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As waste discharge into numerous river systems escalates, the pollution of water bodies typically rises. Given the limited capacity of rivers to withstand pollution and their constrained self-cleaning capabilities, treated pollutants from waste discharge must be released into the river. Despite numerous models and algorithms proposed for managing river water quality to meet standards, literature, to our awareness, lacks the utilization of a comprehensive multi-criteria group decision-making approach for water quality management, particularly in river systems. Therefore, this research introduces a new, comprehensive multi-criteria group decision-making for the management of water quality in the Haraz River basin, located in Iran. To do so, the water quality of the basin, a one-dimensional water quality model, QUAL2Kw, was employed to simulate and calibrate the water quality along the river. The simulation results revealed that the downstream water quality violates the water quality standards. To mitigate this issue, various scenarios for waste load allocation (WLA) were evaluated, including no wastewater treatment, primary wastewater treatment, advanced secondary wastewater treatment utilizing the activated sludge (AS) method, and advanced wastewater treatment via the membrane bioreactor (MBR) method. Utilizing the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) and Fuzzy TOPSIS group decision-making model, it was determined that the optimal solution was the implementation of secondary wastewater treatment utilizing the activated sludge method for the 11 PS of pollution, while still adhering to Iranian water quality standard. In addition, the findings of the present study indicate that the implementation of primary wastewater treatment, advanced secondary wastewater treatment utilizing AS, and advanced wastewater treatment through MBR within the study area led to a significant enhancement in water quality. This enhancement ranged from 35 to 105% across various scenarios when compared to conditions where no actions were taken to the treatment of water.

In this study, a novel multiple-pollutant waste load allocation (WLA) model for a river system is presented based on the National Sanitation Foundation Water Quality Index (NSFWQI). This study aims to determine the value of the quality index as the objective function integrated into the fuzzy set theory so that it could decrease the uncertainties associated with water quality goals as well as specify the river's water quality status rapidly. The simulation-optimization (S-O) approach is used for solving the proposed model. The QUAL2K model is used for simulating water quality in diferent parts of the river system and ant colony optimization (ACO) algorithm is applied as an optimizer of the model. The model performance was examined on a hypothetical river system with a length of 30 km and 17 checkpoints. The results show that for a given number of both the simulator model runs and the artificial ants, the maximum objective function will be obtained when the regulatory parameter of the ACO algorithm (i.e., q0) is considered equal to 0.6 and 0.7 (instead of 0.8 and 0.9). Also, the results do not depend on the exponent of the membership function (i.e., γ). Furthermore, the proposed methodology can find optimum solutions in a shorter time.

Water pollution escalates with rising waste discharge in river systems, as the rivers’ limited pollution tolerance and constrained self-cleaning capacity compel the release of treated pollutants. Although several studies have shown that the non-dominated sorting genetic algorithm-II (NSGA-II) is an effective algorithm regarding the management of river water quality to reach water quality standards, to our knowledge, the literature lacks using a new optimization model, namely, the multi-objective cuckoo optimization algorithm (MOCOA). Therefore, this research introduces a new optimization framework, including non-dominated sorting and ranking selection using the comparison operator densely populated towards the best Pareto front and a trade-off estimation between the goals of discharges and environmental protection authorities. The suggested algorithm is implemented for a waste load allocation issue in Jajrood River, located in the North of Iran. The limitation of this research is that discharges are point sources. To analyze the performance of the new optimization algorithm, the simulation model is linked with a hybrid optimization model using a cuckoo optimization algorithm and non-dominated sorting genetic algorithms to convert a single-objective algorithm to a multi-objective algorithm. The findings indicate that, in terms of violation index and inequity values, MOCOA’s Pareto front is superior to NSGA-II, which highlights the MOCOA’s effectiveness in waste load allocation. For instance, with identical population sizes and violation indexes for both algorithms, the optimal Pareto front ranges from 1.31 to 2.36 for NSGA-II and 0.379 to 2.28 for MOCOA. This suggests that MOCOA achieves a superior Pareto front in a more efficient timeframe. Additionally, MOCOA can attain optimal equity in the smaller population size.

