Predictive Analysis of Municipal Solid Waste Generation Using an Optimized Neural Network Model

: Developing successful municipal waste management planning strategies is crucial for implementing sustainable development. The research proposed the application of an optimized artiﬁcial neural network (ANN) to forecast quantities of waste in Poland. The neural network coupled with particle swarm optimization (PSO) algorithm is compared to the conventional neural network using ﬁve assessment metrics. The metrics are coefﬁcient of efﬁciency (CE), Pearson correlation coefﬁcient (R), Willmott’s index of agreement (WI), root mean squared error (RMSE), and mean bias error (MBE). Selected explanatory factors are incorporated in the developed models to reﬂect the inﬂuence of economic, demographic, and social aspects on the rate of waste generation. These factors are population, employment to population ratio, revenue per capita, number of entities by type of business activity, and number of entities enlisted in REGON per 10,000 population. According to the ﬁndings, the ANN–PSO model (CE = 0.92, R = 0.96, WI = 0.98, RMSE = 11,342.74, and MBE = 6548.55) signiﬁcantly outperforms the traditional ANN model (CE = 0.11, R = 0.68, WI = 0.78, RMSE = 38,571.68, and MBE = 30,652.04). The signiﬁcant level of the reported outputs is evaluated using the Wilcoxon–Mann–Whitney U-test, with a signiﬁcance level of 0.05. The p -values of the pairings (ANN, observed) and (ANN, ANN–PSO) are all less than 0.05, suggesting that the models are statistically different. On the other hand, the P-value of (ANN–PSO, observed) is more than 0.05, suggesting that the difference between the models is statistically insigniﬁcant. Therefore, the proposed ANN–PSO model proves its efﬁciency at estimating municipal solid waste quantities and may be regarded as a cost-efﬁcient method of developing integrated waste management systems.


