SIFNP: Simulation-Based Interval-Fuzzy Nonlinear Programming for Seasonal Planning of Stream Water Quality Management

A simulation-based interval-fuzzy nonlinear programming (SIFNP) approach was developed for seasonal planning of stream water quality management. The techniques of inexact modeling, nonlinear programming, and interval-fuzzy optimization were incorporated within a general framework. Based on a multi-segment stream water quality simulation model, dynamic waste assimilative capacity of a river system within a multi-season context was considered in the optimization process. The method could not only address complexities of various system uncertainties but also tackle nonlinear environmental–economic interrelationships in water quality management problems. In addition, interval-fuzzy numbers were introduced to reflect the dual uncertainties, i.e., imprecision associated with fixing the lower and upper bounds of membership functions. The proposed method was applied to a case of water quality management in the Guoyang section of the Guo River in China. Interval solutions reflecting the inherent uncertainties were generated, and a spectrum of cost-effective schemes for seasonal water quality management could thus be obtained by adjusting different combinations of the decision variables within their solution intervals. The results indicated that SIFNP could effectively communicate dual uncertainties into the optimization process and help decision makers to identify desired options under various complexities of system components.