In this paper, we developed a simulator-optimizer model based on risk analysis to determine Waste Load Allocation (WLA). A new Fuzzy index as Fuzzy Risk Index (FRI) was linked with multi-objective optimization to minimize FRI for the environmental stakeholder and the total cost of sewage treatment for the polluting industries as the other collective stakeholder. Afterwards, the conflict was resolved with the help of Nash bargaining and bankruptcy approach (Constrained Equal Awards Rule). The model was run using quantitative/qualitative data for the KhoramAbad River. To check the efficiency of FRI, the process followed for WLA was reimplemented by the Monte Carlo simulation (MCS). A comparison between the two approaches revealed that the outcomes derived from Fuzzy arithmetic across all aspects, encompassing river qualitative simulation, nondominated curve, Nash bargaining’s agreed point, and bankruptcy output, closely mirrored the results of MCS. The notable distinction lies in the drastic reduction of the model’s execution time by a factor of 450.

A simulation-optimization approach is a suitable tool in waste load allocation problems when considering competing objectives and complex pollutant fate and transport processes in water bodies. Here, an archived multi-objective simulated annealing (AMOSA) algorithm is developed to determine various decision variables related to multi-pollutant waste load allocation (MPWLA) problems. The developed AMOSA algorithm has been coupled to QUAL2Kw in order to derive optimal MPWLA programs in Gheshlagh River, Kordestan, Iran. Minimizing wastewater treatment plant (WWTP) costs, improving the EquityMeasure, and enhancing water quality index (WQI) of the river have been considered as objective functions of MPWLA problems. The applied WQI integrates various water quality parameters (biochemical oxygen demand (BOD), dissolved oxygen (DO), NH4-N, NO3-N, PO4-P, total suspended solids (TSS), and Coliform) in monitoring stations along the river. Results show in the scenario with the best EquityMeasure, higher pollutant removal rates have been allocated to Sanandaj WWTP effluent and pollutant point source No. 7 (creek of landfill leachate) due to their greater contributions to Gheshlagh River contamination. Owing to high pollutant load effluents and unsuitable background conditions in Gheshlagh River, more specific studies show that the water quality index may not be improved over 0.22, no matter how much cost is incurred or equity is sacrificed.

In this paper, a new evolutionary game theoretic methodology is proposed to determine penalty functions that an environmental protection agency should impose on dischargers to achieve water quality standards at monitoring points along the river when the monitoring points are limited. In the proposed methodology, the concept of evolutionary stable strategy in asymmetric matrix games is utilized to model the interactions among dischargers more realistically. A heuristic optimization–simulation model is developed for calculating the evolutionary stable treatment strategies of dischargers considering the mass transport equations, main characteristics of river flow and pollution loads. The proposed methodology is applied to the Zarjub River in the northern part of Iran to illustrate its practical utility. The results show that the proposed approach can determine penalty functions which guarantee that the water quality standards are met. The results of the suggested model are compared with those of a traditional optimization waste load allocation model. The comparisons show that the evolutionary game theory-based model provides stable wastewater treatment strategies which would not be violated by dischargers in practice.

This study focuses on development of equilibrium strategy based on simulated annealing (SA) algorithm for balancing economic and environmental concerns in waste load allocation (WLA) problem. To resolve conflicts among various stakeholders, including Iran Department of Environment (DoE) as governmental authority and industrial and municipal dischargers, Stackelberg and Nash bargaining games have been applied in this WLA problem and the results have been compared. SA algorithm has been coupled to QUAL2Kw model to derive optimal WLA program and the environmental penalty tariff (EPT) in Nash bargaining and Stackelberg games. The proposed tools and methodologies were illustrated in a case study of multi-stakeholders WLA problem in Gheshlagh River, Sanandaj, Kordestan, Iran. The results indicate that lower BOD removal rates are allocated to the pollutant dischargers in the Stackelberg game compared to the Nash bargaining game. Furthermore, the EPT assigned by Iran DoE in Stackelberg and Nash bargaining games are 11.25 and 3.6 Rials/(gr/month), respectively. The estimated EPT in the Stackelberg game is close to the current tariff (10 Rials/(gr/month)) specified by Iran DoE on impermissible BOD discharges.

