The American scholar Walker proposed a method as early as 1973 to estimate the increase in sky luminance Δ I within a certain range from the city center by collecting measurement data and establishing a numerical model Δ I = f r for night sky luminance increment, the evaluation method for light pollution’s environmental impact, based on optical luminance measurement and a series of indices, still requires further analysis and study (Kocifaj et al., 2019). In the realm of light pollution prevention, the Czech government stands out as the sole country to have enacted comprehensive legislation in 2002, specifically aimed at protecting the atmosphere. This decree has made them the world’s only nation with actual light laws. Other regions across the globe have limited light pollution prevention regulations, primarily at the local level. For instance, Lombardy, a northern Italian state, has developed regulations known as “Urban Outdoor Lighting Energy Saving and Light Pollution Prevention Regulations” (LB.17/200). These regulations outline specific guidelines, such as setting the maximum light intensity of lamps at 0cd/klm in the 90-degree direction and requiring measures to control light spillage in inner corners and provide specialized equipment after curfew hours (Pichardo-Corpus et al., 2020). More than 1/3 of the United States have light pollution control regulations, but so far there is no uniform legal document. The Japanese government recognized the existence of light pollution in 1994, and prepared the Guidelines for the Rational Use of Lamps and Light Pollution Control Guidelines in 2002 and 2006 respectively to further curb light pollution. In summary, existing national regulations on environmental impact assessment of construction projects, while providing indicators for assessing potential impacts on the surrounding environment, do not contain explicit provisions for light pollution (Gaston et al., 2013; Tähkämö et al., 2019). The lack of standards and technical support for the inclusion of light pollution in environmental assessments hinders the operation of environmental protection agencies. As a result, the issue of light pollution remains largely unaddressed in the environmental impact assessment process, thus hindering effective control measures.

In terms of legislation, China has not yet introduced formal standards and norms for the prevention and control of light pollution, only to major universities and institutions of scholars to put forward the relevant recommendations mostly, in 2010, Chinese scholars Huang Shuhan in the rule of law of light pollution, put forward the light pollution directory system, the plan planning system, incentives and rewards system, etc. Specifically explaining the types of infringement and the way to take responsibility, but compared with the status quo of legislation in Japan, Europe and the United States and other countries, China in the mandatory, restrictive standards are still a large gap with the international.

In terms of prevention and control technology, some cities in China have introduced technical standards related to light pollution, for example, in 1999, Tianjin City promulgated China’s first technical specification for nights-cape lighting, which put forward limit values for light pollution such as glare, etc. In 2006, Beijing City promulgated the “Technical Specification for Nights-cape Lighting in Cities,” which clearly stipulates the control standards for the interfering light from the windows of the living rooms of the residences and the wards of the hospitals, and limits the vertical illuminance and direct view of luminous body light intensity of the windows in different periods of time (Tähkämö et al., 2019; Owens et al., 2020). In 2006, Beijing promulgated the “Urban Nights-cape Lighting Technical Code,” which clearly stipulates the control standards for disturbing light from windows in residential rooms and hospital wards, limiting the vertical illuminance of windows and the light intensity of luminous bodies in direct view by time.

In summary, existing light pollution technical regulations and technical guidelines around the world focus mainly on the limitation of brightness and illuminance from a lighting design perspective. However, there is no harmonized standard for light pollution technology. Light pollution exhibits similar forms and hazardous characteristics globally, so it is crucial to share valuable experiences and methods of prevention and control across regions (Macgregor et al., 2015). To enhance public awareness of light pollution and develop effective intervention strategies, this paper employs a systematic approach. Firstly, appropriate indicators are selected to establish a quantitative light pollution prediction model, enabling a thorough analysis of the risk level in a given area. Secondly, an extensive and diverse data set is collected, ensuring the inclusion of various locations to enhance the generalization of model. Lastly, utilizing the established risk assessment model and data-set, potential intervention strategies are proposed. Representative locations are chosen to demonstrate the effectiveness of these strategies, thereby confirming the model’s validity and practicality.

Entropy method is an objective allocation method that utilizes data entropy information, i.e., the amount of information for weight calculation. The lower the information entropy, the greater the degree of variation of the indicator, the more information it provides, the greater the role it plays in the comprehensive evaluation, and the higher the weight. This method is applicable to the data of which it is possible to determine the degree of dispersion of a particular indicator. The higher the degree of dispersion, the greater the influence of the indicator on the overall evaluation. Therefore, the entropy value is used to determine the degree of dispersion of a particular indicator.

Step 1: Data pre-processing

Ensuring the integrity of the data during the acquisition process seems to be a challenge. However, having comprehensive data is critical, so we must properly handle any missing data to improve the accuracy and validity of our model. We next supplemented missing values with mean values, similar values, or identical values with like values, and fitted curves when the database was smooth and continuous data were missing.

