Multiplicity of solutions in model-based multiobjective optimization of wastewater treatment plants

Wastewater treatment process design involves the optimization of multiple conflicting objectives. The detection of different equivalent solutions in terms of objective values is crucial for designers in order to efficiently switch to the new optimal operation policies if changes in the process conditions or new constraints occur. In this work, the dynamic multi-objective optimization of a municipal wastewater treatment plant model is carried out. The aim is to simultaneously optimize an economic cost term and an effluent quality index. The selected process variables for the optimization are (1) an aeration factor in the aerated tank previous to the clarifier, and (2) an internal recycle flow rate. Their time profiles are approximated using the control vector parameterization technique. To solve the multi-objective problem and find the Pareto front, the NSGA-II algorithm has been used. The simulation of different realistic scenarios which impose operational constraints (e.g., maintenance operations) reveals that, indeed, multiple solutions exist at least in some areas of the Pareto front. It is observed that different control profiles can produce nearly identical results in terms of Pareto solutions. The a priori knowledge of these equivalent solutions for different scenarios provides the decision makers with alternative choices to be adapted to their organizations policies when events altering decision variables bounds or adding new constraints to the process model occur.