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.

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.