A novel optimization model was developed using the equilibrium optimization algorithm to define the most appropriate management process according to the current state of urban water components in utilities. The basis of the optimization model is the current status analysis and management system, which consists of 11 main headings and 231 components. This model is applied for three utilities, and the results are presented in comparison with real-time data. Currently, the number of components with 0 or 1 score is 28, 19 and 69, respectively. The current average scores of the components in the utilities were obtained as 2.84, 3.43 and 2.48, respectively. Then, the improvement process of these components is optimized by the equilibrium optimization algorithm. The most appropriate targets were defined as 3.90, 4.15 and 3.71, respectively, with the optimization algorithm by considering the current scores in the utilities. The target scores for water supply, wastewater collection and treatment components are determined as 3.81, 4.05 and 3.84 for utility I; 4.03, 4.18 and 4.22 for utility II; and 3.51, 3.56 and 4.05 for utility III. The proposed model will be a reference for defining the most appropriate target and determining the management process.

  • A novel water and wastewater management model was proposed in this study.

  • The proposed model was optimized using the equilibrium optimization algorithm.

  • A unique objective function was defined in this study.

  • The unique constraint for the optimization process was defined in this study.

  • All components of the water and waste water components were defined in this article.

Water supply and distribution, collection, treatment and disposal of wastewater (WW) are quite important for urban water and WW management. Increase in water consumption and demand with population growth and the high-water losses in the transmission and distribution systems make access to clean water resources more difficult. Ensuring normal operating conditions in water distribution systems (WDSs) is critical for the delivery of water to customers safely. However, failures in the WDSs cause the operating inefficiency, poor service quality, customer dissatisfaction, high operating costs and an unmanageable network. Monitoring and analyzing the operation efficiency, customer's complaints and the hydraulic data make significant contributions to urban water management (Yilmaz et al. 2022). Practices such as the analysis of breaks in main lines and building connections (Cabral et al. 2019), non-revenue water management (Chawira et al. 2022), reduction of real losses (Boztaş et al. 2019), reduction of apparent losses (Cordeiro et al. 2022), performance analysis (Doghri et al. 2020), performance analysis and improvement of pumps (Al-Obaidi & Qubian 2022; Al-Obaidi 2023a; Al-Obaidi & Alhamid 2023), cavitation analysis of pumps (Al-Obaidi 2019a, 2019b, 2023b) and economic leakage level modeling (Firat et al. 2021; Moslehi et al. 2021; Yilmaz et al. 2022) have a significant role in WDS management.
Figure 1

Water and WW management Dm matrix optimization model.

Figure 1

Water and WW management Dm matrix optimization model.

Close modal

Mutikanga et al. (2011) emphasized that water losses and revenue losses are at serious rates, especially in developing countries. Appropriate strategies are needed to manage water losses. Haider et al. (2015) stated that the operation of WDSs is one of the most important issues. Walsh et al. (2015) reported that water resources should be managed in conjunction with the current world water use and the projected increase in our dependence on it. D'Ercole et al. (2016) stated that the energy cost of the pumps in WDSs constitutes a large part of the total operating cost. The costs will increase due to the increase in leaks. Zyoud et al. (2016) aimed to determine the most appropriate alternatives within the framework of water loss reduction strategies in the WDSs in developing countries. Aboelnga et al. (2019) emphasized that ensuring urban water security poses great challenges for utilities. Another deficiency is that while water security is assessed at the regional level, measures are not implemented at the urban level. Torkaman et al. (2021) reported that the WDSs have become increasingly important and integrated decision-making has become more important with urban development. Hu et al. (2021) expressed that the WDSs are often designed without planning due to rapid urbanization. For this reason, the planning and projecting phase should be realized before the WDSs are implemented in the field.

Sustainable management of WW systems (WW collection and treatment) is critical for the environment and human health. Urban WW systems contain various components with a complex structure. The sewerage system should have sufficient capacity and operation status for the collection of WW (Dada et al. 2021; Szeląg et al. 2021). Systematic monitoring of the parameters, which are the WW line, building connections and inspection chambers (Eulogi et al. 2021), WW master plan and WW network hydraulic model creation (Jang et al. 2018), analysis of the causative factors and the development of prevention methods (Lee et al. 2021), make a significant contribution to the sustainable management of WW networks.

Silva & Rosa (2015) reported that assessing and monitoring the energy efficiency and performance management components are quite critical in WW treatment plants (WWTPs). Hernandez et al. (2018) stated that the WWTP design and operation processes of different sized municipalities and water utilities have a direct impact on operating costs. According to the Di Cicco et al. (2019), energy consumption in the WWT sector is the approximately 25% of the total consumption in the water sector. Energy optimization strategies are needed since this consumption is expected to increase in the coming years. Fuentes et al. (2020) emphasized that the analysis of operation efficiency in WWTPs contributes to the improvement of environmental and economic performance. Sabia et al. (2020) stated that the field measurements should be made regularly and comparative energy performance indicators should be monitored by considering these data. Schneider et al. (2020) expressed that long-term performance decrease will be observed in the WWTPs that are not integrated into any SCADA system and cannot be monitored. Sheng et al. (2020) noted that the WWTP performance is affected by combined stormwater and WW collection and pipeline damage.

On the other hand, the modeling and optimization techniques have been widely used in the analysis of water and WW problems depending on the development of computer technology. These methods provide significant contributions especially in complex structure and problems with multiple parameters. Awe et al. (2019) stated that optimization methods are used in analyzing the complex WDSs, meeting water demands, and designing the WDSs. Optimization is used either to minimize resource consumption and cost or to maximize profit and system performance. Berhane & Aregaw (2020) aimed to determine the most appropriate pressure level and pipe diameter with the optimization algorithm to ensure operational efficiency and customer satisfaction in the WDS. It was seen that the current maximum pressure is 31.1 m, and the ideal pressure has increased to 38.1 m. Brentan et al. (2020) used the modified k-algorithm in the creation of district metered areas and determined the locations of the isolation valves by particle swarm optimization. Sutharsan (2023) performed the optimization of hydraulic parameters such as system pressure and flow rate to design the most suitable water distribution network in a pilot region. Yilmaz et al. (2023) determined the level of economic loss with the optimization algorithm, by considering the network and customer characteristics, water production cost, water sales price and other system parameters in WDSs.

There are a lot of cost components such as the initial investment, construction, operation and maintenance that create high costs in managing drinking WDSs that meet people's most basic needs. Therefore, the operation and management components of the water transmission and distribution system should be optimized for sustainable management of water resources, ensuring efficiency and minimizing cost components (Sangroula et al. 2022). Blokus-Dziula et al. (2023) stated that optimizing the maintenance, repair, operation and management costs of WDSs and establishing the most appropriate network management are both important issues. Therefore, it should be taken into consideration that water management is a multifaceted and parameterized system.

