Waste Management 56 (2016) 13–22 Contents lists available at ScienceDirect Waste Management journal homepage: www.elsevier.com/locate/wasman Forecasting municipal solid waste generation using artificial intelligence modelling approaches Maryam Abbasi ⇑, Ali El Hanandeh Griffith School of Engineering, Griffith University, Nathan, QLD, Australia a r t i c l e i n f o Article history: Received 23 May 2015 Revised 16 April 2016 Accepted 18 May 2016 Available online 11 June 2016 Keywords: Municipal solid waste Artificial intelligence Support vector machine Artificial neural network k-nearest neighbours Adaptive neuro-fuzzy inference system a b s t r a c t Municipal solid waste (MSW) management is a major concern to local governments to protect human health, the environment and to preserve natural resources. The design and operation of an effective MSW management system requires accurate estimation of future waste generation quantities. The main objective of this study was to develop a model for accurate forecasting of MSW generation that helps waste related organizations to better design and operate effective MSW management systems. Four intelligent system algorithms including support vector machine (SVM), adaptive neuro-fuzzy inference system (ANFIS), artificial neural network (ANN) and k-nearest neighbours (kNN) were tested for their ability to predict monthly waste generation in the Logan City Council region in Queensland, Australia. Results showed artificial intelligence models have good prediction performance and could be successfully applied to establish municipal solid waste forecasting models. Using machine learning algorithms can reliably predict monthly MSW generation by training with waste generation time series. In addition, results suggest that ANFIS system produced the most accurate forecasts of the peaks while kNN was successful in predicting the monthly averages of waste quantities. Based on the results, the total annual MSW generated in Logan City will reach 9.4 107 kg by 2020 while the peak monthly waste will reach 9.37 106 kg. Ó 2016 Elsevier Ltd. All rights reserved. 1. Introduction Accurate projection of municipal solid waste quantities is important for the successful planning of efficient waste management system. Future estimations of municipal solid waste generation serve as a basis in the development of existing waste management infrastructures as well as their further sustainable development and optimization. Imprecise forecasts may lead to widespread problems, such as inadequate or excessive waste disposal infrastructure (collection, incineration, landfilling or processing) (Buenrostro et al., 2001). Therefore, the demand for reliable data concerning waste generation is implicitly included in the majority of national waste management laws (Antanasijević et al., 2013). However, the process of forecasting MSW generation is often challenging and compound by rapidly changing and uncontrollable parameters (Beigl et al., 2008). There is a growing body of literature on forecasting municipal solid waste (MSW) generation which includes a high heterogeneity of applied models from purely application-oriented to highly sophisticated academically inclined tools (Chung, 2010). Over the ⇑ Corresponding author. E-mail address: [email protected] (M. Abbasi). http://dx.doi.org/10.1016/j.wasman.2016.05.018 0956-053X/Ó 2016 Elsevier Ltd. All rights reserved. period from 1970 to 2014, more than 80 studies addressing the topic of forecasting of MSW generation have been published. MSW forecasting methods can be broadly classified into five main categories: descriptive statistical methods (Bider and Franklin, 1980; Even et al., 1981; Sha’Ato et al., 2007); regression analysis (Denafas et al., 2014; Franchetti, 2012; Vivekananda and Nema, 2014; Wei et al., 2013); material flow model (Liu et al., 2014; Schiller et al., 2010; Tonjes and Greene, 2012; Zhang et al., 2012); time series analysis (Katsamaki et al., 1998; Navarro-Esbrí et al., 2002; Xu et al., 2013); and artificial intelligence models (Abbasi et al., 2014; Antanasijević et al., 2013; Kumar et al., 2011; Noori et al., 2010). However, all modelling approaches have their own strengths and weaknesses. Conventional and descriptive statistical methods of forecasting MSW generation usually use population growth and average percapita waste generation as the main predictor (Abdoli et al., 2012). However, this method is no longer effective due to the dynamic characteristics of MSW generation process (Abbasi et al., 2013). Regression analysis is a widely used modelling technique because of the simplicity of underlying mathematics and welldeveloped statistical theory. In regression analysis, MSW generations are associated with economic and demographic variables (Abdoli et al., 2011). In order