Multi-objective Waste Load Allocation Model for Optimizing Waste Load Abatement and Inequality Among Waste Dischargers

Abstract

In allocating the waste load of a river basin, the first priority is to achieve a given water quality goal for that river by utilizing several water quality management methods. Minimizing the waste load abatement cost within the river basin through appropriate, efficient water quality management is an important aspect of this process. In the past, it was common to concentrate on economic factors when constructing a waste load allocation (WLA) model. However, environmental resources (e.g., sub-basin area, population, wastewater flow, etc.) vary in each region of a river, and the fairness in the distribution of the treatment efforts among waste dischargers must be considered. The WLA model in this study was constructed as a multi-objective optimization problem and was established to achieve the economic goal of minimizing waste load abatement and to consider the inequality among waste dischargers. Two types of inequality were introduced into the WLA model. The first type is the inequality in the waste load discharge regarding the environmental resources in each region was computed with the environmental resource-based Gini coefficient. The second type of inequality is the fairness in the distribution of the treatment efforts among waste dischargers. The suitability of this WLA model was verified with its application in a heavily polluted total maximum daily load subject river in South Korea. Furthermore, Pareto-optimal solutions drawn from the multi-objective genetic algorithm were analyzed to infer the least cost solution, the least inequality solution, and the compromise solutions and to verify critical pollution sources.