The management of urban WW components requires different types of teams, equipment, fieldwork and technological infrastructure, which in many cases necessitate high costs. Therefore, the most appropriate management process should be determined to optimize the operation and management cost of urban WW components. The current status of the water and WW management components in utilities should be first analyzed. The current implementation levels of WW components in the utilities, data management and quality, technical, technological, personnel capacity and financial conditions of the utilities should be analyzed (Kılıç et al. 2023). The most appropriate improvement target should be defined for the WW management components based on the current state. In addition, the most appropriate management process should be determined to achieve this defined goal with the least cost.

Therefore, in this study, a novel optimization model was developed using the equilibrium optimization (EO) algorithm to define the most appropriate management process according to the current state of WW components in utilities. The developed model is based on the current situation assessment and process management system proposed by Kılıç et al. (2023) for WW components. The basis of the optimization model is the current situation assessment system (CSAS system), which consists of 11 main headings and 231 sub-components. Each component in the CSAS system is scored between 0 and 5 according to the current situation. The most appropriate management and improvement process of CSAS components is determined by the EO algorithm based on the current scores. The original objective function and constraints are determined for the optimization of the model. The components in the CSAS system, the scoring structure developed for these components, the holistic consideration of WW components, the development of a new optimization model that provides the definition of the most appropriate target and process according to the current scores of the components, and the testing of the developed model with real data in the field strengthen the originality of the study. The developed model was tested using three pilot utilities, and the results were discussed.

The optimization model proposed in this study is based on the current status assessment system developed by Kılıç et al. (2023) for WW practices. This assessment system consists of CSAS, DATA, PAAS and TOOL matrices. The CSAS matrix was created to evaluate the current status of water and WW collection and treatment practices, to question and evaluate the quality of the data and to evaluate the current implementation levels of the practices (Kılıç et al. 2023).

Regular measurement, accuracy and reliability of data are important for accurate analyses of WW performance. Therefore, the DATA matrix containing the most basic data used in the performance indicator calculation was defined in this assessment system. Each component in the DATA matrix is connected with the components of the CSAS matrix. Thus, the data quality is tested based on the scores in the CSAS matrix (Kılıç et al. 2023). The weaknesses in utilities are defined based on the scores of the components in CSAS. Appropriate and applicable targets are proposed for these weaknesses (Kılıç et al. 2023). The CSAS matrix is a critical system for the optimization-based model proposed in this study. The CSAS matrix consists of 231 components under 11 main headings covering WW management practices. The main headings in the CSAS matrix cover the organization structure, data management and monitoring, water loss monitoring, management of water loss components, operation of the water and WW networks, operation of WWTP, and monitoring the water, energy, personnel and financial efficiency (Kılıç et al. 2023).

An original evaluation system was proposed by Kılıç et al. (2023) to evaluate the current status of WW components in utilities, to question the data quality and to determine the current application levels of water and WW management components. In this evaluation system, water and WW components (231 components in total) are scored based on the original scoring system. Thus, the current situation is defined. In addition, the matrices included in the evaluation system (current situation evaluation, data, performance evaluation and method) and the components included in these matrices were discussed.

In this study, the most appropriate target is determined with the optimization algorithm to improve water and WW management components. For this purpose, the scores that each component can reach are determined according to the current scores of the components with the optimization algorithm. Thus, the most appropriate improvement process is defined by the optimization algorithm according to the current situation of the utility and infrastructure characteristics.

The CSAS matrix includes basic, moderate and advanced practices. Basic level contains the primary components in WW management. The applicability and requirements of moderate components are more costly than basic-level components. The advanced-level components need various requirements such as experience, knowledge, financial, technical and technological capacity in utilities (Kılıç et al. 2023). Each component in the CSAS matrix is evaluated and scored between 0 and 5 points (0 points: quite poor, 1 point: poor, 2 points: insufficient, 3 points: moderate, 4 points: good and 5 points: quite good) by conducting onsite inspections and controls at the utilities. Thus, the current situation is revealed by considering 231 components in the utilities (Table 1). The scores of components in the CSAS matrix form the basis of the process management model developed using the EO algorithm. In this assessment system, it is recommended that the components scoring 0 (quite poor), 1 (poor), 2 (insufficient) and 3 (moderate) be improved gradually (Kılıç et al. 2023). Details about the current status assessment system, components and scoring structure are included in the study published by Kılıç et al. (2023).

Table 1

Optimization model matrix for water and WW management

 
 
Table 2

Effect coefficients used in the water and WW management optimization model

 
 

In this study, an original model structure has been developed using the EO algorithm to identify the most suitable management process based on the current status of water and WW components in the CSAS matrix in utilities (Figure 1). It is crucial to improve the components over time, demonstrate institutional development and ensure effective and efficient use of public resources based on their current status. However, the methods to be implemented to improve the performance of the utilities should be determined. Moreover, the components that need priority for improvement should be identified. In these challenging processes, the administrative inadequacy of many water utilities further complicates the process. In the study, the improvement of all these components can be defined as a typical optimization problem by considering the structure of water utility. There are several data that affect the current status matrix. These data should be accurate and directly obtained from the field by the utilities. The components in the CSAS matrix are graded on a scale of 0–5. In addition, each parameter identified directly or indirectly affects another parameter.

As an example, ‘Measurement of Produced Water Volume’ is one of the fundamental components in urban water management. Accurate and systematic measurement of data (having a high score) enables more accurate and reliable implementation of urban water and water loss management activities. The components in the CSAS were identified to directly or indirectly affect other components (Table 2). In this way, the total number of components influenced by the components in the CSAS matrix within the scope of water management (number of components it affects in the CSAS matrix + number of components it affects in the DATA matrix) has been determined. Thus, the numbers of the components represent the level of impact in the proposed optimization model. A linear relationship among the components in the CSAS matrix has been assumed by considering this level of impact (weight coefficient).

The components in the CSAS matrix were initially scored based on the current status in pilot utilities. The components were not scored by the technical staff of the institution. The scoring was conducted by an external team of experts based on examinations conducted within the institution (taking into account reports, data, documents, etc., related to the components) and evaluations. As a result, the current situation of the three pilot utilities in terms of WW management, the current level of implementation of the components and the quality of the data have been revealed.

