Fuzzy Optimization Model for Waste Load Allocation in a River with Total Maximum Daily Load (TMDL) Planning

In traditional waste load allocation (WLA) decision making, water quality-related constraints must be satisfied. Fuzzy models, however, can be useful for policy makers to make the most reasonable decisions in an ambiguous environment, considering various surrounding environments. We developed a fuzzy WLA model that optimizes the satisfaction level by using fuzzy membership functions and minimizes the water quality management cost for policy decision makers considering given environmental and socioeconomic conditions. The fuzzy optimization problem was formulated using a max–min operator. The fuzzy WLA model was applied to the Yeongsan River basin, which is located in the southwestern part of the Korean Peninsula and Korean TMDLs were applied. The results of the fuzzy model show that the pollutant load reduction should be increased in the Gwangju 1 and Gwangju 2 wastewater treatment plants (WWTPs) and in subcatchments with high pollutant load. In particular, it is necessary to perform advanced wastewater treatment to decrease the load of 932 kg ultimate biochemical oxygen demand (BODu)/day in the large-capacity Gwangju 1 WWTP and reduce the BODu emission concentration from 4.3 to 2.7 mg/L during the low-flow season. The satisfaction level of the fuzzy model is a relatively high at 0.81.

Waste load allocation under uncertainty using game theory approach and simulation-optimization process

This article aims to present a new methodology for waste load allocation (WLA) in a riverine system considering the uncertainty and achieve the lowest amount of inequity index, cost, and fuzzy risk of standard violation. To find a surface of undominated solutions, a new modified PAWN method, initially designed for sensitivity analysis, was developed and coupled with a simulation-optimization process using multi-objective particle swarm optimization (MOPSO) algorithm, to consider the uncertainty of all affecting variables and parameters by using their probability distribution. The proposed methodology applied to Sefidrood River in the northern part of Iran. Graph model for conflict resolution (GMCR) as a subset of game theory was implemented to attain a compromise on WLA among the stakeholders of a river system's quality in Iran: Department of Environment, Municipal Waste Water, and Private Sector. Some undominated solutions were used in GMCR model and modeling the conflict among decision makers reveals that their preferences and the status quo do not lead to a solely stable equilibrium; thus the intervention of a ruler as arbitrator leads them to reach a compromise on a scenario that has a median FRVS and cost. Sensitivity analysis was done using the PAWN method to assess the sensitivity of three intended objectives to all variables and parameters.

Multi-objective multi-pollutant waste load allocation model for rivers using coupled archived simulated annealing algorithm with QUAL2Kw

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.