to conform with the theoretical 14 M. Abbasi, A. El Hanandeh / Waste Management 56 (2016) 13–22 assumptions of regression, input variables must meet stringent requirements such as independence, constant variance and normality of errors (Hockett et al., 1995). All of these requirements place limitations on the suitability of regression for predicting MSW generation as a complex real-world problem. The material flow model can fully characterize the dynamic properties in the process of solid waste generation. However, this modelling approach can be used for predicting total waste rather than collected waste (Beigl et al., 2008). Nevertheless, collected waste may still be estimated where recycling and littering rates are known. However, Hockett et al. (1995), after analysing results obtained from input-output models like material flow analysis, highlighted that comparisons of the results with real observed waste data on the highest aggregation levels were questionable due to the presence of different aggregations or because of low consistency within the studies. Hekkert et al. (2000) further suggested that comparison may even prove to be impossible because studies on final consumption are almost completely lacking. In contrast with the previously mentioned methods, time series analysis does not rely on the estimation of social and economic factors; thus it has the advantage of overcoming the lack of social parameters and other predictors. Time series data of waste generation are dynamic in nature, and it is possible to employ non-linear tools in order to discern relationships within the time series. In recent years, artificial intelligence models and machine learning such as support vector machine (SVM), adaptive neurofuzzy inference system (ANFIS) and artificial neural network (ANN) have been gaining popularity because of their high flexibility and proven prediction abilities (Abbasi et al., 2013, 2014; Antanasijević et al., 2013). Intelligent models are shown to be capable of predicting MSW generation on long, medium and short term scales (Abbasi et al., 2014; Abdoli et al., 2012; Jalili Ghazi Zade and Noori, 2008). However, there is limited information about monthly prediction of MSW generation as well as optimal algorithm for this purpose. This paper will review the state of the art of the intelligent modelling approaches for MSW generation forecast and then apply them to a real case scenario in order to identify the most suitable algorithm to predict MSW collected by kerbside service on a medium-term scale. 2. Application of artificial intelligence in forecasting MSW generation Advanced artificial intelligence forecast systems have shown superiority to conventional models in engineering problems as well as in waste management research (Abdoli et al., 2012). Recent research in this topic focused on using artificial intelligence models to deal with the non-linearity of the historical data. In this section, application of the techniques including ANN, ANFIS, SVM and knearest neighbours (kNN) will be reviewed in the field of MSW generation. 2.1. Artificial neural network Artificial neural networks are cellular information processing systems designed and developed on the basis of the perceived notion of the human brain and its neural system (Firat et al., 2010). One of the most beneficial and significant features of ANN in forecasting is its learning ability. ANN can construct a complex nonlinear system through a set of input/output examples. Consequently, ANN has been successfully employed in nonlinear system modelling (Firat et al., 2010). Accordingly, the nonlinear structure of MSW generation makes the ANN an ideal candidate for forecasting waste generation. Literature survey returned applications of ANN to forecast MSW generation in short, medium and long- term periods (Abbasi et al., 2013; Abdoli et al., 2012; Noori et al., 2010). Ordóñez-Ponce et al. (2006) employed multi-layer perceptron neural network to predict long-term generation rate of MSW in Chile. Using a range of variables which covered sociodemographic, economic, geographic and waste-related factors, ANN was able to predict waste generation with great accuracy (R2 = 0.819). Ordóñez-Ponce et al. (2006) concluded that population, percentage of urban population, years of education, number of libraries and number of indigents were the most important factors which affected waste generation in Chile. The ability of ANN to predict short-term MSW generation was also examined by other researchers (Noori et al., 2009a,b). These studies focused on forecasting MSW generation by analysing time series of waste generation rather than analysing effective factors in waste generation. Results showed that feed-forward ANN with one hidden layer and 16 neurons was the best structure to forecast short-term waste generation rates (Noori et al., 2009a,b). However, ANN accuracy may suffer when faced with large database due to the effect of irrelevant, redundant and noise in the data. Therefore, different input selection methods such as principal component analysis, wavelet transform and gamma test were introduced to deal with accuracy loss (Noori et al., 2009a,c). Although ANN model has good ability to forecast MSW generation, its performance suffers because of its tendency to over-fitting training, local minimum, and poor generalization. 