Groundwater quality management is challenging due to the fate and transport of multiple pollutants in the porous media, extensive polluters, and late aquifer responses to pollution reduction practices. Water quality trading (WQT) is an economically incentive-based policy for waste load allocation (WLA) in water resources. This study evaluates the effectiveness of 12 WLA scenarios on reducing groundwater nitrate and chloride, simultaneously using MODFLOW and MT3DMs. Here, the theoretical efficiencies of multi-pollutant WQT are also testified out of these scenarios by developing environmental, economic and practical conditions. For these purposes, Varamin plain, south-eastern Tehran, Iran, was chosen as the study area where both point and non-point pollution sources were considered in WQT. At first, an allowable quality limit (AQL) for the groundwater was set for pollutants regarding groundwater impairment and simulation outcomes. The AQL violations of WLAs were then calculated in addition to their marginal abatement costs and penalties. Here, nitrate abatement ranges between 3.3–18.3%, while chloride abatement ranges between 4.5–23.6%. Our findings show that, 5 WLA scenarios could pass the conditions of not violating any AQLs, and gaining remarkable benefits (> 25%) for all market attendants. Potential WQT strategies are finally prioritised regarding their viability and marginal costs. According to these conditions, trading discharge permits between wastewater treatment plants (WWTPs) with 50% nitrate removal (sellers) and farmers (buyers) are recommended as the optimal WQT alternative, which imposes no penalties or land-use changes. Here, the overall benefits of sellers and buyers exceed 47% and 81%, respectively, in comparison with not attending any WLA scenario. Highlights Varamin aquifer quality is analyzed in 12 WLA scenarios with point and non-point sources. Wastewater treatment and altering crop pattern can reduce pollutants in 10 years. Multi-pollutant WQT is theoretically feasible and has economic benefits. Four conditions are emphasized in order for the feasibility study of potential WQT. A practical WLA with low benefits has privilege over a highly beneficial WLA without practicability Graphical Abstract

In this paper, a new methodology is developed for optimal multiple-pollutant waste load allocation (MPWLA) in rivers considering the main existing uncertainties. An interval optimization method is used to solve the MPWLA problem. Different possible scenarios for treatment of pollution loads are defined and corresponding treatment costs are taken into account in an interval parameter optimization model. A QUAL2Kw-based water quality simulation model is developed and calibrated to estimate the concentration of the water quality variables along the river. Two non-cooperative and cooperative multiple-pollutant scenario-based models are proposed for determining waste load allocation policies in rivers. Finally, a new fuzzy interval solution concept for cooperative games, namely, Fuzzy Boundary Interval Variable Least Core (FIVLC), is developed for reallocating the total fuzzy benefit obtained from discharge permit trading among waste load dischargers. The results of applying the proposed methodology to the Zarjub River in Iran illustrate its effectiveness and applicability in multiple-pollutant waste load allocation in rivers.

This paper presents a bi-level optimization waste load allocation programming model under a fuzzy random environment to assist integrated river pollution control. Taking account of the leader-follower decision-making in the water function zones framework, the proposed approach examines the decision making feedback relationships and conflict coordination between the river basin authority and the regional Environmental Protection Agency (EPA) based on the Stackelberg-Nash equilibrium strategy. In the pollution control system, the river basin authority, as the leader, allocates equitable emissions rights to different subareas, and the then subarea EPA, as the followers, reallocates the limited resources to various functional zones to minimize pollution costs. This research also considers the uncertainty in the water pollution management, and the uncertain input information is expressed as fuzzy random variables. The proposed methodological approach is then applied to Tuojiang River in China and the bi-level linear programming model solutions are achieved using the Karush-Kuhn-Tucker condition. Based on the waste load allocation scheme results and various scenario analyses and discussion, some operational policies are proposed to assist decision makers (DMs) cope with waste load allocation problem for integrated river pollution control for the overall benefits.