Modeling the Amount of Waste Generated by Households in the Greater Accra Region Using Artificial Neural Networks

Waste can be defined as solids or liquids unwanted by members of the society and meant to be disposed. In developing countries such as Ghana, the management of waste is the responsibility of the metropolitan authorities. These authorities do not seem to have effective management of the waste situation, and therefore, it is not unusual to see waste clog the drains and litter the streets of the capital city, Accra. The impact of waste on the environment, along with its associated health-related problems, cannot be overemphasized. The Joint Monitoring Programme report in 2015 ranked Ghana as the seventh dirtiest country in the world. The lack of effective waste management planning is evident in the large amount of waste dumped in open areas and gutters that remains uncollected. In planning for solid waste management, reliable data concerning waste generation, influencing factors on waste generation, and a reliable forecast of waste quantities are required. This study used two algorithms, namely, Levenberg–Marquardt and the Bayesian regularization, to estimate the parameters of an artificial neural network model fitted to predict the average monthly waste generated and critically assess the factors that influence solid waste generation in some selected districts of the Greater Accra region. The study found Bayesian regularization algorithm to be suitable with the minimum mean square error of 104.78559 on training data and 217.12465 on test data and higher correlation coefficients (0.99801 on training data, 0.99570 on test data, and 0.99767 on the overall data) between the target variables (average monthly waste generated) and the predicted outputs. House size, districts, employment category, dominant religion, and house type with respective importance of 0.56, 0.172, 0.061, 0.027, and 0.026 were found to be the top five important input variables required for forecasting household waste. It is recommended that efforts of the government and its stakeholders to reduce the amount of waste generated by households be directed at providing bins, increasing the frequency of waste collection (especially in highly populated areas), and managing the economic activities in the top five selected districts (Ledzekuku Krowor, Tema West, Asheidu Keteke, Ashaiman, and Ayawaso West), amongst others.


Introduction
According to Gentil et al. [1], the amount of municipal solid waste generated in many countries has been increasing for many years and this has necessitated the establishment of waste-related policies by governmental agencies and international organisations to reduce the environmental impacts of poor waste management, including reducing the amounts of waste.
found the waste management service woefully inadequate and recommended private sector participation. ey also recommended the collation of reliable data on rubbish generation.
Miezah et al. [4] confirmed that reliable data on waste generation were nonexistent and therefore proceeded to measure the regional household generation rate and solid waste composition. ey concluded that waste generation in Ghana was on the average 0.47 kg per person per day. e generation rate differed in the various regions with the coastal and forest zones generating more waste than the Northern and Savannah zones. ey also found that the organic fraction constituted 49-68 percent of the waste stream.
Generally, in planning for solid waste management, what is fundamentally required is reliable data concerning waste generation, influencing factors on waste generation, and a reliable forecast of waste quantities [5,6]. Accurate data on waste generation and factors influencing it would aid in estimating the number of waste bins to be supplied, the number of periodic collections to be done, and the landfill sites needed to be made available within a particular period.
It is evident from the above literature that planning and design of an effective municipal solid waste management system require an accurate prediction of solid waste generation.