2.2. Adaptive neuro-fuzzy inference systems Adaptive neuro-fuzzy inference systems (ANFIS) are a wellknown data driven modelling technique that combines ANN and fuzzy logic. ANFIS is composed of two parts, antecedent and conclusion, which are connected to each other by fuzzy rules based on the network form. Limited attempts, 3 studies, to predict waste generation using ANFIS were found in the literature. The studies compared the performance of ANN and ANFIS models ability to predict MSW generation (Chen and Chang, 2000; Noori et al., 2009c; Tiwari et al., 2012). Tiwari et al. (2012) suggested that ANFIS is a more reliable model than ANN for forecasting the aggregate impact of economic trend, population changes, and recycling on solid waste generation. Chen and Chang (2000), on the other hand, demonstrated the ability of ANFIS to forecast waste generation with limited input data. Chen and Chang (2000) and later Noori et al. (2009c) applied fuzzy goal regression method to improve the overall prediction accuracy of ANFIS. 2.3. Support vector machine Support vector machine (SVM), a novel neural network algorithm, was developed by Vapnik and colleagues (Vapnik, 1995). SVMs are a type of maximum margin classifiers which seek to find a maximum margin hyperplane to the best line across data. The hyperplane thus obtained is called the optimal separating hyperplane and the training examples that are closest to the maximum margin hyperplane are called support vectors. While most of conventional neural network models implement the empirical risk minimization principle, SVM implements the structural risk minimization principle. Neural network model seeks to minimize the misclassification error or deviation from correct solution of the training data but the SVM searches to minimize an upper bound of generalization error. Therefore, the solution of SVM may be global optimum while other neural network models may tend to fall into a local optimal solution. Thus, SVM is unlikely to result in overfitting (Kim, 2003). SVM model was used to forecast weekly MSW generation in Tehran city, Iran by Abbasi et al. (2013). They concluded that 15 M. Abbasi, A. El Hanandeh / Waste Management 56 (2016) 13–22 SVM could predict MSW generation in a short term scale with reasonable accuracy. Further, Abbasi et al. (2014) found that preprocessing of input variables by wavelet transform method can improve the accuracy and robustness of the model. 2.4. k-nearest neighbours Due to its simplicity and intuitiveness, k-nearest neighbours algorithm is widely adopted for regression and classification (Wu et al., 2008a). The application of kNN to time series forecasting under nonparametric locally weighted regression condition was presented independently by Yakowitz (1987) and Cleveland (1979). kNN has also drawn attention in the field of time series forecasting because of work presented by Meade (2002). The underlying intuition to apply kNN to univariate time series is that consistent data-generating processes often produce observations of repeated patterns of behaviour. Therefore, if a previous pattern can be identified as similar to the current behaviour of the time series, the subsequent behaviour of previous pattern can provide valuable information to predict the behaviour in the immediate future. In the kNN regression algorithm introduced by Meade (2002), the target variable of a time series forecasting problem is presented as a sequence of interval scaled values. Given a pattern whose future value is to be predicted, the algorithm identifies the k most similar past patterns and combines them. So far, no attempt has been made to evaluate the ability of kNN to forecast MSW generation. 