Optimal design and operation of a wastewater purification system

The two-objective problem is formulated as a single-objective problem through the use of the weighted sum method. The existence of the optimal solution is then demonstrated for an arbitrary set of weights and a first order optimality condition is obtained to characterize that solution. The numerical solution for a realistic case study posed in the ría of Vigo is also accomplished by using the combination of the control vector parametrization approach with a global non-linear programming (NLP) solver. Remark that, as the problem under consideration is two-objective, there is not an unique solution but a set of equivalent solutions, the Pareto solutions, requiring the involvement of a decision maker to select one solution from the set.