Optimal design and operation of a wastewater purification system

Abstract

Due to the importance of coastal areas, is of the highest interest to implement purification systems that with minimum cost are able to assure water quality standards in agreement with the regional legislations. This work addresses the optimal design (outfall locations) and optimal operation (level of oxygen discharges) of a wastewater treatment system. This problem can be mathematically formulated as a two-objective mixed design and optimal control problem with constraints on the states and the design and control variables. 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.