2.5. Summary of present studies Forecasting of MSW generation can be classified into 3 different groups according to how far in the future the forecast period is: short-term forecasting (usually ranging from days to few months); mid-term forecasting (usually range from few months to 3– 5 years); and long-term forecasting (usually attempting to forecast many years ahead). Table 1 summarises the work which applied intelligent modelling approach to forecasting MSW generation. Choosing the best modelling approach for waste generation depends on waste stream type, economic factors, purpose of the modelling, and availability of data (Beigl et al., 2008). However, aside from ANN and ANFIS, no attempt has been made to compare the ability of different artificial models to predict MSW generation, especially in midterm period with monthly time step. The following section will compare the ability of artificial intelligence models including ANFIS, SVM, ANN and kNN for monthly prediction of MSW collected by kerbside service. To the best of the authors’ knowledge, this study is the first to apply kNN for forecasting MSW generation as well as evaluate prediction ability of SVM, ANN and ANFIS models for estimating monthly waste generation. 3. Material and method Time series analysis comprises methods that attempt to understand the nature of the series and is often useful for future forecasting and simulation. In time series forecasting, past observations are collected and analysed to develop a suitable mathematical model which captures the underlying data generating process for the series. The future events are then predicted using the model. This approach is particularly useful when there is not much knowledge about the statistical pattern followed by the successive observations or when there is a lack of a satisfactory explanatory model. Here a model was built to predict one step ahead and the variable which is used as an input is the waste generation, where Wt is the waste generation at time instance t. A simple time series prediction performs the following functional mapping: W tþ1 ¼ f ðW t ; W t1 ; . . . ; W tp1 Þ In Eq. (1), the waste generation at time (t + 1) is a function of the waste generations at previous time. Therefore, at time t, a one step ahead forecast Wt+1 is computed using p number of the past observations Wt, Wt1, . . . , Wtp1. While, p was 12 in this study, Wt+1 was forecasted by waste generation in past twelve month equivalent to a year. To compare forecasting ability of artificial intelligence models to predict MSW generation, real data on waste generation obtained from the city of Logan, Australia was used. 3.1. Theory and development of ANFIS The most basic and common Sugeno method of fuzzy inference structure system which has validation capability by training data was used in this study (Rezaee and Zarandi, 2010). Fig. 1 shows an ANFIS system with two inputs, one output and two rules. This system has two inputs x and y and one output, where its rules are: If x is A1 and y is B1 ; then f 1 ¼ p1 x þ q1 y þ r1 ð2Þ If x is A2 and y is B2 ; then f 2 ¼ p2 x þ q2 y þ r2 ð3Þ Ai and Bi are fuzzy sets, fi is the output within the fuzzy region specified by the fuzzy rule, pi, qi and ri are the design parameters that are determined during the training process. Every node computes the degree of activation of any rules in the second layer. The membership functions are then multiplied in this layer: wi ¼ lAi ðxÞ lBi ðyÞ Forecast period Reference Algorithm Short-term Noori et al. (2009c) Jalili Ghazi Zade and Noori (2008), Noori et al. (2009a,b, 2010) Abbasi et al. (2013, 2014), Noori et al. (2009d) ANFIS and ANN ANN Medium-term Lupu et al. (2008) ANN Long-term Chen and Chang (2000), Tiwari et al. (2012) Abdoli et al. (2012), Antanasijević et al. (2013), Jahandideh et al. (2009), Kumar et al. (2011), Ordóñez-Ponce et al. (2006) ANFIS and ANN SVM ANN i ¼ 1; 2 ð4Þ where lAi (x) is membership degree of x in Ai set, lBi (y) is the membership degree of y in Bi set. The ith node computes (third layer) the ratio of activity degree of i rule to the sum of activation degrees of all rules. wi is normalized membership degree of i rule. ¼ w Table 1 Summary of MSW generation classified by forecast period and algorithm. ð1Þ wi w1 þ w2 i ¼ 1; 2 ð5Þ The output of any node is calculated in the fourth layer: wi f i ¼ wi ðpi x þ qi y þ r i Þ ð6Þ where p, q and r are changeable consequent parameters. The final network output f is produced by the node of the fifth layer as a summation of all incoming signals. The final outputs (number of nodes equals to output parameters) of all nodes are derived in the fifth layer. Ov erall Output ¼ X i P wi f i wi f i ¼ Pi i wi ð7Þ In the ANFIS system, each input parameter might be clustered into several class values to build up fuzzy rules, and each fuzzy rule would be constructed using two or more membership functions 16 M. Abbasi, A. El Hanandeh / Waste Management 56 (2016) 13–22 Fig. 1. Structure of the ANFIS network. (Abraham, 2001). Several methods have been proposed to classify the input data and to make the rules. In this study, the one-pass subtractive clustering algorithm is used for data classification. It is a fast algorithm for estimating the number of clusters and the cluster centres in a set of data by getting the cluster radius (r). The radius (r) of each data cluster should be optimized and may vary between 0.1 and 0.95 (Noori et al., 2009c). 