Interactive decision procedure for watershed nutrient load reduction: An integrated chance-constrained programming model with risk-cost tradeoff

Nutrient load reduction is a well-recognized requirement for aquatic ecosystem restoration. However, decision making is difficult due to challenges related to uncertainty and the interaction between decision makers and modelers, including (a) the quantitative relationship between risks arising from different aspects and the fact that cost is not usually revealed and (b) the fact that decision makers are not significantly involved in the modeling process. In this study, an interactive optimal-decision procedure with risk-cost tradeoff is proposed to overcome these limitations. It consists of chance-constrained programming (CCP) models, risk scenario analysis using the Taguchi method, risk-cost tradeoff and feedback for model adaption. A hybrid intelligent algorithm (HIA) integrating Monte Carlo simulation, artificial neural networks, and an augmented Lagrangian genetic algorithm was developed and applied to solve the CCP model. The proposed decision procedure and HIA are illustrated through a case study of uncertainty-based optimal nutrient load reduction in the Lake Qionghai Watershed, China. The CCP model has four constraints associated with risk levels indicating the possibility of constraint violation. Sixteen risk scenarios were designed with the Taguchi method to recognize the interactions between multiple constraint risks and total cost. The results were analyzed using the signal-to-noise ratio, analysis of variance, and multivariate regression. The model results demonstrate how cost is affected by risk for the four constraints and show that the proposed approach can provide effective support for decision making on risk-cost tradeoffs.