Objective function definition for optimization algorithm

The CSAS matrix was created directly based on field assessments. The relationship between the components was thought to be linear. The mathematical form of the coefficient relationship of the linear matrix (Lm) created according to these evaluations is defined in Equation (1) (Kılıç 2023). The matrix form of the optimization model for water and WW management is shown in Table 1:
formula
(1)
The impact coefficient matrix is a matrix that is determined based on the number of data matrices each component affects. This matrix enhances the effectiveness of the linear model. During the optimization process, values are repeatedly taken from these impact coefficients to calculate the values. As mentioned in previous sections, in total 231 parameters are optimized in the system. The general mathematical model of the impact coefficient matrix can be defined as follows:
formula
(2)
Lm is the linear matrix and w is the impact coefficient. The matrix called Lm was created by performing mathematical operations for the other components that each component in the CSAS matrix is associated with. In the continuation of this study, the aforementioned matrix forms were used. The objective function needs to be calculated after the mathematical model of the optimization is defined. The most appropriate values of the coefficient matrix are sought according to the methodology of the objective function defined in the optimization structure proposed in the study. While analyzing the objective function in the optimization model, the values that the result matrix (R) can take are defined according to each level (Kılıç 2023):
formula
(3)

R is the result matrix. As mentioned earlier, a linear relationship is assumed between the components in the CSAS matrix. In the CSAS matrix, each component is evaluated based on a score of 0 or 1, indicating ‘data quality is very poor and needs improvement’. If a component has a score of 2 or 3, it is evaluated as ‘data quality is questionable and needs improvement’. If a component receives a score of 4 or 5, it is considered as ‘data quality is good or very good’. These score ranges are used to assess the data quality of the components in the CSAS matrix.

Table 3 defines the boundaries of the result scores based on the current condition scores for the pilot utilities and field experiences. The result matrices are controlled against these conditions after each iteration. Based on the results of these checks, the algorithm proceeds to the next iteration if the conditions are met or not. The acceptance or rejection of the results is determined based on compliance with these conditions.

Table 3

Values that the result matrix should take according to the starting points

LevelsInitial scoreResult matrix
Requirements for basic level (each variable in the first seven groups) If the score of the component is 0, 1 or 2 ≤ 4 
If the score of the component is 3 and 4 ≥ current value 
Requirements for intermediate level (each variable in the top seven groups) If the score of the component is 0, 1 or 2 ≤ 4 
If the score of the component is 3 ≥ 3 
If the score of the component is 4 ≥ 4 
Requirements for advanced level (each variable in the top seven groups) If the score of the component is 0, 1 or 2 ≤ 3 
If the score of the component is 3 ≥ 3 
If the score of the component is 4 ≥ 4 
LevelsInitial scoreResult matrix
Requirements for basic level (each variable in the first seven groups) If the score of the component is 0, 1 or 2 ≤ 4 
If the score of the component is 3 and 4 ≥ current value 
Requirements for intermediate level (each variable in the top seven groups) If the score of the component is 0, 1 or 2 ≤ 4 
If the score of the component is 3 ≥ 3 
If the score of the component is 4 ≥ 4 
Requirements for advanced level (each variable in the top seven groups) If the score of the component is 0, 1 or 2 ≤ 3 
If the score of the component is 3 ≥ 3 
If the score of the component is 4 ≥ 4 

In the optimization process, it is assumed that utilities progress from simpler to more complex practices. In the CSAS matrix, the components at the basic level consist of seven elements under each main category. Similarly, in the optimization process, priority is given to improving the components at the basic level first. The intermediate level, which follows the basic level, includes the second set of seven components, and the remaining seven components represent advanced-level practices. This hierarchical approach allows for a systematic improvement process, starting from the basic level and progressing toward more advanced levels of implementation.

The evaluations for the development of the proposed optimization model for water and WW management and the definition of its mathematical structure are as follows:

  • Each component in the CSAS matrix is assigned scores ranging from 0 to 5. Thus, in the optimization model, the score matrix allows each variable to take values of 0, 1, 2, 3, 4 or 5.

  • The desired state for the sustainable and efficient management of the urban water cycle is for each component to have a score of 5. However, considering field conditions and the current state of utilities, achieving this ideal state is not realistic and feasible.

  • Based on the scores in the CSAS matrix, appropriate and attainable targets are defined for each component, and the optimization model provides a roadmap to reach these targets.

  • During the optimization process, an analysis is conducted by assigning integer scores from 0 to 5 for each component based on their initial scores, and the objective function is calculated accordingly.

  • In the optimization model, the assigned values by the algorithm are compared with the previous values of each component in the CSAS matrix. If a component initially had a score of 0 or 1 and the algorithm assigns a score of 2 or 3 to that component, the difficulty coefficient (ZK1) in the model is multiplied by 1.

  • If a component initially had a score of 0 or 1 and the algorithm assigns a score of 4 to that component, the difficulty coefficients (ZK1 and ZK2) in the model are added together and multiplied by 1.

  • If a component initially had a score of 0 or 1 and the algorithm assigns a score of 5 to that component, the difficulty coefficients (ZK1, ZK2 and ZK3) in the model are added together and multiplied by 1.

  • Thus, an algorithmic structure in line with the nature of the optimization problem is defined in the optimization model. Components that initially received scores of 0 or 1 will have different difficulty levels for transitioning to scores of 2 or 3 compared to components that initially had scores of 2 or 3. Similarly, the difficulty level of transitioning from a score of 4 to a score of 5 will be different for components that initially had a score of 4.

  • Water and WW management involve complex and costly processes. Taking into account the challenging nature of the problem, it is more difficult and costly to transition from a good level (score of 4) to an excellent level (score of 5) compared to transitioning from a very poor (score of 0) or poor (score of 1) level to an insufficient (score of 2) or fair (score of 3) level.

  • To reflect this natural structure of the problem in the optimization model and its mathematical structure, the transitions between scores are set to have certain difficulty levels. The difficulty coefficients (ZK1 = 1, ZK2 = 3 and ZK3 = 5) are determined based on real field data obtained from pilot utilities. However, these coefficients can be updated in future studies considering the dynamic nature of the utilities.

  • The objective function (AF) in the proposed optimization model for water and WW management is calculated according to Equation (4), where the target values are represented as HD:
    formula
    (4)

In the optimization algorithm, the objective function considers variables with a minimum value of 0 and a maximum value of 5. In each iteration, a candidate solution is proposed. These proposed solutions first pass through the filters mentioned below. The objective function (AF) is calculated based on these structures. Then, the compatibility of the proposed solution with the field is tested. For this purpose, the conditions in Table 4 are used. If the solution satisfies these conditions, the algorithm accepts the solution. If not, it moves to another parameter vector space. During the optimization process, the following algorithmic structure is used to determine the transition values. NDm(i) represents the new value suggested by the optimization algorithm.