3.2. Theory and development of SVM For forecasting purpose, e-type support vector regression method was employed in this study (Clarke et al., 2005). The einsensitive sparse solution saves CPU time during prediction because it does not take into account small residual errors. In a SVM regression model, the functional dependence of the dependent variable y on a set of independent variables x should be estimate by a deterministic function f(x) (f(x) = wT K(x) + b) plus the addition of some noise (y = f(x) + noise). The noise can be usually defined by error term (e). To find a functional form for f(x) the SVM model should be calibrated on a sample set, a process that involves the sequential optimization of an error function. Then, w and b are derived by minimizing the error function (Eq. (8)) subject to Eq. (9): N N X X 1 T w w þ C ni þ C ni 2 i¼1 i¼1 ni ; ni P 0 ; ; i ¼ 1; 2; . . . ; N The above objective function in Eq. (10) is a convex function, and the solution to Eq. (10) is unique and optimal. Subsequent to the determination of Lagrange multipliers in Eq. (10), the parameters w and b in support vector regression function can be calculated under Karush-Kuhn-Tucker complementarities conditions (Wu, P 2009), where W ¼ Ni¼1 ðai ai Þ/ðxi Þ. Consequently, the support vector regression function can be written as f ðxÞ ¼ N X ðai ai ÞKðxi ; xÞ þ b ð12Þ i¼1 the kernel function K corresponding to Kðxi ; xÞ ¼ /ðxi ÞT /ðxÞ ð13Þ Kernels can be any symmetric function satisfying the Mercer’s condition. Different kernels can be selected to construct different types of SVM. Typical examples include (Noori et al., 2009d): where x and xi is the unlabeled input and each of the training inputs respectively. Where c and a are constants and the parameters of the kernels. Gaussian radial basis function due to its popularity and accuracy was used as a kernel function in this study (Kumar et al., 2011). It is well known that SVM generalization performance depends on a good setting of meta-parameters, especially: regularization parameter (C); precision parameter (e) and kernel parameter (c). The regularization parameter (C) determines penalties to estimation errors, e. The parameter e represents the radius of the tube located around the regression function. In other words, choice of e defines the magnitude of errors that can be neglected. Improper selection of these parameters can cause over-fitting or underfitting problems. In data mining and machine learning 10-fold cross-validation is the most common (Refaeilzadeh et al., 2009). This method has been employed to obtain optimal SVM parameters in two step grid search method. In the first step, a coarse grid search is taken using sets of values for C, c and e. In the second step, a finer grid search is conducted around the optimal values obtained in the first step. N N N X X X yi ðai ai Þ e ðai þ ai Þ 0:5 ðai ai Þ i¼1 0 6 ai 6 C ð9Þ i ¼ 1; . . . ; N ðaj aj Þ/ðxi ÞT /ðxj Þ ð11Þ 1. Polynomial kernels K(x, xi) = [x xi + 1]a 2. Radial basis function (RBF) kernels K(x, xi)=exp(c||x xi||2) 3. Linear kernels K(x, xi) = x xi where C indicates a positive constant, u denotes a set of nonlinear transformations, N is the sample size, and ni and ni are slack variables specifying the upper and lower training error subject to an error term e. In the regression problem, most data examples are expected to be within the e-tube. If a data example falls outside the tube, then an error ni and ni will exist. SVM reduces underfitting and over-fitting problem by minimizing both the regularizaP tion term wT w/2 and the training error term C Ni¼1 ðni þ ni Þ in Eq. (8). Therefore, introducing a dual set of Lagrange multiplier i.e. ai and ai allows the optimization problem to be solved by maximizing the quadratic programming algorithm (Eq. (10)) subjected to Eq. (11). i¼1 i¼1 0 6 ai 6 C ð8Þ wT /ðxi Þ þ b yi 6 e þ ni yi wT /ðxi Þ b 6 e þ ni N X ðai ai Þ ¼ 0 i;j¼1 ð10Þ 17 M. Abbasi, A. El Hanandeh / Waste Management 56 (2016) 13–22 3.3. Theory and development of k-nearest neighbours ðkþ1Þ wij k-nearest neighbours (kNN) regression is an instance based lazy learning algorithm (Wu et al., 2008b). It is a nonparametric method, where a new observation is placed into the class of the observation from the learning set that is closest to the new observation, with respect to the covariates used. The determination of this similarity is based on distance measures. Formally this simple fact can be described as follows: Let L ¼ fðyi ; xi Þ; i ¼ 1; . . . ; nL g ð14Þ be a training or learning set of observed data, where yi 2 {1, . . . , c} denotes class membership and the vector xi = (xi1, . . . , xip) represents the predictor values. The determination of the