Dyson and Chang [7] presented a new approach called "System Dynamics Modeling" for the prediction of solid waste generation in a fast-growing urban area based on a set of limited samples. By yielding more precise estimates, their proposed model outperformed the traditional least-squares regression model. eir new forecasting approach covered a variety of possible causative models and tracked inevitable uncertainties down, whereas the traditional statistical leastsquares regression methods were unable to handle such issues. e limitation, however, of their proposed method is that dynamic systems models may be complex due to the combinations of simpler submodels linked to simulate the system. eir complexity is not only because all factors are simultaneously involved and affected by each other but also because they dynamically occur over time. Also, they failed to explore the concept of feedback within the system due to the difficulty of linking waste generation directly back to consumption activities.
Asante-Darko et al. [8] proposed a Fourier series model to forecast solid waste generation in Kumasi, Ghana. eir approach incorporated some characteristics of the monthly waste data for forecasting solid waste. A one-year forecast from their model revealed that the generation of solid waste will increase as a result of the high rate of urbanization and population growth. Specifically, the Fourier series model was found to have relatively smaller sum of squares error (SSE) of 1.8124 × 10 7 at period 42, making it superior to the ARIMA times series model in the prediction of solid waste generated.
ere have been a series of models developed in the literature for the prediction of waste generation. A holistic review of models developed in the literature from 2005 to 2014 revealed that the most predominant models were deterministic statistical models (multiple regression analysis, time series analysis, and some descriptive/inferential statistics) [9,10]. ese models expressed only cause-and-effect and are only effective in forecasting the amount of waste generated in a short term.
ere are limited studies which adopted some artificial intelligent systems/models to predict the quantity of waste generated in a locality. One of such studies is the work of Ali Abdoli et al. [11] which used artificial neural networks to predict solid waste generation in the long term. eir study found population size, household income, and maximum temperature as effective factors in solid waste generation.
eir results also revealed that the ANN model (specifically the multilayer perception) outperformed the multivariate regression model, yielding a relatively lower mean squared error (MSE) of 0.26, mean absolute percentage error (MAPE) of 0.046, and a higher correlation coefficient (R) of 0.86.
Kannangara et al. [12] developed models for accurate prediction of municipal solid waste (MSW) generation and diversion based on demographic and socioeconomic variables, with planned application of generating Canada-wide MSW inventories. Two machine learning algorithms, namely, decision trees and neural networks, were applied to build the models. eir results showed that machine learning algorithms can successfully be used to generate waste models with good prediction performance. Specifically, the neural network models had the best performance, describing 83% of the variation in the training data and 72% of the variation in the test data with in-sample and out-ofsample prediction errors of 15% and 16%, respectively.
As indicated by Liu and Yu [13], a better understanding of the factors that affect the generation of municipal living refuse and the accurate prediction of its generation are crucial for municipal planning projects and city management. Most of the studies in the literature described some challenges of the solid waste management with recommendations, whereas the very few that modeled the quantity of waste generated mainly used deterministic techniques with some isolated machine learning models. In this study, we harness the predictive power of artificial neural networks to model the quantity of waste generated in some selected municipalities in Ghana by assessing some critical wastegenerating factors. e rest of the paper is organized as follows: Section 2 (Materials and Methods) discusses the mathematical foundations of the adopted algorithms in estimating the neural network model parameters and the evaluation criteria used to assess the algorithms. Section 3 (Results and Discussion) presents and discusses the results of the ANN model and assesses the critical factors used in the prediction of the household solid waste generated. Section 4 examines the findings of the study in comparison with existing works in the literature and finally concludes by summarizing the overall achievements of the study. e section also presents some recommendations and directions for future developments.

