IntroductionSecure clean water availability, quantity, and quality, for all inhabitants under the variability in climate change is fundamental to a resilient environment in modern cities (Tortajada et al. 2019). Freshwater scarcity has appeared as a global challenge because of the impact of climate change and socioeconomic factors. It led to an imbalance between water delivered and water demanded. Worldwide, more than 1 billion individuals lack access to safe potable water (Ahmadi et al. 2020).Several studies conducted in different areas have shown that the magnitude and pattern of precipitation differ as a result of climate change (Szeląg et al. 2021). The high variability of climate change imposes an increasing challenge for the management of freshwater resources (i.e., due to reduced freshwater availability) (Nunes Carvalho et al. 2021), which highlights the increasing need for protecting the quantity and quality of water resources, particularly in sensitive zones (Lama et al. 2021a, b). Management of municipal water planning considering a nuanced quantitative understanding of water needs is fundamental for solving the problem of water security (Capt et al. 2021). Accordingly, forecasting municipal water consumption in the future with greater precision is essential when designing water distribution networks (Pandey et al. 2021).In Iraq, located in the fastest-warming area of the world, the temperature reaches 54°C, which is considered one of the highest temperatures ever measured in the Eastern Hemisphere (Salman et al. 2018). Iraq depends on the Tigris and Euphrates Rivers as primary freshwater resources, which originate outside the Iraqi border with Turkey. The discharge rate of these rivers has reduced to less than a third of normal capacity because of the water policies in Turkey, Iran, and Syria. Moreover, investments in industries after 2003 (e.g., the oil industry) has led to increased water consumption (Osman et al. 2017). Studies have been conducted to assess the quality of fresh water in Iraq and have reported an increase in several contaminants (Ewaid et al. 2018). Based on these problems, coupled with others such as continuing wars, embargo, and terrorism, there is an unclear view of whether decision-makers can manage water resources under conditions of decreased availability.Predicting municipal water demand is crucial to enhancing municipal water security, and monthly estimation is vital in the management of dam reservoirs (Ebrahim Banihabib and Mousavi-Mirkalaei 2019). Accurate forecasting of municipal water demand will help utilities recognize the temporal patterns of water needed to satisfy the balance between water delivered and water ordered, which in turn supports the sustainability of the water system (Altunkaynak and Nigussie 2017).De Souza Groppo et al. (2019) and Ghalehkhondabi et al. (2017) found that forecasting of municipal water consumption has progressed over the last several decades, focusing on machine learning techniques and artificial neural networks (ANNs) as the most popular forecasting techniques. Xenochristou and Kapelan (2020) noted that ANN models have been applied in different fields and have been proven effective in forecasting short-, medium-, and long-term urban water demand (Bata et al. 2020; Tiwari and Adamowski 2015; Zubaidi et al. 2020a). Also, they have been successfully used in ecohydraulic and environmental engineering (Lama et al. 2021a; Pandya et al. 2017; Sadeghifar et al. 2022; Zhu et al. 2022). However, determining the optimum hyperparameters of machine learning models is still considered a substantial challenge. To address this, automated machine learning approaches (such as AutoML) have been proposed to help build hybrid prediction models (He et al. 2021) without extensive knowledge of statistics and machine learning (Zöller and Huber 2021), while reducing human effort and potential bias (Hutter et al. 2019). In addition, recent studies (Archetti and Candelieri 2019; Chatzipavlis et al. 2018; Frazier 2018) have investigated the use of Bayesian Optimization (BO) to identify an optimal configuration of the hyperparameters of a machine learning algorithm within a limited number of trials, especially for long-term data.Although several automated machine learning approaches have been applied in the last decades in forecasting water demand, there is still room for improvement (De Souza Groppo et al. 2019). For example, Candelieri and Archetti (2018) reported a substantial improvement in forecast precision over that reported in other research studies (Candelieri 2017; Shabani et al. 2018). Furthermore, Candelieri and Archetti (2018) intend to utilise the other automated machine learning techniques in other application fields. These research studies highlight the importance of continuing the investigation of new methodologies that may offer useful scientific insights to policymakers. Based on recent literature (Archetti and Candelieri 2019; Chatzipavlis et al. 2018; Frazier 2018), Bayesian optimization (BO) can identify an optimal configuration of the hyperparameters of a machine learning algorithm within a limited number of trials, especially for long-term data.In our study, five