nearest neighbours is based on an arbitrary distance function D (x,xi). Then for a new observation (y, x) the nearest neighbour (y(1), x(1)) within the learning set is determined by: Dðx; xð1Þ Þ ¼ minðDðx; xi ÞÞ ð15Þ ^ ¼ yð1Þ , the class of the nearest neighbour, is selected as predicand y tion for y. The notation x(j) and y(j) here describes the jth nearest neighbour of x and its class membership, respectively. The weighted kNN learning has two user-specific parameters to be determined including the number of nearest neighbours, k, and the weights assigned to the selected neighbours. Specially, the performance of kNN learning mainly depends on the locality control parameter, k, which is usually chosen by empirical crossvalidation. The weights are specified by kernel methods using a density function. In the implementation of kNN regression used in this study, Gaussian kernel method is used with Gaussian density function. 3.4. Theory and development of artificial neural network Multi-layer feedforward neural network is the most popular ANN method. It has been applied widely in many fields because of its superior ability to approximate non-linear functions with high accuracy. Most applications of feedforward neural network use some variation of the gradient technique, back propagation algorithm, to optimize neural networks (He et al., 2005). A feedforward network is made up of several layers of processing elements. The three layer feed forward neural network constructed in this study with input layer, one hidden layer and output layer. Each neuron in a certain layer is connected with all neurons in the next layer. The connection between the ith and jth neuron is characterized by the weight coefficient wij. The output value of xi is determined by Eqs. (16) and (17). X i ¼ f ðni Þ X ni ¼ wij xj ð16Þ ð17Þ where ni is the potential of the ith neuron and function f (ni) is called the transfer function. f ðnÞ ¼ 1=ð1 þ expðnÞÞ ð18Þ The weight coefficients wij is revised to minimize the sum of the squared differences between the computed and required output values. This is accomplished by minimization of the object function E: E ¼ 1=2ðx0 x0r Þ2 ð19Þ where x0 and x0r are the computed and required activities of the output neuron. A back-propagation training algorithm is used to vary the weight coefficients. It holds that ðkÞ ¼ wij k @E @wij ðkÞ ð20Þ where k is the learning rate. The training mode begins with random numbers of the weights and proceeds iteratively. The crucial problem in the model is how to determine the numbers of hidden units. An optimal network topology from the number of inputs and outputs depends critically on the number of training cases, the amount of noise and the complexity of the function or classification. The optimal number of neurons in hidden layer is determined by trial and error in this analysis. 3.5. Evaluation metrics There are many criteria that can be used to evaluate the performances of forecasting models in the numerical study. In this paper, the prediction performance of the proposed forecasting models is evaluated through statistical metrics: coefficient of determination (R2), Root Mean Squared Error (RMSE), Mean Absolute Percentage Error (MAPE), and Mean Absolute Error (MAE). Pn 2 ðW i W i Þ R2 ¼ 1 Pi¼1 2 n i¼1 ðW i W i Þ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 Xn RMSE ¼ jW i W i j2 i¼1 n n 1X W i W i MAPE ¼ n i¼1 Wi MAE ¼ n 1X jW i W i j n i¼1 ð21Þ ð22Þ ð23Þ ð24Þ where W, W⁄ and n is actual weight of generated waste, model output and number of observation, respectively. All computations were run on Windows XP operating system and MATLAB (Version R2009a, Mathwork Inc.). 3.6. Case study and data Logan City Council is one of the fastest growing regions in south east Queensland, Australia. It is situated between the City of Brisbane to the north and Gold Coast to the south as shown in Fig. 2. Logan city has a population of more than 280,000 inhabitants. The city is divided into 63 suburbs and 12 divisions with one Council. Logan has a subtropical climate, typical of the eastern coastal locations of the high pressure belt of the southern hemisphere (Mollasalehi, 2015). Logan Council manages a range of waste services and facilities, across residential and commercial waste streams. In addition, it operates all waste facilities in the City and manages contracts with private companies for collection services. The majority of waste received and managed by the council is classified as MSW. The monthly average MSW generation was 6,400,000 kg in 2014. Based on Council audits of domestic waste bins, Council’s MSW is composed of 25% food waste, 27% garden waste, 15% paper and cardboard (recyclable), 4% textiles, 4% nappies, 6% recyclable glass, metal, and plastics, and 19% ‘others’ (including wood, rubber, leather, non-recyclable paper, cardboard, metal, and glass) (Logan city council, 2014). In this study, monthly time series of MSW generation were collected over a eighteen-year period from July 1996 to June 2014. 