Table 4

Basic hydraulics parameters in pilot water utilities

UtilityDaily treatment capacity of the WWTP (m3/day)Water supply (×106m3)Water network length (km)WW network length (km)
Utility I 135,000 78 2,500 1,400 
Utility II 110,000 92 8,400 4,200 
Utility III 156,620 119 8,592 4,560 
UtilityDaily treatment capacity of the WWTP (m3/day)Water supply (×106m3)Water network length (km)WW network length (km)
Utility I 135,000 78 2,500 1,400 
Utility II 110,000 92 8,400 4,200 
Utility III 156,620 119 8,592 4,560 

When the initial value is 0 or 1, the process of determining the transition coefficient is as follows. First, ZK represents the difficulty function values. Based on the newly obtained value, transition function values are assigned, and the objective function (AF) is calculated according to Equation (5):
formula
(5)
When the initial value is 2 or 3, the transition coefficient is determined using the provided function below (Kılıç 2023):
formula
(6)
In case the initial is 4, the algorithmic process followed in determining the transition coefficient is as follows (Kılıç 2023):
formula
(7)

If the initial value is 5, it indicates that there is no need for optimization for that variable, and it does not contribute to the objective function. Therefore, the difficulty coefficients are set as ZK1 = 0, ZK2 = 0 and ZK3 = 0 for this case. During the optimization process, there is no backward movement of any value to maintain the real-time model of the system. To ensure this condition and prevent the algorithm from getting stuck in local points, the difficulty coefficients are set as ZK1 = 0, ZK2 = 0 and ZK3 = 0. The following sections explain how this process is carried out with the EO algorithm.

EO is an algorithm inspired by the comparison of mass balances on control volumes. This EO achieves the principle of mass conservation in a defined control volume. The first-order differential equation shown below represents this. According to the specified equation, the change in mass over time is expressed as the difference between the total mass entering the system and the total mass leaving the system. The change in mass per unit time is expressed by the following equation (Faramarzi et al. 2020):
formula
(8)
where C is the concentration value in the control volume (V), represents the change in mass in a known volume, Q is the volumetric flow and Ceq is the concentration value at balance. It shows the change in mass in the system proportionally in G (Faramarzi et al. 2020). In fact, the values to be optimized are placed in the C variable. For example, in Equation (9), the derivation rule of the data matrix to be calculated is given as follows (Faramarzi et al. 2020):
formula
(9)
F in Equation (9) is calculated as follows:
formula
(10)

Here, the parameters t0 and C indicate the time and concentration at the initial conditions. In the written expressions, the concentration in the control volume is obtained depending on this rotation speed with the Equation (9) (Faramarzi et al. 2020). Equation (9) introduces three conditions or stages for updating the particles. Each particle operates independently based on these three conditions for updating the concentration.

The first stage is the equilibrium of concentration. This stage represents one of the best solutions randomly selected so far in the pool. This structure is called the equilibrium pool. The pool in the algorithm consists of the four best solutions created around the best solution and their average (Faramarzi et al. 2020). The second stage represents the difference in concentration (density) between the current particle and the equilibrium state. This structure directly affects the search mechanism. In this stage, it enables the particles to search in the parameter vector space to find the global optimum.

The third stage is associated with the derivation rate. This stage plays a role in improving the search process, especially when taking small steps or rates. It has significant contributions to the search process. These three stages mentioned above directly impact the search performance. The structures that affect the search process of the algorithm are explained below (Faramarzi et al. 2020).

Step 1: generating the initialization matrix

Like other metaheuristic optimization algorithms, the EO algorithm uses an initial population to initiate the optimization process. The initial concentration or density is generated using a uniform random distribution based on the number of particles. The initial population is created as follows (Faramarzi et al. 2020):
formula
(11)
is the vector of the initial concentration for each particle. and show the maximum and minimum values of the directions, respectively. is the random vector derived from [0 1]. n represents the number of particles in the population (Faramarzi et al. 2020).

Step 2: generating candidate solutions

The equilibrium state is represented as the final state of the algorithm. This stage is referred to as the global optimal point within the algorithm. At the beginning of the optimization process, there is no information about the equilibrium state. The particles only use equilibrium candidates to initiate the search process. Based on the experiences obtained from solving different types of problems under different conditions, these candidate solutions are four different solutions that are close to the best solution throughout the entire optimization process (Faramarzi et al. 2020):
formula
(12)

Step 3: exponential term (F)

The exponential stage is the period in which the main concentration values are updated. The EO algorithm maintains a reasonable balance between the search and exploitation phases in its algorithmic process. This is because the turnover rate can vary over time within a real control volume. is represented by a random vector within the range [0,1]. This vector is defined as follows (Faramarzi et al. 2020):
formula
(13)
The variable ‘t’ in the equation represents the iteration count. Therefore, as shown in Equation (14), it decreases with respect to the iteration count. The calculation of ‘t’ is as follows (Faramarzi et al. 2020):
formula
(14)
The variables ‘Iter’ and ‘Max_Iter’ in the equation represent the current iteration count and the maximum iteration count, respectively. The constant ‘a2’ represents a fixed value that indicates the utilization capability. By considering Equation (15), the operations are performed to increase the search and operation capabilities, ensuring the algorithm's guarantee to reach the optimal point (Faramarzi et al. 2020):
formula
(15)
The constant ‘a1’ in the equation is a fixed number that controls the search capability. A higher value of ‘a1’ increases the search capability but decreases the usage and operation capabilities. Similarly, a higher value of ‘a2’ increases the usage or operation capability but decreases the search capability. The component ‘’ in Equation (15) directly affects the search and usage conditions. In the study, ‘r’ is a random vector between 0 and 1. The algorithm performs the operations by taking the values a1 = 2 and a2 = 1 in benchmark tests to solve all these problems. These values have been determined through empirical tests (Faramarzi et al. 2020). However, in other problems, it may be necessary to change these values. By substituting Equation (10) into Equation (8), Equation (16) is obtained (Faramarzi et al. 2020):
formula
(16)

Step 4: generation rate (G)

The derivation rate is one of the key components of the proposed algorithm. This rate enhances the algorithm's performance and its ability to reach a complete solution. In many engineering applications, various models are used to determine the derivation rate (Guo 2002). For example, the first-order exponential reduction model, which is one of them, is defined as follows (Faramarzi et al. 2020):
formula
(17)
The final state of the derivation ratio is as follows (Faramarzi et al. 2020):
formula
(18)
The calculation of G0 in the equation is as follows (Faramarzi et al. 2020):
formula
(19)
formula
(20)
The values of r1 and r2 in the equation are random values in the range [0,1]. The generation control parameter (GCP) is the control parameter for the derivation rate. This mechanism is operated according to Equations (19) and (20). To maintain a balance between search and utilization or execution, GP is set to 0.5. Consequently, the update rules of the EO algorithm are as follows (Faramarzi et al. 2020):
formula
(21)

Equation (21) represents the first stage, which is the balance of concentration or density. The second and third stages correspond to the change in concentration. The second stage is responsible for finding the global optimum point in the algorithm. It mainly affects the search phase. In this stage, the difference between the current concentration (i.e., the value in the particle) and the equilibrium concentration is directly taken into account (Faramarzi et al. 2020).