Description of Data.
Primary data were obtained from households. ese data contained information on the independent variables that had influence on solid waste generated in the districts.
To ascertain the critical factors that influence solid waste generation in the Greater Accra region, information was solicited from various households in the region. Information from the households was used to investigate the effect of sociodemographic variables such as age, house type, educational level, religion, residency type, household size, employment category, household waste disposal method, frequency of waste collection, and income levels on solid waste generation in the region.
e study sample of the households was drawn from fifteen of the twenty-six districts in the Greater Accra region. A two-stage sampling approach was used in this study. e approaches comprised stratification with proportional allocation to size and simple random sampling. e randomly selected districts were considered homogeneous units. is was because, with reference to the stratification variable (the amount of solid waste generated), it was expected that the districts would be homogeneous units due to the type of economic activities that exist in the district. Each district therefore represented a stratum.
A sample size of 2102 households was used for the study. is is a representative sample which can be used to make inference about the population on households in the Greater Accra Metropolis with 2.5% margin of error. e average monthly waste for each sampling unit (household) was also recorded to be used as the target variable.
Seventy percent (70%) of the data was used for training the algorithm, while the remaining 30% was used for testing and validation. Table 1 shows the various input variables and the target variables used in this study.

Artificial Neural Networks (ANNs).
According to Gershenson [14], ANNs are named after the neurons in the human brain. ey are a set of algorithms modeled like the human nervous system and are designed to recognize patterns and relationships in data. ey work as neurons in the human body, in that they receive stimuli, work on them, and transmit them to other processing units. Dike et al. [15] identified three learning methods in ANNs; they are unsupervised, supervised, and reinforced learning methods. Unsupervised learning occurs when there is a predictor variable X with no corresponding labeled output variable. Unsupervised learning is able to solve association and clustering problems [16]. Supervised learning involves an input variable X and an output variable Y.
is method of learning is suitable for solving classification and regression problems [16].
Reinforcement learning as described by Dike et al. [15] learns through interconnections with the environment and is usually demonstrated as a Markov decision process. ANNs are mainly categorized by their architecture. e three main types of neural network architecture are feed forward, recurrent [17], and convolutional neural networks [18]. e architecture is called feed forward because the flow of information takes place in the forward direction. A feed forward network defines a mapping y � f(x; p) and learns the value of the parameters p that result in the best function approximation [19].
A feed forward can either be single layered or multilayered.
e single-layer network consists of only one hidden layer. e multilayered neural network is also known as the deep learning network. e distinguishing feature of this network is the fact that it has multiple hidden layers for complex processing. e hidden layer can be seen as a distillation layer that distills some of the important patterns from the inputs and passes them onto the next layer [20].
e ANN architecture best suited to the data and therefore adopted for the study is the feed forward multilayered neural network. e network structure as earlier described includes multiple hidden layers for complex processing which involves estimating the parameters p that result in the best function approximation.
In this study, we adopted two algorithms (Levenberg-Marquardt (LM) and Bayesian regularization (BR)) for solving the nonlinear equations that resulted in the estimation of the parameters p.

Levenberg-Marquardt (LM) Algorithm.
In fitting a model y(X, p) of an independent variable X and a vector of n parameters p to a set of m data points (x i , y i ), i � 1, 2, . . . , m, the convention is to minimize the sum of weighted squares of the errors between the data y i and the fitted curve with function y(X, p). e expression which represents the weighted residuals (weighted squares of errors) between y i and y(X, p) is the error function given as � y T Wy − 2y T Wy + y T Wy. (1) is nonlinear with the model parameters p; then, a reduction of the error function χ 2 (p) can only be obtained iteratively. e goal of each iteration will be to find a small change δ in the parameters p that reduces χ 2 (p).
LM is one of many algorithms used to perform the iteration. LM is said to be made up of two processes, namely, the gradient descent and Gauss-Newton methods. e LM algorithm can be represented as follows: Journal of Environmental and Public Health where δ lm is the change in parameters due to the LM algorithm. Also, μ is a strictly positive scalar referred to as the damping term [21] I is the identity matrix and J � zy(p)/zp (the matrix whose entries are the partial derivatives of y(p) with respect to the parameters p) In LM, the damping term is adjusted at each iteration. When p is far from the solution, the damping term is set to a large value and as a result, the LM algorithm approaches the gradient descent algorithm. is is because where [J T WJ + μI] − 1 represents the length of the step in gradient descent.
As the values of p approach the required solution, the damping term is reduced and the LM algorithm approaches the Gauss-Newton algorithm.
is is because (1) Converging Criteria. According to Lourakis et al. [22], iteration will progress until one of the following criteria is met: (ii) e relative change in the magnitude of μ drops below a threshold ε 3 . (iii) e error ξ T ξ falls below a threshold ϵ 4 . (iv) e maximum number of iterations is completed.

Bayesian Regularization (BR) Algorithm.
In applying the Bayesian concept to the regression framework, assume an underlying functional model If we assume that the ϵ i ∼ N(0, σ 2 ), then it follows that Given that the x i ′ s is mutually independent, the likelihood of all the data observed will therefore be e Bayesian prior specifies the belief about the parameter to be determined. According to anh et al. [23], we may choose a zero-mean Gaussian prior and introduce another parameter which controls the strength of our belief about the parameter W. e prior can therefore be given as   Journal of Environmental and Public Health Now, we consider the normalizing constant or the evidence used in updating one's belief about the parameter.
is is normally a constant which is usually ignored in the posterior calculations.
Completing the squares of the right hand side of equation (9), we obtain We can therefore conclude that W ∼ N m (μ, Σ) (a multivariate normal distribution) is specified as Now, Journal of Environmental and Public Health P y|α, σ 2 � P y|W, x i , σ 2 P(W|α)dW We now solve the normal equations as follows: to obtain Tipping [24] introduced a parameter c which determines the influence of the posterior and likelihood on w i . As c ⟶ 0, the influence of the prior is captured and as c ⟶ 1, the influence of the likelihood is captured.