4. Result and discussion This study simulated monthly MSW generation by 4 different artificial intelligence models, SVM, ANN, ANFIS and kNN, to find the best predictive model. Before starting the modelling process, 18 M. Abbasi, A. El Hanandeh / Waste Management 56 (2016) 13–22 Fig. 2. Location of Logan city in Australia. we needed to determine the best model structure for each algorithm by determining model parameters. These parameters are different according to each model theory as discussed above. One-pass subtractive clustering algorithm was used for data classification in ANFIS, radius, r, was determined by trial and error method. The cluster radius indicates the range of influence of a cluster and consequently number of rules. In general, as the number of rules is increased, the difference between the predicted and the obtained values decreases and more complex relations can be modelled with a large number of rules. In this study, ANFIS model was developed with different cluster radius to determine the number of clusters by results obtained from the model. Results showed the best fuzzy structure in neural-fuzzy network for estimating MSW generation was at radius of 0.14 where R2, MAE, RMSE, and MAPE values were 0.98, 52.16, 175.88, and 0.008 respectively. Fig. 3 demonstrates the model performance with different r values with the optimum value marked by an arrow. For SVM model, optimization using grid search method showed that optimum values for C, c and e were 100, 41 and 0.001, respectively. Optimal values were obtained by R2 and MAPE estimators as shown in Fig. 4(a), and (b) respectively. Fig. 4 visually illustrates parameter interdependencies, as expected, of C and c. In SVM, the trade-off between complexity of decision rule and frequency of error is controlled by changing the parameter C. the c parameter defines the influence of a single training input. The bulge in Fig. 4 suggest that increasing C and c lead to better results but no longer after the optimum value. Moreover, same results were obtained using MAE and RMSE. In kNN method, a large k value produces more precise predictions as it reduces the overall noise; however, the compromise is M. Abbasi, A. El Hanandeh / Waste Management 56 (2016) 13–22 19 Fig. 5. Determining k variable in kNN method. Fig. 3. Optimal r to construct the best structure for ANFIS model. that the distinct boundaries within the feature space are blurred. Fig. 5 provides optimization information. As it can be seen, optimum k was 6 with R2 = 0.51, MAE = 250.26, RMSE = 308.19 and MAPE = 0.4. As mentioned above, ANN includes the interconnections of a number of neurons. The information received by the input layer is processed by neurons in hidden layer with appropriate nonlinear transfer functions. The number of hidden neurons affects the network complexity. If the network is too small, it will not completely solve the problem or parts of it, and a too complex network has the tendency to memorize the data. It concentrates too much on the data presented for learning and tends toward modelling the noise which may lead to underfitting or overfitting. Number of neurons needs to be optimized by trial and error method. The Optimal number of neurons in hidden layer was determined to be 8 where R2 is 0.46 as shown in Fig. 6. As expected, performance of the model was improved as number of neurons increased to 8 and then performance decreased due to overfitting problem. Fig. 4. SVM parameter optimization by grid search method. 20 M. Abbasi, A. El Hanandeh / Waste Management 56 (2016) 13–22 Fig. 6. Determining optimal neuron number in ANN method. 4.1. Forecasting monthly MSW generation by artificial intelligence models In order to get an effective evaluation of kNN, ANN, ANFIS and SVM models performance, the best model structures were used. 85% of the data was used for training, 15% for testing and 10% of the training dataset for validation. Monthly MSW generation in Logan city was predicted by ANFIS, ANN, SVM and kNN as shown in Figs. 7 and 8. Moreover, Table 2 summarises accuracy of each model during training and testing stages. As evident from Figs. 7 and 8 and Table 2, the results indicated that all models performed well during the training stage with a high R2, more than 0.8. However, during the test stage, there were substantial differences between the models. ANFIS performed the best (R2 = 0.98). It showed good agreement with the observed data, and close predictions of the observed peaks. SVM ranked second in terms of its accuracy in matching the observed data (R2 = 0.71). However, it tended to