Step 2: Entropy weighting determination

First, we arrange the original index data into a matrix A. The elements of this matrix, denoted as x i j , x j , min and x j , max , represent the maximum and minimum values of the j t h evaluation index, respectively. In this context, 1 ≤ j ≤ m. For the data corresponding to these indicators, normalization is necessary, yielding a processed value identified as f i j .

Specifically, for the positive evaluation indicator, the function is: f i j = x i j − x j , min x j , max − x j , min . (1)

The function of the inverse evaluation index is: f i j = x j , max − x i j x j , max − x j , min . (2)

Next, the matrix is normalized by applying the polarization method to the values Z i j , the formula is as follows: Z i j = f i j ∑ i = 1 n f i j 2 , i = 1,2,3 . . . , n , j = 1,2 . . . , m . (3)

Finally, based on the normalized processed information entropy is calculated by entropy weight method W i j ,0≤ W i j ≤1 and Σ W i j = 1, Let y i j be the weight of the total number of standard values for the i t h sample year and the value e i j , h i be the information entropy value of the j t h indicator, and the related formula is as follows: e i j = y i j ∑ i = 1 n f i j 2 . (4) h j = − 1 Ln n ∑ i = 1 n e i j ⁡ ln e i j . (5) w i j = 1 − h j n − ∑ j = 1 m h j . (6)

The subjective weighting method uses Analytic Hierarchy Process (AHP). Compared with other methods, this method requires less quantitative data and analyzes the nature of the problem to be studied, the factors involved in the problem, and the intrinsic connections more clearly and thoroughly. It breaks down the elements associated with decision making into multiple levels such as objectives, criteria and options. Subsequently, qualitative and quantitative analyses are carried out at these levels. Modeling using AHP can be executed in four steps broadly as follows:

◊Establish quantitative criteria: When measuring the relative importance of indicators, the AHP method generally introduces a scale of relative importance in the ninth percentile according to the requirements of psychology, and constitutes a judgment matrix A. The elements of matrix A, A _ij , represent the two-by-two comparison of the relative importance of indicators in the horizontal rows to indicators in the columns B _i (B is the next level of indicators of A). The results of the calculations are shown in Table 2.

Using entropy method to obtain objective assignment of 15 index weights α = α 1 , α 2 , . . . , α 15 . According to the above AHP method to obtain the subjective assignment of 15 index weights β = β 1 , β 2 , . . . , β 15 . According to the formula, combined subjective and objective assignment method for portfolio assignment. c j = α j β j ∑ j = 1 n α j β j j = 1,2 , . . . , 15 . (9)

The calculation results of various weights are shown in Figure 2.

The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is a multi-objective decision analysis method. It is particularly appropriate for comparing multiple solutions or objects, enabling the identification of the best solution or the most competitive object.

Step 1: After calculating the weights of each indicator using the entropy weighting method, and noting as w i j , Construct the weighted decision matrix Z , Z i j is the element in the matrix, the calculation formula is:

Determine the positive ideal solution Z + and negative ideal solutions Z − Z + = Z 1 + , Z 2 + , . . . , Z m + = max i Z i j | j = 1,2 , . . . , m . (11) Z − = Z 1 − , Z 2 − , . . . , Z m − = min i Z i j | j = 1,2 , . . . , m . (12)

Calculate the Marxist distance from the evaluation object to the positive ideal solution Y + and the negative ideal solution Y _ , respectively.

Distance to positive ideal point: d A i , Z + = Z i − Z + T Σ − 1 Z i − Z + . (13)

Distance to negative ideal point: d A i , Z − = Z i − Z − T Σ − 1 Z i − Z − . (14)

Where ∑ − 1 represents the inverse matrix of the covariance matrix of matrix Z. The relative posting progress of the evaluation object is calculated: t i = d A i , Z − d A i , Z + + d A i , Z − . (15)

Where t i is the closeness of the evaluation object to the ideal solution, the larger t i is, the smaller d A i , Z + is, the closer the evaluation object A is to the positive ideal solution, the better the evaluation results, the lower the level of light pollution risk; conversely, the worse the evaluation results, the higher the level of light pollution risk.

After calculating, the ratings of light pollution prevention in urban, suburban, rural and nature reserves in Beijing were obtained and the results are shown in Figure 4 below.

Based on the above scoring results, we performed a one-way ANOVA on the biases caused by the indicators in different environments among them.

One-way ANOVA, also known as one-dimensional ANOVA, is used to analyze whether there are significant differences in the means of the dependent variables when individual control factors are taken at different levels.