Evaluation of the Study Algorithms.
To evaluate the performance of the ANN models, three indices were assessed: mean square error (MSE), correlation coefficient (R), and coefficient of determination (R 2 ). Other metrics such as the number numerical iteration (n) and the runtime of the algorithms were computed. e accuracy and suitability of the models were determined using these criteria.
e MSE is an important measure of the algorithms' precision since the adopted algorithms (BR and LM) for solving the nonlinear problems only aid in the estimation of the ANN model parameters for prediction. e correlation coefficient measures the degree of linear association between the target variable (average waste generated) and the predicted output, whereas the coefficient of determination (R 2 ) describes the percentage of variation in the study data explained by the fitted model. An algorithm with the minimum MSE and relatively higher R and R 2 is preferred. Figure 1 presents the neural network diagram/architecture used for the study.

Results and Discussion
ere were 18 input variables (predominant age category, house type, educational level, religion, residential status, household size, employment category, household waste disposal method, frequency of waste collection, income levels, etc.), 10 allowed hidden neurons, and 1 target variable (average monthly waste in tonnes per household). Figure 2 shows a regression fit between the target variable and the predicted output using the Levenberg-Marquardt algorithm. e subgraphs in Figures 2(a)-2(d) show the regression fits between the target variable and the predicted output on training data, validation data, test data, and the overall data, respectively.
From Figure 2, the correlations between the target variable (average monthly household waste generated) and the predicted output are 0.99648 (for training data), 0.99717 (for validation), 0.99412 (for test data), and 0.99627 (for the overall data). is indicates a very good fit since there exists a very strong positive linear relationship (in all cases) between the target variable (monthly household waste generated) and the predicted output using the LM algorithm. Figure 3 shows a regression fit between the target variable and the predicted output for the training data, test data, and the overall data using the BR algorithm.
It can be seen from Figure 3 that the correlations between the target variable (average monthly household waste generated) and the predicted output are 0.99801 (for training data), 0.99570 (for test data), and 0.99767 (for the overall data). is signifies a very good fit since there exists a very strong positive linear relationship (in all cases) between the target variable (monthly household waste generated) and the 6 Journal of Environmental and Public Health Journal of Environmental and Public Health predicted output using the Bayesian regularization algorithm for prediction. e error distributions of the LM and BR algorithms are shown in Figure 4.
It can be inferred from the error histogram in Figure 4 that the error distribution for both algorithms is approximately normal.
is makes it suitable to generalize the predictions of the algorithms. More so, this satisfies the underlying assumption of the Bayesian regularization algorithm; that is, the errors (ϵ i ) are expected to be normally distributed with mean 0 and a constant variance of σ 2 . Table 2 contains the mean square errors (MSEs), the correlation coefficient between the target variable and the predicted output (R), the coefficient of determination (R 2 ), the number of numerical iterations (n), and runtime of the study algorithms.
It is evident from It can be inferred from this finding that the BR algorithm has a relatively better precision in estimating the parameters of the neural network model.
Generally, the correlations between the target variable and the predicted output were relatively higher (with a correlation of 0.99801 for training/in-sample prediction and  Journal of Environmental and Public Health 0.99570 for testing/out-of-sample prediction) when the BR algorithm was used for estimating the neural network model parameters. It is worthy to note that the validation of the BR algorithm is inherent. is accounts for the missing values shown in Table 2. e ANN model explained 99.30% of the variation in training data, 99.43% of the variation in the validation data, and 98.83% of the variation in test data when the LM algorithm was used to estimate the model parameters, whereas the model described 99.60% of the variation in the training data and 99.14% of the variation in test data when the BR algorithm was used to estimate the model parameters.
From the results of the coefficient of determination (R 2 ), it can be concluded that the fitted ANN model explains relatively higher variations in the study data when the BR algorithm is used to estimate the model parameters.
e LM algorithm converged after 60 iterations with a runtime of about 1.5 seconds, whereas the BR algorithm converged after 540 iterations with a runtime of about 4 seconds. is means that the LM algorithm converges faster than the BR algorithm. is was expected as the Bayesian regularization algorithm is a more data-driven mechanism which requires more time but usually results in better generalization. Figure 5 shows some independent input variables ranked according to their level of importance.
It can be seen from Figure 5 that household size was the most important variable in predicting the amount of waste generated by a household. Household size recorded a variable importance value of 0.56 of 1. It turned out that highly populated households generated more waste than moderately and less populated households. e district in which a household is situated was the next important variable with a variable importance of 0.172 of 1, in predicting the amount of waste generated. e employment category (formal, informal, retired, and other) was the third most important variable in the prediction of the amount of household waste generated (0.061 of 1). Table 3 shows the average monthly waste generated by households based on the various subgroups of the important independent variables. As stated earlier, there were 15 districts in the study sample. It can be seen from Table 3 Figure 5: A graph of some important independent input variables.
error of 0.1378.
is can be attributed to the fact that households in these districts have relatively lower household sizes.
Considering the employment category variable, households whose members are predominantly formal workers generated the highest average monthly waste (87.5443 tonnes) with a standard error of 5.6529. is was closely followed by households whose members are predominantly informal workers with an average monthly waste of 81.9569 tonnes (standard error of 4.6827).
is could be because households with predominantly formal workers are more likely to use the regular methods of waste disposal such as collection by waste-disposal agents, whereas the households with predominantly informal workers are more likely to use the traditional methods of disposal such as burning and burying. Waste disposed using the traditional methods could not be accounted for.
Households whose members are predominantly Christian generated the highest average monthly waste of 85.3959 tonnes with a standard error of 4.0806, followed by Muslims with an average of monthly waste of 78.7520 tonnes (standard error of 6.6658). Households whose members are from traditional and other religions were in the minority and generated the lowest waste. It is worth noting that most of the survey districts contain predominantly Christian communities.
Considering the house type variable, flat/apartments generated the highest average monthly waste of 150.0595 tonnes with a standard error of 2.4592. is was followed by semidetached households which generated an average monthly waste of 111.2652 with a standard error of 6.2138. Residents of uncompleted buildings were the third group in this category with an average monthly waste of 82.8600 tonnes (standard error of 16.8051). Standalone households tend to generate the lowest waste with an average monthly waste of 40.1873 tonnes (standard error of 9.7802).
is could be attributed to the household sizes of these house types.