Step 5: saving memory of particles

In this section, the positions and fitness values of particles in the parameter vector space are recorded. This structure is similar to the concept of the best value in the particle swarm optimization (PSO) algorithm. The fitness value of the current particles is compared with the fitness values from the previous iteration. If there is an improvement, the current value is updated by overwriting the best value (Faramarzi et al. 2020).

Step 6: the search capability of the EO algorithm

This mechanism has actually been explained in detail in previous sections, but in this section, the parameters affecting this mechanism are described in detail.

a1 is a coefficient that controls the scanning structure. It determines how far the particle's new position is from the equilibrium candidate solution. As mentioned in previous sections, a large value of a1 provides high search capability. Therefore, this value should be sufficiently large to enhance search capability. The limit of 3 for this value has been empirically determined. Similar constraints exist in other metaheuristic optimization algorithms (Faramarzi et al. 2020).

Step 7: generating probability

It controls the probability of concentration contributions based on the generation probability. When GP = 1, it indicates no changes in the optimization process, reflecting a high scanning capacity. When GP = 0, it shows that the rate of change affects the candidate solutions in the optimization process. Based on empirical tests, GP = 0.5 has been chosen to achieve a balance between search and exploitation processes.

Step 8: equilibrium pool

This vector consists of five elements or particles. The selection of these five parameters is sometimes arbitrary and sometimes based on empirical tests. In the initial iteration, all candidate solutions are separated by a certain distance from each other.

Step 9: ability to use and operate the EO algorithm

In this stage, the algorithm performs the utilization and local search phases. The parameters that affect this stage are as follows (Faramarzi et al. 2020):

a2: is the parameter that is similar to the parameter a1. However, a2 controls the amplitude of the utilization or trial phase. It determines the extent of utilization and allows trials to be conducted around the best solution.

Step 10: saving memory

It records the best and worst values of the particles in the relevant population. This structure directly influences the utilization process used in the optimization algorithm.

Step 11: equilibrium pool

With the repetition of parameters, the search phase disappears and the trial phase becomes active. Therefore, in the last iteration, if the equilibrium candidates are close to each other, the concentration update procedure will assist in performing local searches around candidate solutions and contribute to the utilization phases.

Optimization of the proposed MDA model using the EO algorithm

Step 1: Enter the initial values for the problem.

Step 2: Select the objective function and its associated constraints in the algorithm.

Step 3: Determine the optimized parameters, which are the Dmvalues, for the optimization problem.

Step 4: Then, initialize the population of objects with random positions using Equation (3).

Step 5: Evaluate the initial population and select the one with the best fitness value.

Step 6: Execute the developed equilibrium, comparative planning to minimize from this step.

Step 7: Evaluate each object and select the one with the best fitness value.

Step 8: The algorithm iterates for a maximum number of iterations and then stops.

In this study, three utilities that are Malatya Water and Sewerage Administration General Directorate (Utility I), Kayseri Water and Sewerage Administration (General Directorate (Utility II) and Kahramanmaraş Water and Sewerage Administration (utility III), were selected as study area to test the optimization model (Figure 2, Table 4).
Figure 2

Pilot water utilities.

Figure 2

Pilot water utilities.

Close modal

Utility I, located in eastern Turkey, serves a total of 812,000 people in an area of 12,312 km2. WW collected with the WW system is treated in an advanced biological WWTP. The daily treatment capacity of the advanced biology WWTP, which has been operating since 2003, is 135,000 m3/day.

The main source that meets the water of the city center is obtained from the catchment located in Gündüzbey neighborhood of Yeşilyurt district. The water resource is located 19 km from the city center and at an altitude of 1,208 m. The flow rate of the catchment varies seasonally between 2,000 and 2,900 L/s.

Utility II, located in central Turkey, serves a total of 1,421,455 people in an area of 17,193 km2. The water sources in the utility are monitored with the SCADA system. The daily treatment capacity of the advanced biology WWTP, which has been operating since 2004, is 110,000 m3 /day. The GIS infrastructure is used in an integrated manner with other systems and up-to-date data can always be accessed.

Utility III, located in southern Turkey, serves a total of 1,179,107 people in an area of 14,525 km2. The utility provides 119 million m3 of drinking water per year to the city, according to 2021 data, with a drinking water network of 8,592 km. In addition to the supply of drinking water, it provides services in its area of responsibility with 1,135 water tanks with a total volume of 156,620 m3. The total length of the WW networks is 4,560 km. The daily treatment capacity of the advanced biology WWTP is 127,500 m3/day.

Evaluation of optimization results for utility I

The components in the CSAS matrix were scored between 0 and 5 points based on the onsite examinations and evaluations in utility I. While the current scores of the utilities were questioned, the most suitable one for the gradual scoring structure was selected. The average of the initial scores in utility I is 2.7338 for components including water management practices, 2.9333 for components including WW network (sewage) management practices and 2.8596 for components including WW treatment practices (Table 5). Since the initial score is below 3 in all three main fields of activity, it can be said that the current scores of this utility are quite low. The most appropriate targets were identified for each component by the optimization model (Figure 3) based on the current scores obtained for utility I.
Table 5

The current scores and optimization results for Utility I

Utility IMain componentCurrent average scoreTarget_OTarget average scores
 Water supply 2.7338 18 3.8117 
 WW collection 2.9333 4.0500 
 WW treatment 2.8596 3.8421 
Utility IMain componentCurrent average scoreTarget_OTarget average scores
 Water supply 2.7338 18 3.8117 
 WW collection 2.9333 4.0500 
 WW treatment 2.8596 3.8421 
Figure 3

Current scores and optimization target scores for utility I.

Figure 3

Current scores and optimization target scores for utility I.

Close modal

Basic-level components have scored 2 or more points in the current status. In the moderate-level components, there is no component with a score of 0, and there are 5 components with a score of 1. In total, 21 components at the advanced level have a score of 0 or 1. There is no 0-point component in the basic- and moderate-level components. However, the components A4-9, A10-9, A4-10, A3-13 and A6-13 with a score of 0 or 1 are in the intermediate level.

The system is optimized considering the effect coefficients and score increase conditions of the components. It is seen that the improvement levels are suggested by the model for these components in the result matrix. The components of A7-16, A11-16, A2-17, A7-17, A9-18 and A7-21 at the advanced level initially were scored as 0. These components, whose current score is 0, have been improved by the model in accordance with the determined conditions.