Introduction
Municipal solid waste (MSW) has emerged as a new challenge to the United Nations' global sustainability strategy [1][2][3]. MSW is defined as garbage generated in houses or other sources that contains no hazardous chemicals [4]. The MSW accumulation problem has been worrying both local and international policymakers and stakeholders, posing serious health and environmental problems [5]. Nearly 2.01 billion tonnes of MSW are generated annually all over the world, with a projected increase of 3.40 billion tonnes by 2050 [6]. Most of the countries in the Middle East/North Africa (MENA) region are known for high MSW generation, with waste output exceeding 2 kg per capita per day on average [7]. In learning approaches. The correlation among the relevant factors was evaluated using principal component analysis and Pearson correlation. The employed machine learning models included ANN, random forest, and regression analysis. The correlation coefficients of R 2 = 0.6973, R 2 = 0.9608, and R 2 = 0.9923 were reported for linear regression, random forest, and ANN, respectively. Therefore, ANN outperformed linear regression and random forest models in terms of accuracy.
Kulisz and Kujawska [9] applied neural network modeling to forecast MSW in Poland. The MSW was divided into five categories: glass, biodegradable, paper and cardboard, plastics and metals, and miscellaneous waste. Selected explanatory factors were incorporated in the suggested models to reflect the influence of economic, demographic, and social aspects on the quantity of generated wastes. Different neural network models were applied by changing the number of hidden neurons from 2 to 10. The prediction accuracy of the developed models was measured using the Pearson correlation coefficient (R) and mean squared error (MSE). The ANN model with six hidden neurons showed good prediction accuracy by yielding a high R-value (i.e., 0.914) for categorized wastes. Using the statistical data from 2013 to 2019, the model projected a 2% rise in future waste output in 2024. The findings affirmed the suitability of the ANN model as a cost-efficient method for developing integrated waste management systems. Oguz-Ekim [31] modeled the MSW generation rate in Turkey using support vector regression (SVR), backpropagation neural network (BPNN), and general regression neural network. It can be concluded that SVR and BPNN techniques can be used to predict MSW generation, with BPNN marginally outperforming SVR. The developed models could be generalized in other countries across the world.
Daoud et al. [32] studied the rising problem of solid waste in the MENA area, with an emphasis on construction and demolition waste in Egypt. The study analyzed the most recent official reports, technical studies, and research papers on the subject. The key barriers to effective and efficient solid waste management systems, as well as recommendations for improvement, were compiled in this study. Policymakers, local and national governments, construction industry practitioners, and academics dealing with the challenges of solid wastes in the MENA area were likely to benefit from the findings of this study. ElSaid and Aghezzaf [33] performed a system analysis of MSW management in Cairo, Egypt. To describe an underlying model of the MSW management system, a restricted non-linear mathematical model was developed for six waste material flows (glass, cardboard and paper, metals, plastics, organic material, and others). Combinations of five treatment options were incorporated in the developed model, which included landfilling, incineration, anaerobic digestion, composting, and mechanical biological treatment. The model determined the capability of treatment techniques, as well as feasible best design solutions and recommendations. The environmental and economic effects of alternative scenarios were studied and analyzed. The gap between the current status quo and the proposed improved methods for diverting waste from landfills and reducing carbon dioxide emissions was elaborated in this study.
Ayeleru et al. [34] used ANN and SVM techniques to estimate MSW generated in the City of Johannesburg, South Africa. Furthermore, a projection was developed up to 2050 based on the gathered historical data. The research findings confirmed the effectiveness of machine learning approaches for MSW forecasting. The ANN model with 10 neurons outperformed other models, yielding an R 2 value of 0.999, whereas the linear model performed best in the SVM models, with an R 2 value of 0.986. Based on the ANN10 model, the total quantity of MSW in the City of Johannesburg was expected to reach 1.95 × 106 tonnes in 2050, with an average yearly waste of 1.78 × 106 tonnes. Coskuner et al. [35] used a multilayer perceptron ANN to forecast the yearly generated rates of commercial, household, and construction and demolition wastes in Bahrain. The prediction models incorporated several explanatory variables to account for the impact of economic, social, geographic, demographical, and touristic aspects on waste generation rates. To assess the efficacy of the generated models, the MSE and R 2 performance metrics were employed. According to the findings, the ANN model was associated with high R 2 and low MSE values, indicating good prediction accuracy. This demonstrated the capability of the proposed ANN model at predicting waste generation rates from a variety of sources and that it could be used to construct integrated MSW management systems.
In summary, the ANN models could be applied for modeling MSW quantities given limited data. The flexibility of neural network tools is a feature that allows for the consideration of a variety of additional factors, including economic, demographic, geographic, social, technological, legislative, and administrative, all of which may play a role in determining the final quantity of municipal wastes. Despite the excellent ability of standalone ANN models, their training algorithms may trap in local optimums or may be slow to convergence. Optimization algorithms are regarded as viable alternatives to standard training algorithms because they avoid trapping in local optimums [36,37]. However, limited research was undertaken to examine the performance of hybrid ANN models to forecast MSW generation quantities. Furthermore, it is necessary to assess the performances of pure and hybrid ANN models using numerous evaluation indices. In this regard, this research involves training and evaluating the performance of conventional and hybrid ANN models in predicting MSW quantities. Because of its high prediction accuracy and consistency over time, the ANN is coupled with the particle swarm optimization (PSO) algorithm in this research study. The capacity to estimate MSW at a city level allows local waste management organizations and government agencies to develop robust waste management strategies. In addition, the developed prediction model may be incorporated into legal laws and systems to reduce municipal waste generation rates, improve the efficiency of waste energy recovery, and improve adherence to sustainable development principles.
The major contributions of this research could be summarized as follows: 1.
Incorporating the influence of economic, demographic, and social aspects on the quantity of generated wastes.

2.
Estimating the waste quantities using traditional and hybrid neural network models and comparing their performances using several evaluation metrics.

