The multiple linear regression is a commonly used ML method to estimate the marginal effects of independent variables (or called feature vector in machine learning techniques) on the dependent variable. It is widely applied to waste prediction of desirable explanatory power in different regions and countries (Beigl et al., 2008). In China, this approach is also employed to predict the MSW production in “Calculation and Prediction Method of Municipal Solid Waste Production (CJ/T 106-1999)”, which is the official guide compiled by the Ministry of Construction, China.

The model can be expressed as Eq. 1: Y = β 0 + β 1 X 1 + … + β k X k + ϵ , (1) where Y is MSW generation in this paper, β 0 denotes regression constant,   β 1 ∼ β k are regression coefficients, X 1 ∼ X k are explanatory variables, ϵ marks the regression residuals.

Usually, MLR uses the ordinary least squares (OLS) method to estimate the parameters that can achieve the lowest sum-of-squared errors between the observed and predicted responses. Under the OLS estimation, MLR’s results could be easily interpreted. However, some drawbacks have to be considered in MLR. For instance, the multicollinearity among the predictors can result in estimation errors, as well as the omitted variables could induce a biased estimation. In this paper, we mainly concentrated on the performance of each ML model and considered the variables selection based on earlier studies (Kannangara et al., 2018; Namlis and Komilis, 2019; Niu et al., 2021; Nguyen et al., 2021). The multicollinearity and omitted variables problems are not our concerns.

SVM was originally used to deal with pattern recognition problems, and recently extended to estimate regression models due to its properties of the sparse solution and good generalization (Demir and Bruzzone, 2014). By introducing an ε -tube to reformulate the optimization problem, the SVM model could be transformed to an SVR model and finds the optimal approximation of the continuous-valued function while balancing the complexity and prediction error of the prediction model (Huang et al., 2021b). In addition, the accuracy of an SVR model heavily relies on three parameters: a penalty parameter ( C ), the kernel width ( γ ) and the precision parameter ( ε ) (Abbasi and El Hanandeh, 2016; Li et al., 2021). Specifically, the smaller C is, the smaller the fitting error and the weaker the generalization ability would be. The larger γ is, the more support vectors; and vice versa. ε is a precision parameter representing the tube’s radius located around the regression function. In other words, the choice of ε donates the magnitude of errors that can be neglected. Since the above three parameters are critical to the adaptability of the model, we will tune them using a grid optimization approach in Results to optimize the SVR model.

A great body of literature has discussed the SVR and SVM models in predicting the generation of MSW. For example (Abbasi and El Hanandeh, 2016), adjusted the hyper-parameters of SVR by combining the grid search method and applying the model with the optimal parameters to the monthly prediction of MSW in Logan City, Australia. They found that SVR can effectively reduce the mean absolute error (MAE) and root-mean-square error (RMSE), and improve prediction performance (R-square). Besides (Nguyen et al., 2021), applied SVM to the prediction of MSW production in Vietnam with an MAE of 131.07, which confirmed that the SVM model performed a better prediction. Kumar et al. (2018) applied it to the prediction of the production rate of plastic waste, and found that the prediction result of SVM ( R 2 =0.74) is better than RF ( R 2 =0.66) and lower than artificial neural network (ANN) ( R 2 =0.75). Mehrdad et al. (2021) argued that SVM was superior to both the adaptive neuro-fuzzy inference system and artificial neural network models in predicting methane generation.

Random Forest is an evolution of Bagging which aims to reduce the variance of a statistical model, simulates the variability of data through the random extraction of bootstrap samples from a single training set and aggregates predictions on a new record (see Breiman, 1996). It performs a more stable and better prediction of explained variables than other machine learning models (Huang et al., 2021b). Generally, the RF algorithm implementation can be expressed as follows:

1) Bagging is used to randomly generate sample subsets;

The RF model was widely used in the prediction of waste. Kumar et al. (2018) used RF for the prediction of plastic waste generation rate that showed an R-square of 0.66. The size of the random forest, that is, the number of decision trees ( N t r e e s ) and the number of features tried in each segmentation ( N f e a t u r e s ) have a significant impact on the predictive ability of the RF model (Hariharan, 2021). When N t r e e s exceed a certain value, the prediction performance of the model converges. In this case, increasing the number of decision trees will not improve the model performance, but will result in model redundancy. In addition, using a smaller number of   N t r e e s reduces the similarity in the forest, but also reduces the complexity and strength of the model. Conversely, the increase in N t r e e s can make each tree more powerful, but also increase the correlation between the trees. Therefore, in the following section, we will optimize these two hyper-parameters to acquire better results.