underestimate the peaks and generated volumes. Prediction ability of kNN was in middle. Nevertheless, it was the closest in estimating monthly average values of generated waste. ANN was the least accurate in matching the observed data (R2 = 0.46). ANFIS is a class of adaptive networks that provides nonlinear ability, capacity for fast learning, and adaptation capability (Tiwari et al., 2012). Earlier studies demonstrated good ability of SVM and ANFIS for forecasting MSW generation (Abbasi et al., 2014; Noori et al., 2009c). Results obtained from this study support these findings, but also shows the superiority of ANFIS algorithm Fig. 8. Comparison of models’ performance by R2 and RMSE. for forecasting monthly waste generation. Although kNN was less accurate than ANFIS, it could predict average value of waste generation accurately. This can be explained according to the fundamental of kNN theory which estimates future values based on nearest data. In addition, results revealed ANN had the lowest performance in comparison with the other models. Estimating maximum and average quantities of waste produced by household in a region is critical for designing and operating the waste management system. Understanding maximum waste generated in a city allows managers to estimate required facilities related to waste collection and disposal accurately at the highest demand. In addition, regular operation of a waste management system depends on estimating an average generation rate in a year. As shown in Fig. 6, ANFIS could produce accurate estimates at peaks, while results obtained from kNN model were close to the average value of waste generated in Logan City Council region. Therefore, in the next section, ANFIS and kNN were employed to determine maximum and average of monthly waste generation for the future period 2015–2020. 4.2. Projection of monthly MSW generation in Logan city As demonstrated in the previous section, ANFIS accurately estimated waste generation at peaks while kNN was successful in estimating monthly average values. Fig. 9 shows projections of monthly MSW generation in Logan city for the coming five years period (2015–2020). Results predict that 1,270,000 kg will be added to the monthly average value of generated waste by 2020. Fig. 7. Modelling results produced by ANFIS, ANN, SVM and kNN. 21 M. Abbasi, A. El Hanandeh / Waste Management 56 (2016) 13–22 Table 2 Accuracy of SVM, ANFIS, ANN and kNN models to forecast monthly MSW generation in Logan city. Train ANFIS SVM ANN kNN Test 2 MAE RMSE MAPE R MAE RMSE MAPE R2 0.001 203.03 335.03 251.80 0.002 300.70 498.43 387.21 3.39E06 0.05 0.07 0.06 0.99 0.93 0.83 0.88 52.16 206.42 226.50 250 175.18 231.99 290.55 308.19 0.008 0.033 0.037 0.040 0.98 0.71 0.46 0.51 Fig. 9. Monthly MSW generation predicted by ANFIS, SVM and kNN. Moreover, peak waste flow is forecast to grow by 2.7% in comparison to year 2014 peak value. Therefore, Logan Council may need more facilities to deal with the peak demand over the next 5 years period. 5. Conclusion To ensure suitable MSW management in a town, the problem must be addressed from its roots. Forecasting solid waste generation is a fundamental step in planning and operation of a waste management system. Therefore, it is necessary for MSW managers and decision makers to develop a tool for accurate predictions of solid waste quantities generated. Due to limitation of conventional methods of waste generation estimation, choosing one statistical model may limit the ability to find the best predictive model for waste generation data. In artificial intelligence models, the data inform the choice of model rather than imposing a specific model a priori. In this study, four algorithms of artificial intelligence were compared for their accuracy of predicting waste generation rates. They were then employed to forecast monthly MSW generation in Logan city, Australia. Our results showed that artificial intelligence models provide promising tools that may allow decision makers to successfully forecast future trends in MSW generation for planning and design of MSW management purposes. Based on the results obtained from the study, it can be concluded that kNN, ANFIS and SVM models can give good prediction performance and may be applied to establish the forecasting models that could provide accurate and reliable monthly MSW generation prediction. In addition, results suggest that ANFIS model produced more accurate forecasts than kNN and SVM. This study is also the first to apply kNN modelling to waste generation forecasting. kNN was able to estimate average monthly waste generation rates with good accuracy. Acknowledgements The authors would like to acknowledge Logan Council for providing municipal waste generation data. 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