h,av) is 24.701–25.644 lx, exceeding the minimum specification of 10 lx; the recommended value for E_(v,av) is 0.541–0.939 lx, below the specification values (pre-curfew: 10 lx, post-curfew: 2 lx); no strict requirements exist for SMT, SH, SS, or SD.

). It is important to emphasize that the numerical values of the recommended solutions in this paper primarily serve to demonstrate the applicability and reference value of the methodology. Their purpose is to showcase the potential of the optimization framework, rather than to provide definitive conclusions with binding implications. These two solutions achieve a good balance in the two core evaluation indexes of ${\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{v}}$ and ${\mathrm{E}}_{\mathrm{h},\mathrm{a}\mathrm{v}}$. It is worth noting that there are both feasible and Pareto optimal solutions within the Cluster2 solution set. Among them, the Pareto frontier solution set is already in the optimal equilibrium state in the objective space, and further optimization of any objective would need to sacrifice the performance of other objectives, which provides the decision maker with a multi-dimensional choice space [70]. Designers can choose appropriate design solutions based on the actual environment. For the feasible solutions of the cluster space, decision makers can adjust the design parameters according to the trend between the feasible solutions and the frontier solutions, so that decision makers can get more solutions aligned with the specific project. The diversity of the solution space precisely verifies the essential characteristics of the complex lighting performance optimization problem, and this kind of data-based decision-making support avoids the blindness of the traditional design based on experience, and also provides a quantifiable scientific basis for night lighting design. With the widespread adoption of adaptive dimming strategies, incorporating such approaches into subsequent parameter optimization would further enrich the scope of this study and enhance the operational feasibility of the proposed framework [71,72]. In addition, this research framework also has the following practical significance: optimization framework developed in this research improves the efficiency of lighting systems by reducing redundant illumination and minimizing light trespass, thus lowering overall energy consumption; in the context of China’s “dual carbon” goals, energy savings in urban lighting directly translate into reduced electricity demand and carbon emissions [73]. Furthermore, our framework provides quantitative guidance for selecting design parameters that support low-carbon lighting strategies. By ensuring outdoor visibility and simultaneously mitigating indoor light trespass, the framework addresses both safety and health concerns, contributing to residents’ comfort and aligning with the UN Sustainable Development Goal on sustainable cities and communities [74]. Finally, optimizing lighting conditions can enhance nighttime visibility and improve the sense of security in public spaces, thereby potentially reducing nighttime crime rates [3].

5. Conclusions

Taking the night lighting design of activity places in old multi-story residential areas in Shijingshan, Beijing, as an example, this study constructs a collaborative optimization framework integrating parametric modeling, multi-objective optimization, correlation analysis, and decision support, systematically reveals the mechanisms of the role between design variables and lighting performance, and provides practical guidance and quantitative basis for the rational design of night lighting in residential areas. Previous studies have primarily focused on street lighting or urban-scale optical remote sensing analysis; our research, however, centers on micro-spaces within old multi-story residential areas in cities, aiming to balance illumination in night outdoor activity places with indoor light trespass. Secondly, although NSGA-II and clustering methods have been applied in other fields, their systematic integration within the specific context of optimizing urban residential lighting has not been explored in prior research. We combined these approaches to cluster multi-objective optimization solutions, thereby establishing a systematic framework for decision support. Furthermore, this study not only delivers technically optimal solutions but also integrates them with energy-saving and carbon-reduction objectives, providing interdisciplinary practical significance for lighting design.

The results of the study show that there is a certain linear relationship between lighting performance indicators and design variables, with ${\mathrm{E}}_{\mathrm{h},\mathrm{a}\mathrm{v}}$ showing a significant positive correlation with SH (0.79), a weak positive correlation with SMT (0.072), and a weak negative correlation with SS (−0.1), SD (−0.16), and DBS (−0.2). This suggests that moderately raising SH can effectively improve the activity place’s lighting uniformity, while ${\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{v}}$ shows a medium-strength positive correlation with SMT (0.54) and a strong significant negative correlation with DBS (−0.76), indicating that reasonable control of the scale of SMT as well as DBS is a key factor in preventing and controlling indoor light trespass. There is a synergistic growth trend between ${\mathrm{E}}_{\mathrm{h},\mathrm{a}\mathrm{v}}$ and ${\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{v}}$ with some linear relationship (0.2), which confirms that there is a structural conflict between the two metrics that should be weighed in the actual design. In addition, the correlation heat map indicates the coupling angle between the five design parameters, which possess good independence and adjustability, and are conducive to the realization of synergistic regulation of multidimensional parameters in the actual lighting design.

Through clustering analysis, this study not only effectively identifies representative solution sets for different lighting preferences, but also finds that the solution set in Cluster2 performs well in two lighting metrics, ${\mathrm{E}}_{\mathrm{h},\mathrm{a}\mathrm{v}}$ and ${\mathrm{E}}_{\mathrm{v},\mathrm{a}\mathrm{v}}$, and contains multiple Pareto-optimal solutions and well-performing feasible solutions inside. Meanwhile, the Cluster2 solution set is highly robust and insensitive to the perturbation of design parameters, making it suitable as a recommended solution region for practical lighting design. The representative solutions finally selected for the study strike an optimal balance between multiple objectives.

• Combining the sample concentration and performance of SMT in Cluster2, it is concluded that the lighting design of residential areas should prioritize the use of a 2 × 2 SMT.
• Appropriate control of the distance between buildings and streetlights (DBS)—an appropriate increase in this distance—can effectively improve the indoor nighttime comfort, with a recommended DBS between 10~14 m.
• Optimize SH to avoid uneven lighting of the activity place; SH should be controlled within 4.9~5 m.
• A reasonable arrangement of horizontal and vertical distances between streetlights can reduce indoor light trespass; SS and SD should be prioritized to take values in the range of 35~41 m and 16~18 m, respectively.

In summary, the core contribution of this study lies in translating the outcomes of multi-objective optimization and cluster analysis into an actionable research framework and foundational design guidance tailored to the real-world context of residential area night lighting. Although this study reveals the design logic of night lighting in urban residential areas, there are some limitations. First, the study area was primarily selected as Beijing’s Shijingshan District, emphasizing the need for localization adjustment and secondary verification when facing high-rise communities, suburbs, or other countries and regions. To provide an operational, multi-objective decision support tool for optimizing the light environment, the paper focuses on investigating the overall impact of activity area lighting parameters in residential zones on indoor spaces. Factors (e.g., adopting adaptive lighting strategies, lamp type, spectral characteristics, ground reflectance, facade reflectance, different sky conditions, refined grid scale, glazing type, balcony presence, and window layouts) outside the activity areas are treated as control variables, with emphasis placed on evaluating the performance of different parameter combinations. Second, K-means clustering is sensitive to the choice of K. While this study involves some manual intervention, it yields satisfactory results. Future research could enhance decision robustness by incorporating DBSCAN, hierarchical clustering, or artificial neural networks. Third, this study employed illuminance as the sole evaluation metric. In subsequent research, we will incorporate additional assessment criteria and adaptive lighting strategies, such as glare, brightness, human perception, and comfort, to enhance the framework’s practical applicability. We will address these limitations in subsequent studies to ensure this framework holds interdisciplinary practical significance.