XGBoost algorithm, proposed in 2016, is a relatively new approach (Chen and Guestrin, 2016). Different from RF model using bagging integration method, XGBoost model is an integration tree model using boosting method to integrate classification and regression tree (CART). It has the advantages of fast training speed and high prediction accuracy. The result of XGBoost is the sum of prediction scores of all CARTs (Chen and Guestrin, 2016) as formed in Eq. 2: y ^ = ∑ n = 1 N f m ( X ) , (2) where N represents the number of trees in the model,   f m represents each CART tree and y ^ is predicted result.

Since its introduction, the XGBoost model has been widely used in the prediction of oil price (Costa et al., 2021) and energy usage (Feng et al., 2021). However, up to date, XGBoost model has not been applied to the research of MSW generation prediction. Similar to RF, the number of integrated CARTs ( N t r e e s ) in XGBoost has a great influence on the prediction performance. Therefore, in order to increase the model’s performance in predicting the MSW generation, it is necessary to optimize this hyper-parameter. In Results, we also use the grid search method to confirm the different combinations of these two parameters to obtain the optimal model structure.

KNN algorithm is a non-parametric learning method first proposed by Cover and Hart (Cover and Hart, 1967). Since its introduction, it has been widely used in regression and classification due to its simple and intuitive mathematical form (Wu et al., 2008). It is essentially a supervised learning technique that via the clustering algorithm classify the similarity between the test sample and K nearest training samples (Zheng et al., 2020). Here, K is a user-defined number, normally an odd number, and the similarity is measured by the commonly used Euclidean distance. The test sample is classified based on the most frequent classification among the training samples. The mean value of the K nearest training samples is regarded as the predicted value. The mathematical measurement of Euclidean distance is expressed in Eq. 3: d ( x , y ) = ( x 1 − y 1 ) 2 + ( x 2 − y 2 ) 2 + … + ( x n − y n ) 2 = ∑ i = 1 n ( x i − y i ) 2 (3)

One drawback of KNN approach is the pre-selected number of K, a hyperparameter, because it would greatly influence the numbers of nearest samples (Wu et al., 2008; Zheng et al., 2020). In the following section, we first limit K to positive integers between 1 and 30, and then cross-verify them on a 10-fold sample to avoid this drawback.

Several studies applied the KNN approach into the prediction of MSW. For example, (Abbasi and El Hanandeh, 2016) first attempt to evaluate the ability of KNN to forecast MSW generation. They concluded that KNN can give good prediction performance and may be applied to establish the forecasting models that could provide accurate and reliable MSW generation prediction. Nguyen et al. (2021) predicted the MSW production in Vietnam and the R-square was over 0.96, which indicated that more than 96% of MSW production would be explained by the KNN model.

The ANN model is a computational system composed of multiple layers of neurons (input-hidden-output) (Al-Dahidi et al., 2019). This model is widely used in waste management because of its strong fault-tolerant ability to describe the complex relationship between variables in a multivariate system. (Abbasi and El Hanandeh, 2016; Mehrdad et al., 2021; Nguyen et al., 2021; Niu et al., 2021). The deep neural network is a branch of ANN based on a perceptron model. Indeed, an ANN model with multiple hidden layers is called a DNN since it has to train and process through multiple layers (Liu et al., 2017). The structure of DNN also includes input layer, hidden layer, and output layer. In general, the structure of DNN and ANN is similar, and their training algorithm is not different. However, studies showed that DNN tends to provide better performance and accuracy than conventional ANN models (Yang et al., 2021).

In this paper, a DNN with four layers of structure is constructed, namely the input layer, the first hidden layer, the second hidden layer and the output layer with one neuron. The number of neurons in the hidden layer has a great influence on the prediction performance of DNN. The smaller the number of neurons, the more likely it is to lead to insufficient fitting. On the contrary, an excessive number of neurons may lead to over-fitting. Therefore, selecting the appropriate number of neurons for DNN is also one of the bases to improve the model performance. In this paper, the number of neurons in the first hidden layer ( N h 1 ) and the number of neurons in the second hidden layer ( N h 2 ) are optimized to gain better results. Specifically, we first specify the numerical space of the number of neurons, and then test on the train and test samples, taking the optimal result as the optimal network structure.

