A fuzzy multi-objective optimisation model was investigated for water quality management in a river under uncertain conditions. In this study, to deal with multiple pollutants simultaneously, the National Sanitation Foundation's water quality index was considered as one of the model's objective functions based on fuzzy set theory. This made it possible to investigate the overall effect of uncertainties on simultaneous changes. Another objective function was the total treatment costs for wastewater discharged into the river. A water quality simulation model and a non-dominated-archiving ant colony optimisation algorithm were used to determine the values of water quality parameters and the model's optimal solutions, respectively. Furthermore, a simulation–optimisation approach was adopted for facilitating the problem-solving process and applied to a hypothetical case study resembling a river system in Iran. The results show that the proposed model significantly reduced the total wastewater treatment costs compared with a similar single-objective model with a more cautious and a cost-effective approach. Although the treatment costs were increased compared with the similar deterministic model, more feasible approach was taken by considering the uncertainties associated with the objectives. With suitable modifications, the model could be easily adapted for other river systems.

中文翻译：

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基于蚁群算法的河流模糊多目标多污染物模型

研究了不确定条件下河流水质管理的模糊多目标优化模型。在本研究中，为了同时处理多种污染物，基于模糊集理论，将美国国家卫生基金会的水质指标作为模型的目标函数之一。这使得研究不确定性对同时变化的总体影响成为可能。另一个目标函数是排入河流的废水的总处理成本。分别采用水质模拟模型和非支配归档蚁群优化算法确定水质参数值和模型最优解。此外，采用模拟优化方法来促进问题解决过程，并将其应用于类似于伊朗河流系统的假设案例研究。结果表明，与类似的单目标模型相比，所提出的模型显着降低了废水处理的总成本，方法更加谨慎和具有成本效益。尽管与类似的确定性模型相比，处理成本增加了，但考虑到与目标相关的不确定性，采取了更可行的方法。通过适当的修改，该模型可以很容易地适应其他河流系统。结果表明，与类似的单目标模型相比，所提出的模型显着降低了废水处理的总成本，方法更加谨慎和具有成本效益。尽管与类似的确定性模型相比，处理成本增加了，但考虑到与目标相关的不确定性，采取了更可行的方法。通过适当的修改，该模型可以很容易地适应其他河流系统。结果表明，与类似的单目标模型相比，所提出的模型显着降低了废水处理的总成本，方法更加谨慎和具有成本效益。尽管与类似的确定性模型相比，处理成本增加了，但考虑到与目标相关的不确定性，采取了更可行的方法。通过适当的修改，该模型可以很容易地适应其他河流系统。