nature-inspired optimization algorithms were integrated in the ANN model to simulate monthly stochastic water demand data. These algorithms include (1) the slime mold algorithm (SMA), which was proposed by Li et al. (2020) and successfully applied in feature selection (Abdel-Basset et al. 2021), wind power prediction (Yan and Wu 2020), and image segmentation (Abdel-Basset et al. 2020a); (2) the marine predators algorithm (MPA), which was proposed by Faramarzi et al. (2020) and effectively applied in COVID-19 detection (Abdel-Basset et al. 2020b), engineering applications (Ghafil and Jármai 2020), and tensile behavior prediction (Abd Elaziz et al. 2020); (3) multiverse optimizer (MVO), which was efficiently utilized in engineering optimization (Sulaiman et al. 2020), streamflow prediction modeling (Mohammadi et al. 2020), and design optimization of a cam-follower mechanism (Abderazek et al. 2020); (4) backtracking search algorithm (BSA), which was successfully used in identification of soil parameters (Jin and Yin 2020), parameter estimation of power signals (Mehmood et al. 2020), and optimization of photovoltaic models (Zhang et al. 2020); and (5) crow search algorithm (CSA), which was effectively applied in feature selection (Ouadfel and Abd Elaziz 2020), reinforced concrete applications (Sultana et al. 2020), and solving optimal control issues (Turgut et al. 2020).Currently, urban water demand forecasting is extremely challenging for water companies that are struggling to adapt water systems, specifically in terms of increasing concerns about the impact of climate change and water security. Additionally, there are very few studies about forecasting the stochastic signal of water needed, based on climatic factors. Consequently, considerable uncertainty still exists concerning the unexpected growth of stochastic patterns in water demand resulting from the stochastic impact of climatic factors (Zubaidi et al. 2018, 2020c). Based on the literature review, the innovation of this research is to (1) assess, for the first time in Iraq, the extent to which climatic factors have driven urban water demand; (2) integrate the ANN model and the recently developed MPA algorithm to create MPA-ANN, the first application in the field of urban water demand forecasting; (3) compare MPA-ANN with four nature-inspired optimization algorithms (SMA, MVO, BSA, and CSA) to increase the forecasting range and decrease uncertainty; (4) apply a novel methodology (data preprocessing and hybrid model) to forecast the monthly stochastic pattern of water demand; and (5) offer a scientific view to decision-makers of the impact of climatic factors on water demand to satisfy sustainability in a country that faces a unique environment of climate change and water scarcity.MethodologyThe urban water demand methodology suggested here allows medium-term time series demand forecasting to be calculated based on climatic factors. Fig. 1 shows the steps needed to build it.Forecast Model DataHistorical data can assist in estimating and extrapolating possible impacts in the future, and the forecast will contribute to building a looked-for future (Partidário 2007). Development of the urban water demand-forecast model necessitates the availability of historical water consumption and climatic factors time series data. Accordingly, in this study nine climatic factors were used to simulate monthly municipal water demand (million cubic meters; MCUM) over 11 years (2003–2013) in Baghdad City. These climatic factors have been used effectively to forecast water demand in different scenarios in studies focusing on different regions. Here they included maximum temperature, Tmax (°C), minimum temperature, Tmin (°C), mean temperature, Tmean (°C), precipitation, P (mm), wind, W (m/s), solar radiation, Srad (MJ/m2), relative humidity, RH (%), dew point temperature, Tdp (°C), and surface pressure, Sp (kPa).Socioeconomic factors (e.g., population) are deterministic components (Rasifaghihi et al. 2020; Zubaidi et al. 2020c) and therefore out of the scope of this study, which focused on the impact of climatic factors, which have stochastic behavior, on water consumption.Data PreprocessingData preprocessing is a substantial phase that brings the data to a state that enables to easy and accurate forecasting by the developed model. It can be divided into normalization, cleaning, and choice of model input (Tabachnick and Fidell 2013). Haque et al. (2018) claimed that time series should be scaled down (normalized) to make the output space smoother and reduce the impact of outliers; Cleophas and Zwinderman (2016) suggested applying natural logarithm to normalize the time series.Data cleaning means decomposing time series trends, seasonal (nonstationary) components, the stochastic (stationary) component, and noise, and then selecting the stochastic component only for dependent and independent factors because of the stochastic relationship between climatic factors and water consumption (Zubaidi et al. 2020c). Thus, the pretreatment signal approach was used here to implement this step.The main aim of a factor choice procedure is to find the right independent factors, which have a significant