3.
Enhancing the performance metrics of the developed prediction models in the literature.

Feed-Forward Artificial Neural Network
ANN is a machine learning algorithm that is inspired by the human brain's anatomy [38]. This network is used to capture the non-linear relationship between the input and output factors. It has been widely applied in waste management problems such as the type or quantity of waste produced and its relationship to socioeconomic variables [39,40]. It has gained increasing popularity because of its unique benefits over other approaches, such as the clear network architecture, high-performance quality, and simple implementation [41][42][43]. Figure 1 depicts the structure of the neural network. It comprises input, hidden, and output layers. Data are supplied into the network through the input layer, and it is then processed utilizing hidden layers to get and report the desired output in the output layer. The number of neurons in the input layer is developed based on the number of input variables while the number of different outcomes determines the number of neurons in the output layer [44]. The weights and biases are assigned to channels linking neurons in subsequent layers. The activation state of the neuron is then determined by passing this value through an activation function. The data are propagated forward through activated neurons in the different layers until the result is delivered in the last layer. The network is trained by comparing the anticipated output to the actual result. The weights are then adjusted based on the computed prediction error in the back-propagation process. The forward and backward propagation procedures are repeated iteratively until the network can correctly predict the output [45]. The forward and backward propagation procedures are repeated iteratively until the network can correctly predict the output [45].

Particle Swarm Optimization Algorithm
One of the most well-known evolutionary algorithms is PSO that has been widely employed in a wide range of scientific and industrial applications [46]. The flowchart of the PSO algorithm is illustrated in Figure 2. This algorithm is based on how a school of fish or flock of birds navigates and moves. It finds a global optimum solution by populating the search space with particles where each particle has three vectors that store the present position, the moving direction, and the optimal location in the entire swarm. The ideal local position of a particle, as well as the experience of its neighbors, influence its migration. The global best position in the solution space is updated as nearby particles discover better places in the search space. This acts as a guide to assist the swarm in determining the optimal solution. Finally, the optimum solution is determined by the current best particle position in the swarm [47].

Particle Swarm Optimization Algorithm
One of the most well-known evolutionary algorithms is PSO that has been widely employed in a wide range of scientific and industrial applications [46]. The flowchart of the PSO algorithm is illustrated in Figure 2. This algorithm is based on how a school of fish or flock of birds navigates and moves. It finds a global optimum solution by populating the search space with particles where each particle has three vectors that store the present position, the moving direction, and the optimal location in the entire swarm. The ideal local position of a particle, as well as the experience of its neighbors, influence its migration. The global best position in the solution space is updated as nearby particles discover better places in the search space. This acts as a guide to assist the swarm in determining the optimal solution. Finally, the optimum solution is determined by the current best particle position in the swarm [47].

Neural Network Optimized Using Particle Swarm Optimization Algorithm
In this study, a neural network is used to forecast the MSW quantities in the different Polish cities. Optimization algorithms allow neural networks to avoid overfitting and local minima during training [48,49]. The PSO algorithm is utilized in this study to train the ANN model to figure out what the best weights and biases are. This algorithm is considered one of the most popular and effective ANN training methods [37,50]. Figure 3 depicts the flowchart of the improved ANN model. The optimization algorithm establishes the weights and calculates the fitness function to train the network. The network fitness is interpreted in this study by calculating the error as shown in Equations (1) and (2). When the global best solution, which is associated with the least error function, is found, the optimization process ends.
Processes 2021, 9, 2045 6 of 16 where N MSE represents the normalized mean squared error, n represents the total number of data points, and a i and p i represent the actual and predicted values, respectively. esses 2021, 9, x FOR PEER REVIEW Figure 2. Flowchart of PSO algorithm.

Neural Network Optimized Using Particle Swarm Optimization
In this study, a neural network is used to forecast the MSW Polish cities. Optimization algorithms allow neural networks to cal minima during training [48,49]. The PSO algorithm is utilized ANN model to figure out what the best weights and biases are. ered one of the most popular and effective ANN training method

Performance Assessment Metrics
The performance of the conventional and optimized neural network mode pared using five performance assessment criteria; coefficient of efficiency (Equa Pearson correlation coefficient (Equation (4)), Willmott's index of agreement ( (5)), root mean squared error (Equation (6)), and mean bias error (Equation (7 metrics are used for assessing the robustness of the relationship between mod observed data. It should be noted that higher values of the first three metrics, a lower values of the last two metrics, imply that the anticipated and actual valu excellent agreement, and vice versa [51][52][53].

