## Abstract

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.

## HIGHLIGHTS

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.

## INTRODUCTION

*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.

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.

## ASSESSMENT SYSTEM FOR WATER AND WW COMPONENTS

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).

## DEVELOPMENT OF 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

*L*) 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:

_{m}*L*is the linear matrix and

_{m}*w*is the impact coefficient. The matrix called

*L*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 (

_{m}*R*) can take are defined according to each level (Kılıç 2023):

*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.

Levels . | Initial score . | Result 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 |

Levels . | Initial score . | Result 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 (ZK

_{1}) 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 (ZK

_{1}and ZK_{2}) 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 (ZK

_{1}, ZK_{2}and ZK_{3}) 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 (ZK

_{1}= 1, ZK_{2}= 3 and ZK_{3}= 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:

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. ND* _{m}*(

*i*) represents the new value suggested by the optimization algorithm.

Utility . | Daily treatment capacity of the WWTP (m^{3}/day)
. | Water supply (×10^{6}m^{3})
. | 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 |

Utility . | Daily treatment capacity of the WWTP (m^{3}/day)
. | Water supply (×10^{6}m^{3})
. | 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 |

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 ZK_{1} = 0, ZK_{2} = 0 and ZK_{3} = 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 ZK_{1} = 0, ZK_{2} = 0 and ZK_{3} = 0. The following sections explain how this process is carried out with the EO algorithm.

## OPTIMIZATION OF THE PROPOSED MDA MODEL WITH THE EO ALGORITHM

*et al.*2020):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

*C*

_{eq}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):

Here, the parameters *t*_{0} 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

*et al.*2020): 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

*et al.*2020):

### Step 3: exponential term (*F*)

*et al.*2020):

*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):

_{2}’ 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):

_{1}’ in the equation is a fixed number that controls the search capability. A higher value of ‘a

_{1}’ increases the search capability but decreases the usage and operation capabilities. Similarly, a higher value of ‘a

_{2}’ 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 a

_{1}= 2 and a

_{2}= 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):

### Step 4: generation rate (*G*)

*et al.*2020):

*et al.*2020):

*r*

_{1}and

*r*

_{2}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):

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.

a_{1} 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 a_{1} 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):

a_{2}: is the parameter that is similar to the parameter a_{1}. However, a_{2} 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 D _{m}*

*values, 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*.

## STUDY AREA AND DATA

Utility I, located in eastern Turkey, serves a total of 812,000 people in an area of 12,312 km^{2}. 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 m^{3}/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 km^{2}. 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 m^{3} /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 km^{2}. The utility provides 119 million m^{3} 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 m^{3}. The total length of the WW networks is 4,560 km. The daily treatment capacity of the advanced biology WWTP is 127,500 m^{3}/day.

## RESULTS AND DISCUSSION

### Evaluation of optimization results for utility I

Utility I . | Main component . | Current average score . | Target_O . | Target average scores . |
---|---|---|---|---|

Water supply | 2.7338 | 18 | 3.8117 | |

WW collection | 2.9333 | 4.0500 | ||

WW treatment | 2.8596 | 3.8421 |

Utility I . | Main component . | Current average score . | Target_O . | Target average scores . |
---|---|---|---|---|

Water supply | 2.7338 | 18 | 3.8117 | |

WW collection | 2.9333 | 4.0500 | ||

WW treatment | 2.8596 | 3.8421 |

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.

### Evaluation of optimization results for utility II

Utility II . | Main component . | Current average score . | Target_O . | Target average scores . |
---|---|---|---|---|

Water supply | 3.3312 | 13 | 4.0390 | |

WW collection | 3.2667 | 4.1833 | ||

WW treatment | 3.6842 | 4.2281 |

Utility II . | Main component . | Current average score . | Target_O . | Target average scores . |
---|---|---|---|---|

Water supply | 3.3312 | 13 | 4.0390 | |

WW collection | 3.2667 | 4.1833 | ||

WW treatment | 3.6842 | 4.2281 |

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.

### 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.

Utility III . | Main component . | Current average score . | Target_O . | Target average scores . |
---|---|---|---|---|

Water supply | 1.8312 | 16 | 3.5195 | |

WW collection | 2.2333 | 3.5667 | ||

WW treatment | 3.3860 | 4.0526 |

Utility III . | Main component . | Current average score . | Target_O . | Target 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.

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.

## CONCLUSION

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.

## ACKNOWLEDGEMENTS

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

## DATA AVAILABILITY STATEMENT

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

## CONFLICT OF INTEREST

The authors declare there is no conflict.

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