The preprocessing methods adopted include linear normalization (Range) and standard deviation normalization (Scale), as shown in Eq. 4 and Eq. 5 respectively. For ML models (such as KNN) that need to calculate the distance between samples, different orders of magnitude between variables will greatly affect the performance of the model. We retained the original input data in this paper (Raw), and conducted two normalization strategies of Range and Scale to reduce the influence of data’s dimensions and skewness on the predictions. Thus, the results of the three preprocessing methods would be comparable. x = x − x m i n x m a x − x m i n , (4) x = x − x ¯ σ 2 , (5) where x m i n represents the minimum value of variables while x m a x represents the maximum value.   x ¯ represents the numerical average value and σ 2 is the variance of each variable.

To minimize the deviation caused by sampling and prevent the model from over-fitting, we adopted the 10-folds cross validation method of resampling technique to create a random sample subset of input data as a training set. The remaining data was used as test set to obtain the generalization ability of the algorithms.

To evaluate the performance of each machine learning algorithm, we use three metrics of the MAE, RMSE and the coefficient of determination ( R 2 ) (Chai et al., 2021; Nguyen et al., 2021). These measurements are formulated as Eqs 6–8. M A E = ∑ i = 1 n | y i − x i | n , (6) R M S E = ∑ i = 1 n ( y i − x i ) 2 n , (7) R 2 = 1 − ∑ i = 1 n ( y i − x i ) 2 ∑ i = 1 n ( y i − x ¯ ) 2 , (8) where n is the number of samples, x i is the predicted response by the model, y i is the actual value of the response, x i ¯ is average estimated value.

In this section, parameters of machine learning models are tuned, excluding multiple linear regression approach because it doesn’t involve any hyper-parameters. Specific adjustment for parameters is shown in Table 2.

In the tuning process of SVR, we conduct the aforementioned three data preprocessing strategies (the Raw, Range, and Scale) respectively. As shown in Table 3, in the Raw strategy, that is to retain the original form of input data, the penalty parameter ( C ) varies from 1 to 4000, compared with that in the Range strategy of 0.01–10. The precision parameter (ε) is an interval between 0.0001 and 0.001 in the Range and Scale strategies, compared with that of an interval from 0 to 5000. The kernel width ( γ ) doesn’t show any differences among the three strategies. The processing strategies of Range and Scale can effectively improve the normalization and scaling of the distributions of input variables.where S c a l e d and A u t o in γ represent the results of Eq. 11 and Eq. 12 as the γ value of the SVR. S c a l e d : γ = 1 N S × S 2 , (11) A u t o : γ = 1 N S   , (12) where N S represents the number of sample features and S 2 represents sample variance. The optimization results are shown in Figure 4.

The hyper-parameters in other ML models are also tuned. For RF, the number of variables tried in each segmentation ( N f e a t u r e s ) is set as positive integers between 1 and 9 in terms of nine input variables in this paper. The forest size ( N t r e e ) is set as positive integers between (50,400). The optimization results of hyper-parameters are shown in Figure 5. In Figures 4, 5, the redder the color is, the higher the R 2 of the parameter combination (therefore, the better the prediction), and vice versa. For KNN, the number of neighbors K is set as a positive integer between 1 and 29. For the XGBoost, the number of trees ( N t r e e ) is set to 23 positive integers between 50 and 490. For DNN, the number of neurons in the first hidden layer ( N h 1 ) is set as a positive integer increasing by 16 between (16,240), and the number of neurons in the second hidden layer ( N h 2 ) is set as one half of the number of the first hidden layer.

Moreover, the Adma method is used as the optimization method, MAE is set as the loss function and the maximum number of epochs is set to 200. Meanwhile, to prevent over-fitting of the DNN, the EarlyStop mechanism is introduced, and the minimum learning rate is set as 0.003 and the tolerance is set as 20. The hyper-parameter selection results of KNN, XGBoost, and DNN are shown in Figure 6. The hyper-parameters adopted by each method are shown in Table 4.