In the result matrix, it is seen that the components with a high impact coefficient and initial scores of 0 or 1 take values in accordance with the conditions. Good level scores are recommended as a result of optimization for components with insufficient points in the basic-level components. The improvement levels are determined for the intermediate components after the scores of the basic-level components are corrected by the optimization model. The components with low scores in moderate level were improved in accordance with the conditions determined at the beginning. In this way, new scores are suggested considering the dynamic nature of the model and where the maximum benefit is expected. In the advanced components with quite poor scores, it is seen in the result matrix that there are improvements in line with the conditions determined at the beginning.

When examining Figure 4, it can be observed that the defined error function moves in a decreasing direction during the optimization process. This result indicates that the performance of the utilized optimization algorithm is good.
Figure 4

Objective function (error function) converge curve for utility 1.

Figure 4

Objective function (error function) converge curve for utility 1.

Close modal

Evaluation of optimization results for utility II

The components in the CSAS matrix were scored between 0 and 5 points based on the onsite examinations and evaluations in utility II. While the current scores of the utilities were questioned, the most suitable one for the gradual scoring structure was selected. The average of the initial scores in utility II is 3.3312 for components including water management practices, 3.2667 for components including WW network (sewage) management practices and 3.6842 for components including WW treatment practices (Table 6). It is observed that the initial score remains above 3 (above the average) in all three main fields of activity. The most appropriate targets were identified for each component by the optimization model (Figure 5) based on the current scores obtained for utility II.
Table 6

The current scores and optimization results for utility II

Utility IIMain componentCurrent average scoreTarget_OTarget average scores
 Water supply 3.3312 13 4.0390 
 WW collection 3.2667 4.1833 
 WW treatment 3.6842 4.2281 
Utility IIMain componentCurrent average scoreTarget_OTarget average scores
 Water supply 3.3312 13 4.0390 
 WW collection 3.2667 4.1833 
 WW treatment 3.6842 4.2281 
Figure 5

Current scores and optimization target scores for utility II.

Figure 5

Current scores and optimization target scores for utility II.

Close modal

In the study, when evaluating the current state matrix for utility 2, it can be seen that in the basic level, 2 components receive a score of 0 or 1; in the intermediate level, 6 components receive a score of 0 or 1; and in the advanced level, 11 components receive a score of 0 or 1. In the result matrix, it is observed that the components with higher weight coefficients and the components that already have a score of 0 or 1 increase according to the conditions. For the components that are insufficient in basic-level applications, optimization is performed to recommend a higher level. In the advanced level, there are currently 11 components receiving a score of 0 or 1, and the improvement levels for the components are seen in the result matrix. Thus, the levels that each component should have in the new state are determined based on the current state of the Utility.

Among the basic-level components, component A1-5 is specified to have a minimum initial score of 4 in a water utility, so it appears as 4 in the result matrix. Another component at the same level, A11-7 ‘Monitoring Water Consumption and Resource Efficiency,’ initially received a score of 0. In the result matrix, this component, which should have a minimum score of 4, has been improved to 4. In the current state matrix, the intermediate-level components A10-9, A11-9, A9-11, A6-13, A8-14 and A10-14 received scores of 0 or 1. These components have been improved according to the conditions predetermined by the model.

In the advanced level, the current state matrix shows that components A5-15, A9-15, A7-16, A7-17, A11-17, A5-18, A7-18, A11-18, A10-20, A4-21 and A7-21 received scores of 0 or 1.

In the result matrix obtained after optimization, the levels of the components in basic-level applications are generally recommended as good or very good. Since the basic-level components are essential and include the most fundamental components in a water utility, improving the levels of these components should be prioritized. For the components to be implemented in intermediate- and advanced-level applications, the current levels of basic-level components need to meet the required conditions and be at a good level. Therefore, the newly proposed scores by the model are considered to be compatible with the natural structure of the problem. After improving the current scores of the components at the basic level, it is possible to improve the components at the intermediate and advanced levels.

When examining Figure 6, it can be observed that the defined error function moves in a decreasing direction during the optimization process. This result indicates that the performance of the utilized optimization algorithm is good.
Figure 6

Objective function (error function) converge curve for utility II.

Figure 6

Objective function (error function) converge curve for utility II.

Close modal
Figure 7

Current scores and optimization target scores for utility III.

Figure 7

Current scores and optimization target scores for utility III.

Close modal

Evaluation of optimization results for utility III

The components in the CSAS matrix were scored between 0 and 5 points based on the onsite examinations and evaluations in utility III. While the current scores of the utilities were questioned, the most suitable one for the gradual scoring structure was selected. The average of the initial scores in utility III is 1.8312 for components including water management practices, 2.3333 for components including WW network (sewage) management practices and 3.3860 for components including WW treatment practices (Table 7). Since the initial score is below 3 in all three main fields of activity, it can be said that the current scores of this utility are quite low. The most appropriate targets were identified for each component by the optimization model (Figure 7) based on the current scores obtained for utility III.

Table 7

The current scores and optimization results for utility III

Utility IIIMain componentCurrent average scoreTarget_OTarget average scores
 Water supply 1.8312 16 3.5195 
 WW collection 2.2333 3.5667 
 WW treatment 3.3860 4.0526 
Utility IIIMain componentCurrent average scoreTarget_OTarget average scores
 Water supply 1.8312 16 3.5195 
 WW collection 2.2333 3.5667 
 WW treatment 3.3860 4.0526 

When examining the results of the current situation analysis for this utility, it is observed that 11 basic-level components, 21 intermediate-level components, and 37 advanced-level components receive a score of 0 or 1 in the current condition matrix. It is evident that the performance of advanced-level applications is quite poor in the result matrix, and improvement levels are recommended for most of these components. The new scores proposed by the model for basic-level components are generally good or very good. Therefore, it is recommended to improve the data quality in the utility and enhance the current implementation levels of the components related to all activities of a water utility as indicated in the current situation analysis.

In the analysis of the current situation for utility 3, the following components have received a score of 0 or 1 in basic-level applications: A3-2, A6-2, A6-3, A1-4, A3-4, A6-4, A7-4, A4-5, A4-6, A6-7 and A11-7. Upon examining these components, it is understood that the most fundamental components directly related to managing water losses, such as resource management and monitoring/utility of administrative losses, should be brought to a good level in basic-level applications.