effect on the dependent factor and yield a robust forecast model (Seo et al. 2018). In this research, the tolerance technique was used to select the model input factors by avoiding multicollinearity. Each independent factor in the best scenario had to have a tolerance coefficient of more than 0.2 to ensure that there was no collinearity (Cleophas and Zwinderman 2016).Artificial Neural NetworkANN is currently the most common machine learning technique applied in the hydrological area, particularly learning using a feedforward back-propagation (FFBP) structure The FFBP was used in precisely simulating municipal water needed across various spatiotemporal scales because of its ability to map the nonlinear (i.e., trend and seasonal) behavior of water data (Shirkoohi et al. 2021; Zounemat-Kermani et al. 2020).The Levenberg-Marquardt (LM) algorithm was used to train the ANN approach because it is known to minimize prediction error and efficiently simulate any predictor/response map (Bayatvarkeshi et al. 2018; Zare Abyaneh et al. 2016). As in Zubaidi et al. (2020c), the topology of the ANN was classified into four layers of neurons, including the input layer, which contained the predictor factors (i.e., climatic factors), two hidden layers, and the output layer, which contained the response factors (i.e., water demand) (Fig. S2). The tansigmoidal activation function was chosen in the first and second hidden layers, while the linear activation function was employed in the output layer. The process of ANN training was repeated many times over an epoch (i.e., 1,000 iterations) until the error between the actual and simulated urban water time series data reached its minimum. In this study, for each variable, 70% of the data set (92 out of 132 data points) was used for training, 15% was used as the test set (20 out of 132 data points), and 15% was used for validation (20 out of 132 data points). Choosing these percentages followed earlier studies, (e.g., Chyad et al. 2022; Zubaidi et al. 2020b, c).Indeed, ANN performance relies on the optimization of its hyperparameters, which define topology options and ANN learning. Recently, ANN models were successfully integrated by various metaheuristic algorithms to select the best hyperparameters for the short and long term. However, these combined techniques were applied in limited way in the urban water demand field and additional research effort is required to develop more effective and precise combined models in the future (Shirkoohi et al. 2021; Zounemat-Kermani et al. 2020).In this study, the ANN model was combined with the MPA algorithm to select the learning rate (Lr) and the number of hidden neurons (N1 and N2) for the first and second hidden layers instead of the trial-and-error approach. The MPA-ANN algorithm was compared with SMA-ANN, CSA-ANN, BSA-ANN, and MVO-ANN to increase the forecasting range and decrease the uncertainty.Marine Predators AlgorithmThe marine predator algorithm (MPA) is a novel metaheuristic optimization algorithm in which the behavior of ocean creatures in their search for food is simulated. These creatures include sharks, monitor lizards, sunfish, equine fishes, and swordfish. In the ocean, both predators and prey strive to get food to survive. Their behavior inspired researchers to follow this approach to derive a sound algorithm in terms of fitness. Formulation of MPA begins with assigning an initial random set of solutions based on the search space, as illustrated in Eq. (1) (1) Z=Xlower+rand×(Xupper−Xlower)where Xlower and Xupper = lower and upper bound of the search space, respectively; and rand = random number with a range of [0, 1].Two matrices must be defined in MPA because of the nature of the algorithm, in which both predator and prey are looking for food. Therefore, both are considered search agents. These two matrices are referred to as elite (for predator) and prey, respectively, as shown in Eqs. (2) and (3). According to the concept of “survival of the fittest,” the top predators should be the ones with higher hunting kills and merits in the search space. As such, the elite matrix should include only the fittest agents in the search space (predators). Then, depending on the prey positions, the matrix is updated. The dimensions of the prey matrix must be the same as for the elite matrix. In Elite matrix, the predator updates its position based on Prey matrix (2) Elite=[X111X211··Xn11X121X221··Xn21·····X1d1X2d1··Xnd1](3) Prey=[X11X12·X1dX21X22·X2d····Xn1Xn2·Xnd]where X11 = optimal predator vector; n = number of search agents; and d = number of dimensions.In the two matrices, the positions of the predators and preys are updated according to three phases. These phases are merely dependent on the velocity difference between the two. To simulate the whole life of both predator and prey in nature, a designated number of iterations should be assigned in each phase. The details of each phase are discussed in the following subsections.Phase 1: High-Velocity RatioIn Phase 1, the predator is faster than the prey. This phase occurs in one-third of the total number of iterations (i.e., 1/3tmax). The step size of prey movement is updated as in