Performance Assessment Metrics
The performance of the conventional and optimized neural network models is compared using five performance assessment criteria; coefficient of efficiency (Equation (3)), Pearson correlation coefficient (Equation (4)), Willmott's index of agreement (Equation (5)), root mean squared error (Equation (6)), and mean bias error (Equation (7)). These metrics are used for assessing the robustness of the relationship between modeled and observed data. It should be noted that higher values of the first three metrics, as well as lower values of the last two metrics, imply that the anticipated and actual values are in excellent agreement, and vice versa [51][52][53].
Processes 2021, 9, 2045 where p and a represent the average predicted and actual values.

Model Development
The flowchart of the proposed model is illustrated in Figure 4. The main objective of this research study is to forecast the MSW quantities in Polish cities based on socioeconomic factors. For this purpose, the neural network models have been developed and their prediction performance is evaluated using five assessment metrics. Furthermore, the significance level of the outcomes delivered by the conventional and trained neural network models is determined using the Wilcoxon-Mann-Whitney U-test. Finally, the best forecasting model is suggested based on the reported results and findings.
Processes 2021, 9, x FOR PEER REVIEW 8 of 16 where ̅ and represent the average predicted and actual values.

Model Development
The flowchart of the proposed model is illustrated in Figure 4. The main objective of this research study is to forecast the MSW quantities in Polish cities based on socio-economic factors. For this purpose, the neural network models have been developed and their prediction performance is evaluated using five assessment metrics. Furthermore, the significance level of the outcomes delivered by the conventional and trained neural network models is determined using the Wilcoxon-Mann-Whitney U-test. Finally, the best forecasting model is suggested based on the reported results and findings.

Case Study
The data used in this research is acquired from a previous research study in Poland [9]. The waste generation characteristics of many cities with varying social and economic aspects in 2019 are provided in Table 1. The input factors comprise population (capita), revenue per capita, employment to population ratio (%), number of entities enlisted in the official national register of business entities (REGON) per 10,000 population, and number of entities by type of business activity while the output factor refers to the total MSW quantities. MSW volume is found to be positively and substantially correlated with population and income level in research studies [54]. This can be attributed to the fact that rapid population growth increases the amount of waste generated. Moreover, individuals in the affluent class consume more than those in the lower-income class, leading to an increased rate of waste generation for the former [55]. The unemployment rate impacts the population's purchasing power, which could have a direct impact on waste disposal levels [56]. Finally, the number of entities and type of business activity (e.g., construction, industrial) in each entity impact the quantity and composition of generated waste [4]. The distribution of MSW quantities and waste per capita (total MSW quantities divided by population) in Polish cities is visualized in Figure 5. It is worth noting that Warszawa city is the most densely populated city (i.e., 1,790,658 persons) and it generates the highest quantities of wastes (i.e., 129,111.64 Mg). On the contrary, Oles'nica city has the lowest population density of 1839 persons and it is associated with the lowest quantities of wastes (i.e., 167.35 Mg). Meanwhile, Lublin city is characterized by the highest waste per capita of 2.61 Mg/person. Table 2 depicts the statistical data on MSW, which illustrates that the wastes do not follow the normal distribution and are rather right-skewed due to their positive skewness value. szawa city is the most densely populated city (i.e., 1,790,658 persons) and it generates the highest quantities of wastes (i.e., 129,111.64 Mg). On the contrary, Oles'nica city has the lowest population density of 1839 persons and it is associated with the lowest quantities of wastes (i.e., 167.35 Mg). Meanwhile, Lublin city is characterized by the highest waste per capita of 2.61 Mg/person. Table 2 depicts the statistical data on MSW, which illustrates that the wastes do not follow the normal distribution and are rather right-skewed due to their positive skewness value.  Figure 6 shows the correlation between all of the factors used to forecast municipal wastes. Variables having correlation coefficients between 0.5 and 0.7 can be classified as moderately correlated. This is true for the following pairs: revenue per capita and wastes, and number of entities enlisted in REGON per 10,000 population and wastes. In addition, variables with correlation coefficients of 0.7 to 0.9 have a strong correlation. This is true for the variables of population and revenue per capita, population and number of entities enlisted in REGON per 10,000 population, population and total wastes, revenue per capita and number of entities enlisted in REGON per 10,000 population, revenue per capita and number of entities by type of business activity, number of entities enlisted in REGON per 0.00 0.50    Figure 6 shows the correlation between all of the factors used to forecast municipal wastes. Variables having correlation coefficients between 0.5 and 0.7 can be classified as moderately correlated. This is true for the following pairs: revenue per capita and wastes, and number of entities enlisted in REGON per 10,000 population and wastes. In addition, variables with correlation coefficients of 0.7 to 0.9 have a strong correlation. This is true for the variables of population and revenue per capita, population and number of entities enlisted in REGON per 10,000 population, population and total wastes, revenue per capita and number of entities enlisted in REGON per 10,000 population, revenue per capita and number of entities by type of business activity, number of entities enlisted in REGON per 10,000 population and number of entities by type of business activity, and number of entities by type of business activity and total wastes. Furthermore, the population and employment to population ratio, revenue per capita and employment to population ratio, employment to population ratio and number of entities enlisted in REGON per 10,000 population, employment to population ratio and number of entities by type of business activity, and employment to population ratio and waste quantities variables have an inversely proportionate relationship. Finally, the population is correlated to the largest extent with the number of entities by type of business activity. tities by type of business activity and total wastes. Furthermore, the population and employment to population ratio, revenue per capita and employment to population ratio, employment to population ratio and number of entities enlisted in REGON per 10,000 population, employment to population ratio and number of entities by type of business activity, and employment to population ratio and waste quantities variables have an inversely proportionate relationship. Finally, the population is correlated to the largest extent with the number of entities by type of business activity.   Figure 6. Correlation between input and output parameters for MSW prediction.