Figure 7 presents the prediction performance of different ML models by using three preprocessing strategies. Several findings can conclude from the comparison among models. First, the prediction performance of MLR is the worst among all the methods because it doesn’t involve hyper-parameter and responding adjustments. Second, the overall performances of SVR and KNN are similar, but the prediction ability of SVR is slightly higher than that of KNN except for results in Scale processing. Normally, the conducting SVR model needs a more complex process than KNN. By inputting different forms of data, the KNN only needs to adjust one super parameter, which requires less work than SVR. Third, the RF and XGBoost models present significant and similar advantages in predicting MSW production compare with MLR, SVR, and KNN according to the performance measurement of R 2 . Fourth, the DNN has the best predictive performance among all the algorithms.

In this study, the RF and DNN models showed high R 2 values ( > 0.9 ) during all preprocessing methods. That means the developed ML models had a good power of explanation and were not over-fitted or over-trained. Compared with the ML method for MSW prediction developed in the earlier studies, our results were significantly better in prediction accuracy. For example (Niu et al., 2021), developed LSTM and ANN models for predicting MSW generation and during the testing phase, the R 2 value were 0.92 and 0.74, respectively (Table 5). In addition, (Nguyen et al., 2021), reported a DNN model with predictive performance ( R 2 ) of 0.9 for MSW production projections in Vietnam. According to Kumar et al. (2018) and Kannangara et al. (2018) the ANN, SVM and other ML models for predicting MSW generation showed R 2 even lower than 0.8. Thus, the machine learning model developed in this paper promotes the effective prediction of MSW production.

Figure 8 shows the SHAP summary plot that orders features based on their importance to predict MSW production. Specifically, a higher SHAP value of a feature indicates higher-ranked importance to the MSW production volume. For example, the difference in the region’s GDP has the greatest impact on the model’s prediction of MSW production. It is likely because waste production is highly related to the household wealth that directly influences one’s daily consumption and potential production of MSW (Malinauskaite et al., 2017). Moreover, higher value of this feature result in higher SHAP values, which correspond to a higher output amount of MSW.

In addition, the industry structure presents a great influence on MSW production because of its indirect impacts on the citizens’ consumption. For instance, a higher degree of the added value of wholesale and retail trade indicates higher production of MSW compared with other industries (e.g., transportation, warehousing, and postal services industries). Some studies have argued that consumption patterns and population increase are important factors that contribute to MSW production in developing countries (Liu et al., 2019; Nguyen et al., 2021). Besides, the urban population also shows a significant impact on MSW production, because of its functioning on the total amount of MSW production. In contrast, other socio-economic features have a relatively insignificant impact on MSW in China. In the following paper, we will continue to analyze the dependency among these three features to discover the generation mode of MSW in China.

Figure 9 plots the relationship between a feature and its SHAP value dependent on another feature in the RF model. We select N u p and I n W A R as the features to discuss and identify their variation as changes of I n G D P . As shown in Figures 9A,B, the red points represent a higher value of InGDP, and the blue points represent the lower one.

Figure 9A plots the moderating effects of GDP on the impacts of urban population on MSW production. It shows that under the condition of a low N u p and a low I n G D P , the SHAP value of N u p is below zero, which indicates that the impact of N u p would negatively impact the MSW production under these circumstances. In other words, the less developed region might undermine the impact of the urban population on MSW production, although the local urban population increases. In contrast, with the economic growth, the increase of the urban population will promote the production of MSW. It could be recognized by the red color of the SHAP value in this figure.

Figure 9B reflects the interaction between GDP and the added value of wholesale and retail industries on MSW production. For example, before I n W A R reached 600 billion, its SHAP value is always negative. However, if I n W A R exceeds 600 billion yuan as the increase of total GDP, the increase of the added value of wholesale and retail trade plays a positive role in promoting the production of MSW. It means that if the added value of the wholesale and retail industry remains at a low level (less than 6,000 billion yuan), these industries have little effect on MSW production. However, if the added value is more than the threshold of 6000 billion yuan, the regional GDP would promote the impact of the WAR industry added value. Correspondingly, the SHAP value of I n W A R indicates a significant promotion on MSW production.