Eq. (4) (4) Si=RB⊗(Elitei−RB⊗Preyi),i=1,2,…,n(5) where R = random vector with a range of [0, 1]; P=0.5=a constant number; RB = random vector referring to Brownian motion; and ⊗ = element-wise multiplication.Phase 2: Unit Velocity RatioIn Phase 2, the predator and prey are moving at the same pace. The prey is represented by Levy flight while the predator is represented by Brownian motion. This phase occurs in the second third of the total iterations (i.e., 1/3tmaxFADwhere r = random value ranging 0–1; r1 and r2 = random indices of prey matrix; FADs=0.2 = probability of FADs effect; U¯ = binary vector; and Xmax,Xmin = vectors of lower and upper bounds of dimensions.In the MPA technique, memory saving should be done so that the old position of the prey can be saved to compare the fitness values of the old position with other successive solutions in which prey update their positions during the simulation. The flowchart of the MPA-ANN algorithm is presented in Fig. S3.Performance Evaluation CriteriaThe parameters of statistical criteria indicate the accuracy of prediction, so forecast error plays a significant role in the choice of an appropriate model that diminishes deviations in future forecasts (Donkor et al. 2014). Because there are no global performance criteria, it is essential to select criteria that are proper for a particular application (Seo et al. 2018). In this study, different performance criteria were considered for assessing the performance of the model. These criteria included coefficient of determination (R2), coefficient of efficiency (CE), Nash-Sutcliffe index (NSI), root mean-square error (RMSE), mean absolute error (MAE), and mean bias error (MBE). The forecast technique has good accuracy and high performance in simulating the water advance time when satisfying one of these values of R2, when CE is more than 0.9, when RMSE, MAE, and MBE approach zero (Dawson et al. 2007; Li et al. 2013), or if the value of NSI approaches 1 (Jain and Sudheer 2008).The augmented Dickey-Fuller (ADF) test and the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test were conducted to examine and determine the stochastic signal of all-time series of the dependent and independent variables.ResultsData PreprocessingThe first step in data preprocessing is to normalize the time series of dependent and independent variables and detect and treat outliers (as discussed in “Methodology”). Figs. 2 and 3 highlight the differences between the raw data and the normalized and cleaned data.Our main emphasis in this study was on the stochastic component only (as earlier discussed). To develop a water demand model based on climatic factors, water consumption, and climatic factor time series should first be decomposed using the pre-treatment signal approach. Fig. 4 shows the normalized and cleaned water time series coupled with the first four signals (trend, seasonal, stochastic, and noise). The stationarity of the stochastic signal for the all-time series is assessed and confirmed by the ADF and KPSS tests.Table 1 shows the difference in correlation coefficient between dependent and independent variables in raw and stochastic stages. It is obvious that the values corresponding to climatic factors in the stochastic stage are much higher than the values in the raw data. For example, the R between water consumption and precipitation increased from −0.535 to −0.931.Table 1. Correlation of dependent and independent factors in raw and stochastic stagesTable 1. Correlation of dependent and independent factors in raw and stochastic stagesDataTmaxTminTmeanPWSradTdpRHSpRaw0.5580.5850.571−0.5350.3960.4530.376−0.541−0.523Stochastic0.920.930.926−0.9310.8350.7280.794−0.917−0.869In the final part of data preprocessing, it is necessary to determine the highly correlated predictors (climatic factors) and at the same time avoid multicollinearity. According to the tolerance technique described in the section “Data Preprocessing,” the scenario of selecting the best model input is repeated several times to choose predictors with a tolerance coefficient not less than 0.2. Accordingly, Table 2 reveals P, Srad, and Tdp as the optimum scenario with coefficients of more than 0.2, meaning that there was no multicollinearity.Table 2. Collinearity statistics for chosen predictorsTable 2. Collinearity statistics for chosen predictorsPredictorTolerance coefficientP0.35Srad0.23Tdp0.33Model ConfigurationThe systematic configuration of the ANN model rather than by trial and error is necessary to build an accurate water demand prediction model. Accordingly, five hybrid metaheuristic algorithms (MVO-ANN, SMA-ANN, BSA-ANN, CSA-ANN, and MPA-ANN) were used to locate the ANN model’s optimal hyperparameters (Lr, N1, and N2). Five swarm sizes (10, 20, 30, 40, and 50) were attempted by combining different algorithms with ANN, and each swarm for each algorithm was implemented five times to obtain the optimal solution (e.g., the MPA-ANN algorithm in Fig. S4, the best swarms are 10-3, 20-2, 30-3, 40-5, and 50-4). After that, the optimal swarm for each algorithm was selected to compare it with other swarms for the same algorithm (Fig. S5). From the figure, one can see that the best swarms are 30 for CSA-ANN, 40 for