In intermediate-level applications, the following components have received a score of 0 or 1: A4-8, A5-8, A11-8, A3-9, A4-9, A11-9, A3-10, A4-10, A5-10, A9-10, A11-10, A2-11, A7-11, A9-11, A11-11, A6-12, A11-12, A4-13, A6-13, A10-13, A11-13 and A10-14. All of these components have been improved according to the minimum value they should have based on the initial matrix and the optimization results.

In the analysis of the current situation, 37 advanced-level components have also been improved according to the conditions determined prior to the modeling. In conclusion, the model developed within the scope of this study:

  • takes into account the scoring results of water utilities for each component included in the current situation analysis and proposes new levels in accordance with the natural structure and field experience of the utilities,

  • recommends prioritizing the improvement of basic-level components in utilities,

  • suggests gradual scores for intermediate- and advanced-level components based on the current scores and structure of water utilities.

When examining Figure 8, it can be observed that the defined error function moves in a decreasing direction during the optimization process. This result indicates that the performance of the utilized optimization algorithm is good.
Figure 8

Objective function converge (error function) curve for utility III.

Figure 8

Objective function converge (error function) curve for utility III.

Close modal

As it is known, there are a lot of components to be considered in water and WW management. In the literature, efficiency, cost analysis and performance improvement studies are carried out by considering one or more of these components at the same time. These studies are generally implemented in pilot regions with limited data. However, the most basic step is the accurate and systematic measurement and monitoring of data within the scope of water and WW management. The accuracy of the analyses depends on the quality of the data. In addition, water and WW management includes processes consisting of certain stages. All processes and components are considered in this study for sustainable management. Thus, the current situation of the urban water cycle components was analyzed in a holistic manner and the most appropriate targets were defined according to the current situation. In this respect, unlike the studies in the literature, the dynamic structure of the utility is considered and component-based or system-wide targets are defined. The components, method, algorithm and methodology constitute the strengths of the study and reveal the difference from the literature. It is thought that this study will contribute to water and WW management practitioners using utilities.

In this study, an original model structure was developed using the EO algorithm to define the most suitable management process based on the current state of water and WW components in utilities. The optimization model was tested in three pilot utilities. First, the current status of the water and WW management practices were scored using a unique scoring system. The current average scores of the components in the utilities were obtained as 2.84 (utility I), 3.43 (utility II) and 2.48 (utility III). The current average scores of the water supply components are 2.73 (utility I), 3.33 (utility II) and 1.83 (utility III). The current average scores of the WW collection components are 2.93 (utility I), 3.26 (utility II) and 2.23 (utility III). The current average scores of the WW treatment components are 2.85 (utility I), 3.68 (utility II) and 3.8 (utility III).

The management and improvement process of these components is optimized by the EO algorithm. The most appropriate target scores were defined as 3.90 (utility I), 4.15 (utility II) and 3.71 (utility III) using the optimization algorithm by considering the current situation and scores of the utilities. The most appropriate target scores for water supply components were defined as 3.81 (utility I), 4.03 (utility II) and 3.51 (utility III). The most appropriate target scores for WW collection components were defined as 4.05 (utility I), 4.18 (utility II) and 3.56 (utility III). The most appropriate target scores for WW treatment components were defined as 3.84 (utility I), 4.22 (utility II) and 4.05 (utility III).

In conclusion, it is believed that the model developed in this study, which comprehensively performs the current situation analysis in utilities, has a gradual scoring structure. Moreover, this model defines realistic targets based on the current situation and determines the most appropriate method according to the dynamic structure of the utilities and will provide significant advantages to managers and technical personnel during the execution of all activities in a water and sewage administration. In this study, 231 components were determined based on field experience and literature within the scope of water and WW management. The developed model has this flexibility. The main problem encountered in this model is the scoring of its components in utilities. That is, it is important to score the components accurately to describe the current state. The reports and data regarding the activities in the utility should be recorded, and the scoring should be done by experts outside the institution. In this study, field experience was taken as the basis in determining the effect levels of the components. In other words, the impact of the components on WW management was defined. However, in future studies, the weight coefficients of the components can be determined by different methods such as multi-criteria decision-making methods.

The authors acknowledge the Inonu University, Scientific Research Project Funding for their financial support (FBA-2021-2457).

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.