The test results are shown in the following Table 3, Table 4 and Table 5. The level of significance is 0.05 (Note, PL: Protected land, RC: Rural communities, SC: Suburban communities, UC: Urban communities).

The results of the quantitative analysis of effects showed that based on the composite score index, the Eta-squared (η ² value) was 0.996, indicating that 99.6% of the variance in the data stemmed from differences between groups. Cohen’s f value was 15.117, indicating that the degree of variance quantified by the effects of the data was a large degree of variance.

One-way ANOVA results in the p-value of “≤0.001” ≤0.05, the statistical results are significant further prove that different communities have significant differences in the composite score, E ₄ (urban community) composite score index 0.167 significantly smaller than E ₁ (nature reserve) composite index score 0.834, resulting in the final conclusion E _1risk < E _2risk < E _3risk < E _4risk , which means that the urban community has the highest level of light pollution risk.

Since there are many factors affecting light pollution, in order to determine the specific content of the policy, we use the random forest feature selection method to obtain the importance of the feature indicators, and select the top three important features as the indicators for evaluating the effect of the policy. Corresponding solution measures are proposed according to the first three important indicators.

Step 1

Algorithm principle steps: random forest is an integrated learning algorithm that consists of several weak classifiers combined into one strong classifier. A number of subsets are obtained from the original dataset with put-back sampling, and random features are selected for each decision tree on the basis of bagging. These m samples are modeled as m decision trees (Mishina et al., 2015; Schonlau and Zou, 2020). Finally, the results are obtained by voting through these m decision tree models. The specific steps are as follows:

◇Input training set D.

Step 2

Feature Importance Evaluation: the random forest model uses feature importance assessment to determine which features are most relevant. Feature importance assessment measures the predictive power of features for the target variable. In this code, feature importance assessment values are obtained by calculating the average reduced impurity of each feature across all decision trees. The calculation of the average impurity may vary from implementation to implementation, but the most commonly used metric is Gini impurity or entropy. We denote the variable importance measures (VIM) by VIM and the Gini index by GI. Suppose there are J features X 1 , X 2 , . . . , X J , I decision trees and C categories, now we want to calculate the Gini index score for each feature X J (Jing Zhu et al., 2022). The Gini index of the ith tree node q is calculated as: G I q i = ∑ c = 1 c ∑ c ′ ≠ c p q c i p q c ′ i = 1 − ∑ c = 1 c p q c i 2 . (16)

Where C denotes that there are C categories and P q c denotes the proportion of category c in node q.

According to the parameters of max depth, min samples split, min samples leaf of the decision tree and the number of trees and maximum number of features of the decision tree in the random forest, the data were trained to obtain the results of the importance ranking of light pollution risk level indicators features, as shown in Figure 6. The top three ranking of the feature indicators are: street Light Brightness (SLB), Lighting Hours (LH), Energy Cost (EC).

Street light bulbs uniformly have a power rating of 400 W. Even in unforeseen circumstances where the bulb may fail, the brightness of the bulb remains consistent regardless of usage.

Based on the previous assumptions, we can derive the following expression for the total cost: Total cost is equal to the sum of price cost and social cost. Let ‘P’ denote the total cost, ‘P1’ represent the cost of the lamp, ‘UT’ denote the usage time of the lamp, ‘B’ represents the brightness of the lamp, and ‘LS’ symbolize the lifetime of the lamp. We set a range of values for each parameter as constraints. The initial guess for the objective function is [20, 5,000, 11], which is a reasonable initial value because it is within the range of our parameters. Then by iterating, the objective function finds the optimal combination of parameters. P = P 1 + 400 * U T − L S * 0.2 * B − 3500 / 1000 (17) S . t P 1 ∈ 10,20,30 B ∈ 3500,6500 U T ∈ 10,12 . (18)

The results obtained from the python run are shown as Figure 7.

The image generated using Python is a 3D visualization of the solution as well as a three-view. The horizontal coordinate represents the cost of the lamp, the vertical coordinate represents the brightness of the lamp, and the vertical coordinate represents the time the lamp is used. The color scheme on the 3D graph reflects the total cost. In general, the darker the color, the smaller the total cost value, and the lighter the color, the larger the total cost value.

The visualization chart allows us to visualize the impact of the cost, brightness and usage time of the lamps on the total cost, and shows the impact of different combinations between them on the total cost. The darkest area of the graph corresponds to the lowest total cost due to the combination of cost, brightness and usage time.

The one marked by the red arrow is the optimal price. The lowest cost is achieved when using a bulb with a price of about $10, a brightness of about 5,000 lumens, and a usage time of 10 h. This result suggests that implementation of this policy could reduce nighttime crime and traffic accidents while keeping operating costs within reasonable limits. Therefore, this policy appears to pose less risk to the community while achieving optimal results.