Controlling wasteloads from point and nonpoint sources to river system by GIS-aided Epsilon Robust Optimization model

Abstract

A stochastic multiobjective programming model, an var epsilon-RO (Epsilon Robust Optimization) model as a simulation–optimization model with an embedding approach, is developed for river water quality management under hydro-environmental uncertainty. The model is a hybrid of the var epsilon-constraint method and the robust optimization framework, which depresses the high sensitivity of the model to the input data uncertainties by introducing a plausible set of scenarios. Possible pollutant sources (all kinds of point and nonpoint pollutant sources excepting forests) are treated as controllable. The finite element method is employed for approximations to COD (Chemical Oxygen Demand) and DO (Dissolved Oxygen) transport equations with convection and dispersion terms. Realizations for the in-stream COD–DO interactive events, thus described in discrete forms, are embedded as equality constraints in the model. Controlling wasteloads from a variety of sources is implemented by seeking noninferior solutions (management alternatives) that maximize total COD load to the stream while minimizing COD load deviations and in-stream water quality violations. Demonstrative operation of the model is made with its application to the Yasu River, Japan. It is shown that there is indeed an alternative management strategy to improve in-stream water quality as a whole while increasing the total allowable load to the stream. The var epsilon-RO model developed could thus be a viable alternative to the conventional river water quality management models.