Conclusion and Recommendation
e study successfully assessed two algorithms (Levenberg-Marquardt and Bayesian regularization) for estimating the neural network model parameter to aid in the prediction of average monthly waste generated by households in some selected districts in the Greater Accra region of Ghana using some sociodemographic characteristics of the households.
e Bayesian regularization algorithm outperformed the Levenberg-Marquardt algorithm, producing a comparatively lower MSE of 104.78559 on training data and 217.12465 on test data. e BR algorithm also gave the highest correlation coefficients (0.99801 on training data, 0.99570 on test data, and 0.99767 on the overall data) between the target variable (average monthly waste) and the predicted output.
is signifies a good fit and makes Bayesian regularization a suitable and preferred algorithm estimating the ANN model parameters to aid in the prediction of average waste generated by households in the long term. Also, the fitted ANN model explains relatively higher variations in the study data when the BR algorithm is used to estimate the model parameters.
Although the LM algorithm was faster in convergence (with 60 iterations and a runtime of about 1.5 seconds) than the BR algorithm (with 540 iterations and a runtime of about 4 seconds), the BR algorithm is a more data-driven mechanism which enables generalization of the predicted outputs.
e study also revealed that household size, districts, employment category, dominant religion, and house type with a respective importance of 0.56, 0.172, 0.061, 0.027, and 0.026 were the five most important independent input variables required to predict the amount of waste generated by a household. Specifically, highly populated households generated more waste than moderately and less populated households. is result is consistent with the findings of Ali Abdoli et al. [11].
Ledzekuku Krowor, Tema West, Asheidu Keteke, Ashaiman, and Ayawaso West were the five districts (arranged in order) that generated the highest waste. is could possibly be due to the type of economic activities in the district and the population size of the districts. e study also found households which are flat/apartment and semidetached and uncompleted buildings (arranged in order) as the top three house types which produce relatively higher waste. is could be accounted by the number of people or the household size of these house types. It is recommended that efforts of the government and its stakeholders to reduce the amount of waste generated by households be directed at providing bins, increasing the frequency of waste collection, and managing the economic activities in the top five selected districts (Ledzekuku Krowor, Tema West, Asheidu Keteke, Ashaiman, and Ayawaso West), amongst others.
Despite the prediction of the average waste generated and assessing the effect of some important critical factors, the study failed to isolate the components of the household solid waste generated. Future studies would focus on assessing the components of the household solid waste to aid in the development of effective solid waste management systems.
e ANN (with Bayesian regularization option) is also recommended as a suitable algorithm for predicting the amount of waste generated by households using some critical waste generation factors. e model can also be used in application areas that require the prediction of specified targets in the long term.

Data Availability
e .xlsx data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that there are no conflicts of interest.