Results
The ANN parameters have to be specified such that the number of hidden neurons is estimated to be 10. The same number of hidden neurons is assumed for the ANN-PSO model in order to provide a fair evaluation of the models. For PSO, the maximum number of iterations and population size are assumed to be 200 and 50, respectively. Furthermore, the inertia weight, inertia weight damping ratio, personal learning coefficient, and global learning coefficient are determined to be 1, 0.99, 2, and 2, respectively. Finally, the MATLAB R2019a software is used to develop the neural network models. Figure 7 shows a comparison between anticipated and actual MSW quantities in Poland. As shown in Table 3, there are five different metrics used to evaluate the performance of neural network models, namely CE, R, WI, RMSE, and MBE. The greatest CE, R, and WI are indicative of a model's best performance. In addition, the best models are    The significant level of the neural network models' output is evaluated using the Wilcoxon-Mann-Whitney U-test, with a significance level of 0.05. The test validates the null hypothesis, which asserts that the two rankings are equal. The alternative hypothesis, on the other hand, indicates that the two models are ranked differently. The null hypothesis is rejected in favor of the alternative hypothesis if the p-value is less than the significance level. The null hypothesis is accepted if the p-value is larger than the degree of significance. The p-value of (ANN-PSO, observed) is more than 0.05, suggesting that the difference between the models is statistically insignificant (i.e., null hypothesis is true). The P-values of the pairings (ANN, observed) and (ANN, ANN-PSO) are all less than 0.05, suggesting that the models are statistically different (i.e., null hypothesis is false).
The outcomes of the proposed ANN-PSO model are compared to the results reported in the literature, as summarized in Table 4. For the goal of making short-term weekly predictions, Noori et al. [39] used ANN and principal component regression to estimate MSW output in Tehran. The ANN had R and average absolute relative error (AARE) values of 0.837 and 0.044, respectively. These metrics were considered better than that of the principal component regression (R = 0.445 and AARE = 0.066). Furthermore, Kulisz and Kujawska [9] forecasted the MSW (glass, biodegradable, plastics and metals, paper and cardboard, and other waste) generation rate in Poland by developing an ANN  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24   The significant level of the neural network models' output is evaluated using the Wilcoxon-Mann-Whitney U-test, with a significance level of 0.05. The test validates the null hypothesis, which asserts that the two rankings are equal. The alternative hypothesis, on the other hand, indicates that the two models are ranked differently. The null hypothesis is rejected in favor of the alternative hypothesis if the p-value is less than the significance level. The null hypothesis is accepted if the p-value is larger than the degree of significance. The p-value of (ANN-PSO, observed) is more than 0.05, suggesting that the difference between the models is statistically insignificant (i.e., null hypothesis is true). The p-values of the pairings (ANN, observed) and (ANN, ANN-PSO) are all less than 0.05, suggesting that the models are statistically different (i.e., null hypothesis is false).
The outcomes of the proposed ANN-PSO model are compared to the results reported in the literature, as summarized in Table 4. For the goal of making short-term weekly predictions, Noori et al. [39] used ANN and principal component regression to estimate MSW output in Tehran. The ANN had R and average absolute relative error (AARE) values of 0.837 and 0.044, respectively. These metrics were considered better than that of the principal component regression (R = 0.445 and AARE = 0.066). Furthermore, Kulisz and Kujawska [9] forecasted the MSW (glass, biodegradable, plastics and metals, paper and cardboard, and other waste) generation rate in Poland by developing an ANN model. The model accounted for the influence of economic, demographic, and social parameters on waste generation quantities. The model exhibited high prediction accuracy by acquiring a high R-value (R = 0.914) and low MSE value.  [58] employed ANN to estimate the physical waste streams in the city of Johannesburg based on meteorological factors. The input factors comprised humidity, wind speed, and maximum/minimum temperature. For forecasting organic, paper, plastics, and textile waste, optimal topologies acquired R-values of 0.916, 0.862, 0.834, and 0.826, respectively. In this study, the ANN-PSO model is associated with CE, R, WI, RMSE, and MBE metrics of 0.92, 0.96, 0.98, 11,342.74, and 6548.55, respectively. Therefore, the proposed model improves the performance metrics reported in the literature.