MPA-ANN, and 50 for SMA-ANN, MVO-ANN, and BSA-ANN.Among all five hybrid metaheuristic algorithms, MPA-ANN was superior (Fig. 5). It yielded the lowest fitness function (RMSE) of 0.003993 after 42 iterations (fewer than the other algorithms). As such, adopting MPA-ANN is feasible and warranted. The 40 swarms of the MPA-ANN algorithm yielded Lr, N1, and N2 values of 0.213, 7, and 1, respectively.Evaluation of Model PerformanceAfter integrating the ANN approach by determining the optimum hyperparameters, the model was run several times to locate a better network (weights and biases) that can precisely forecast the monthly stochastic signal of water demand. Various kinds of statistical tests were carried out to evaluate the ANN’s ability to generalize stochastic water demand data depending on climatic factors in the validation phase.Five statistical indicators were used to gauge the performance of the model as presented in Table 3. CE and NSE assessed the linear dependency between observed and predicted water demand, while MAE, RMSE, and MBE evaluated the nonlinear dependency between observed and predicted water demand. According to the limitation in the section “Performance Evaluation Criteria,” the ANN model offered good accuracy.Table 3. MPA-ANN model statistical indicators in validation phaseTable 3. MPA-ANN model statistical indicators in validation phaseDataMAERMSECENSEMBEValidation0.00570.00710.9980.975−0.0007The estimated model was further validated to double-check the model’s power to accurately predict water consumption in the city of Baghdad. The target data of water consumption (x-axis) was plotted against simulated data (y-axis), with a 95% confidence interval (CI) (Fig. 6). It is noticeable that the target and simulated data reveal a high level of consistency with R=0.978, which supports the accuracy of the prediction model based on the limitation described in the section “Performance Evaluation Criteria.”According to the statistical tests used, the model demonstrated good performance in forecasting water consumption data in the validation stage.DiscussionThe selection of the stochastic component improved the correlation coefficients to climatic factors much higher than the counterpart values in the raw data. For example, between water consumption and precipitation, R increased from −0.535 to −0.931. The tolerance technique was shown to be very helpful in selecting the best model input among the nine independent variables. The climatic factors P, Srad, and Tdp were selected to be the optimum scenario with tolerance coefficients of more than 0.2, which means no multicollinearity existed.When the five metaheuristic algorithms were combined with the ANN for obtaining the hyperparameters at various numbers of swarms, the optimum swarm size was different for each algorithm based on the RMSE value. The performance of the metaheuristic algorithms was then compared at these optimum swarm sizes as there was no direct guide for selecting a swarm size for all of them. Comparing the performance of hybridized ANN, it was observed that MPA-ANN provided the highest prediction accuracy with the lowest RMSE value in fewer iterations than needed by the other hybrid algorithms. Consequently, the ANN optimum hyperparameters values were determined. Model validation process showed the model’s very good performance in forecasting future values of water consumption with a coefficient of determination value of R2=0.978.Wolpert and Macready (1997) noted that, according to the “no free lunch” (NFL) concept, there is no specific theorem that can deliver the best solution compared with other theorems for all optimization problems. Using NFL, Faramarzi et al. (2020) developed the combined MPA theorem for guaranteeing a global solution depending on several strategies and techniques during optimization. Different foraging strategies have inspired MPA in the biological interaction between the prey and predators. Consequently, the Brownian and LF distributions were designed not only to have a systematic, efficient explorer-exploiter tendency but also to significantly enhance the search capability in each implementation. These permitted the MPA algorithm to precisely locate the global optima to solve the optimization issues considered in this research.As a final note, since the size of the data set used in this study was relatively small, Bayesian optimization could have been used in conjunction with the MPA algorithm to increase execution speed and accuracy. Also, further methodological advances in ANN may substantially increase model performance after a limited number of iterations (i.e., faster convergence time). Since computation time was not a critical consideration in our study given that the measured data was obtained offline, we did not require Bayesian optimization. Bayesian optimization methods become relevant when using online data, which involves prolonged training and is computationally expensive. The main objective of our study was to reduce the error between the measured and simulated data.References Abd Elaziz, M., T. A. Shehabeldeen, A. H. Elsheikh, J. Zhou, A. A. Ewees, and M. A. A. 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