River water quality management using an integrated multi-objective optimization-simulation approach based on bankruptcy rules

The aim of this research is to allocate the river's self-purification (acceptance capacity of pollution) fairly between the beneficiaries (pollutant sources) using bankruptcy theory. For this purpose, four bankruptcy rules (CAE, CEL, P, and TAL) were called using the link of the water quality simulation model (QULA2Kw) to an evolutionary optimization algorithm (multi-objective imperialist competition algorithm (MOICA)). The objective functions were reducing polluters' wastewater treatment costs and preventing biochemical oxygen demand (BOD) violations of the standard level along the river. The applicability of the approach is demonstrated by the case study that was carried out on the Dez River in Iran. According to the results, the CEL scenario is the most effective method for the Dez River when taking into account the most optimal state for both objective functions (selecting the best compromise solution from the Pareto front). This is because it has the lowest violation value of the standard level for BOD along the river when compared to other scenarios. Alternatively, when considering Solution 20, which focuses on the maximum cost of treating the polluters while staying within the acceptable level of pollution in the river, the results indicated that the CEA rule emerged as the most favorable option. This is due to its lower treatment cost (156.9 (1000$)) and higher pollution discharge to the river (681.91 g/s).