Conclusions
An accurate prediction of the municipal solid waste (MSW) generation rate is critical for sustainable and efficient MSW management. Neural network models have been recently used and proved their efficiency for modeling MSW quantities. Though previous work on waste generation prediction had been undertaken, this is the first time the optimized artificial neural network (ANN) model using particle swarm optimization (PSO) had been applied. This research applied an ANN model coupled with the PSO algorithm and conventional ANN to forecast MSW quantities in Polish cities. The performance of the models was compared using five assessment metrics, namely, coefficient of efficiency (CE), Pearson correlation coefficient (R), Willmott's index of agreement (WI), root mean squared error (RMSE), and mean bias error (MBE). To represent the effect of economic, demographic, and social factors on the rate of waste generation, selected explanatory factors were integrated into the developed models. Population, employment-to-population ratio, revenue per capita, number of entities by type of commercial activity, and number of businesses enlisted in REGON per 10,000 people were the considered criteria.
The ANN-PSO model (CE = 0.92, R = 0.96, WI = 0.98, RMSE = 11,342.74, and MBE = 6548.55) surpassed the standard ANN model (CE = 0.11, R = 0.68, WI = 0.78, RMSE = 38,571.68, and MBE = 30,652.04), according to the findings. The Wilcoxon-Mann-Whitney U-test was used to determine the significance level of the reported outputs, with a significance level of 0.05. The p-values for (ANN, observed) and (ANN, ANN-PSO) were all less than 0.05, indicating that the models were statistically distinct. On the contrary, the p-value of (ANN-PSO, observed) was more than 0.05, indicating that the difference between the models was statistically negligible. As a result, the suggested ANN-PSO model had demonstrated its efficacy in estimating MSW volumes. Furthermore, it could successfully offer the foundation for the development of modern waste management systems when used in the evaluation and forecasting of waste management demands. As for the model limitations, each city is characterized by a different model that is dependent on its associated collected data. In addition, there needed to be records for the accumulated quantities of MSW in each city. Using statistical data in different cities, the given approach may be generalized to any city across the world. However, depending on the uniqueness of the studied country, adjusting this approach may demand matching influencing parameters. This research could be extended in the future by examining the performance of different optimization algorithms to train ANN for simulating MSW quantities. In addition, the proposed model could be further improved by applying dimensionality-reduction methods such as Principle Component Analysis (PCA) to select the most important input factors in the dataset. Data Availability Statement: Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.

Conflicts of Interest:
The authors declare no conflict of interest.