Fuzzy Waste Load Allocation Model: Simulation-Optimization Approach

Abstract

The problem of waste load allocation (WLA) for water quality management of a river system is addressed with a simulation-optimization approach. The WLA model developed in the study provides the best compromise solutions to the pollution control agency (PCA) responsible for maintaining the water quality and the dischargers disposing pollutants into the river system. A previously developed fuzzy waste load allocation model (FWLAM) is extended to incorporate QUAL2E, a water quality simulation model developed by the U.S. Environmental Protection Agency for modeling the pollutant transport in a river. The imprecision associated with establishing water quality standards and the aspirations of the PCA and dischargers are quantified using fuzzy goals with appropriate membership functions. The membership functions of the fuzzy goals represent the variation of the goal satisfaction in the system. A genetic algorithim (GA) is used as an optimization tool to find optimal fraction removal levels to the dischargers and the corresponding satisfaction level. Because a GA is an unconstrained optimization tool, it is extended to handle constraints by complementing it with homomorphous mapping (HM), a constraint handling method for evolutionary algorithms. The GA directs the decision vector in an encoded form to HM. HM, after a few interactions with QUAL2E, redirects the decoded solution back to the GA. The GA assigns a fitness value to the feasible solution vector and applies operators to refine the solution. This interaction among the GA, HM, and QUAL2E continues until a prespecified criterion for global optimality is met. Application of the model is illustrated with a case study of the Tunga-Bhadra River in South India.