Aboelnga
H. T.
,
Ribbe
L.
,
Frechen
F. B.
&
Saghir
J.
2019
Urban water security: Definition and assessment framework
.
Resources
8
(
4
),
178
.
Al-Obaidi
A. R.
2019a
Experimental and Numerical Investigations on the Cavitation Phenomenon in A Centrifugal Pump
.
PhD Thesis
,
University of Huddersfield
.
Al-Obaidi
A. R.
2023b
Experimental diagnostic of cavitation flow in the centrifugal pump under various impeller speeds based on acoustic analysis method
.
Archives of Acoustics
48
(
2
),
159
170
.
Al-Obaidi
A. R.
&
Alhamid
J.
2023
Investigation of the main flow characteristics mechanism and flow dynamics within an axial flow pump based on different transient load conditions
.
Iranian Journal of Science & Technology Transactions of Mechanical Engineering
47
,
1397
1415
.
Al-Obaidi
A.
&
Qubian
A.
2022
Effect of outlet impeller diameter on performance prediction of centrifugal pump under single-phase and cavitation flow conditions
.
International Journal of Nonlinear Sciences and Numerical Simulation
23
(
7–8
),
1203
1229
.
Awe
O. M.
,
Okolie
S. T. A.
&
Fayomi
O. S. I.
2019
Optimization of water distribution systems: A review
.
Journal of Physics: Conference Series
1378
(
2019
),
022068
.
doi:10.1088/1742-6596/1378/2/022068
.
Berhane
T. G.
&
Aregaw
T. T.
2020
Optimization of water distribution system using WaterGEMS: The case of Wukro Town, Ethiopia
.
Civil and Environmental Research
12
(
6
), 1–14.
Blokus-Dziula
A.
,
Dziula
P.
,
Kamedulski
B.
&
Michalak
P.
2023
Operation and maintenance cost of water management systems: Analysis and optimization
.
Water
15
,
3053
.
https://doi.org/10.3390/w15173053
.
Boztaş
F.
,
Özdemir
Ö.
,
Durmuşçelebi
F. M.
&
Firat
M.
2019
Analyzing the effect of the unreported leakages in service connections of water distribution networks on non-revenue water
.
International Journal of Environmental Science and Technology
16
,
4393
4406
.
Brentan
B. M.
,
Carpitella
S.
,
Izquierdo
J.
&
Meirelles
G.
2020
District metered area design through multicriteria and multiobjective optimization
.
Mathematical Methods in the Applied Sciences
2021
,
1
18
.
doi:10.1002/mma.7090
.
Cabral
M.
,
Loureiro
D.
,
Almeida
M.
&
Covas
D.
2019
Estimation of costs for monitoring urban water and wastewater networks
.
Journal of Water Supply: Research and Technology – AQUA
68
(
2
),
87
97
.
Chawira
M.
,
Hoko
Z.
&
Mhizha
A.
2022
Partitioning non-revenue water for Juru Rural Service Centre, Goromonzi District, Zimbabwe
.
Physics and Chemistry of the Earth, Parts A/B/C
103111
.
doi:10.1016/j.pce.2022.103113
.
Cordeiro
C.
,
Borges
A.
&
Ramos
R.
2022
A strategy to assess water meter performance
.
Journal of Water Resources Planning and Management
148
(
2
),
05021027
.
Di Cicco
M. R.
,
Spagnuolo
A.
,
Masiello
A.
,
Vetromile
C.
,
Nappa
M.
,
Corbo
G.
&
Lubritto
C.
2019
Assessing energy performance and critical issues of a large wastewater treatment plant through full-scale data benchmarking
.
Water Science and Technology
80
(
8
),
1421
1429
.
Doghri
M.
,
Duchesne
S.
,
Poulin
A.
&
Villeneuve
J. P.
2020
Comparative study of pressure control modes impact on water distribution system performance
.
Water Resources Management
34
(
1
),
231
244
.
doi:10.1007/s11269-019-02436-z
.
Eulogi
M.
,
Ostojin
S.
,
Skipworth
P.
,
Shucksmith
J. D.
&
Schellart
A.
2021
Hydraulic optimisation of multiple flow control locations for the design of local real time control systems
.
Urban Water Journal
18
(
2
),
91
100
.
Faramarzi
A.
,
Heidarinejad
M.
,
Stephens
B.
&
Mirjalili
S.
2020
Equilibrium optimizer: A novel optimization algorithm
.
Knowledge-Based Systems
191
,
105190
.
Fırat
M.
,
Yılmaz
S.
,
Ateş
A.
&
Özdemir
Ö
.
2021
Determination of economic leakage level with optimization algorithm in water distribution systems
.
Water Economics and Policy
7
(
3
),
1
38
.
Fuentes
R.
,
Molinos-Senante
M.
,
Hernandez-Sancho
F.
&
Sala-Garrido
R.
2020
Analysing the efficiency of wastewater treatment plants: The problem of the definition of desirable outputs and its solution
.
Journal of Cleaner Production
267
,
121989
.
Guo
Z.
2002
Review of indoor emission source models
.
Part 1. Overview. Environmental Pollution
120
(
3
),
533
549
.
Haider
H.
,
Sadiq
R.
&
Tesfamariam
S.
2015
Multilevel performance management framework for small to medium sized water utilities in Canada
.
Canadian Journal of Civil Engineering
42
,
889
900
.
Hernández
N.
,
Caradot
N.
,
Sonnenberg
H.
,
Rouault
P.
&
Torres
A.
2018
Support tools to predict the critical structural condition of uninspected pipes for case studies of Germany and Colombia
.
Water Practice and Technology
13
(
4
),
794
802
.
Jang
J.-H.
,
Chang
T.-H.
&
Chen
W.-B.
2018
Effect of inlet modelling on surface drainage in coupled urban flood simulation
.
Journal of Hydrology
562
,
168
180
.
Kılıç
S.
2023
Developing the Most Appropriate Strategy Model and Performance Assessment System for Sustainable Water and Wastewater Management
.
PhD Thesis
,
Inonu University
.
Moslehi
I.
,
Jalili-Ghazizadeh
M.
&
Yousefi-Khoshqalb
E.
2021
Developing a framework for leakage target setting in water distribution networks from an economic perspective
.
Structure and Infrastructure Engineering
17
(
6
),
821
837
.
Mutikanga
H. E.
,
Sharma
S. K.
&
Vairavamoorthy
K.
2011
Multi-criteria decision analysis: a strategic planning tool for water loss management
.
Water Resources Management
25
,
3947
3969
.
http://doi.org/10.1007/s11269-011-9896-9
Sangroula
U.
,
Han
K.-H.
,
Koo
K.-M.
,
Gnawali
K.
&
Yum
K.-T.
2022
Optimization of water distribution networks using genetic algorithm based SOP–WDN program
.
Water
14
,
851
.
https://doi.org/10.3390/w14060851
.
Schneider
M. Y.
,
Furrer
V.
,
Sprenger
E.
,
Carbajal
J. P.
,
Villez
K.
&
Maurer
M.
2020
Benchmarking soft sensors for remote monitoring of on-site wastewater treatment plants
.
Environmental Science and Technology
54
(
17
),
10840
10849
.
Sheng
X.
,
Qiu
S.
,
Xu
F.
,
Shi
J.
,
Song
X.
,
Yu
Q.
,
Liu
R.
&
Chen
L.
2020
Management of rural domestic wastewater in a city of Yangtze Delta region: Performance and remaining challenges
.
Bioresource Technology Reports
11
,
100507
.
Sutharsan
M. E.
2023
Optimizing the water distribution network of community water supply using different computer simulation techniques
.
Journal of Science of the University of Kelaniya
16
(
1
),
01
14
.
http://doi.org/10.4038/josuk.v16i1.8070
.
Szeląg
B.
,
Kiczko
A.
,
Lagod
G.
&
De Paola
F.
2021
Relationship between rainfall duration and sewer system performance measures within the context of uncertainty
.
Water Resources Management
35
,
5073
5087
.
Torkaman
N.
,
Ahmadi
H.
&
Aminnejad
B.
2021
Calibration of the continuous water model based on the NRW patterns
.
Journal of Applied Water Engineering and Research
9
(
3
),
194
202
.
Walsh
B. P.
,
Murray
S. N.
&
O'Sullivan
D. T. J.
2015
The water energy nexus, an ISO50001 water case study and the need for a water value system
.
Water Resources and Industry
10
,
15
28
.
Yilmaz
S.
,
Firat
M.
,
Ateş
A.
&
Özdemir
Ö
.
2022
Analyzing the economic water loss level with a discrete stochastic optimization algorithm by considering budget constraints
.
AQUA-Water Infrastructure, Ecosystems and Society
71
(
7
),
835
848
.
Zyoud
S. H.
,
Kaufmann
L. G.
,
Shaheen
H.
,
Samhan
S.
&
Fuchs-Hanusch
D.
2016
A framework for water loss management in developing countries under fuzzy environment: Integration of Fuzzy AHP with Fuzzy TOPSIS
.
Expert Systems with Applications
61
,
86
105
.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (CC BY-NC-ND 4.0), which permits copying and redistribution for non-commercial purposes with no derivatives, provided the original work is properly cited (http://creativecommons.org/licenses/by-nc-nd/4.0/).