Optimal control in wastewater management: a multi-objective study

This work deals with the management of a sewage treatment system consisting of several purifying plants discharging treated sewage into the same region, for instance, an estuary or a lake. The management of this system involves economical aspects (given by the treatment cost in the plants) and also environmental aspects (related to water quality in the sensitive areas of the region). By assuming a unique manager for all plants, the problem is formulated as a multi-objective parabolic optimal control problem, and it is studied from a cooperative viewpoint. Pareto-optimal solutious are completely characterized, a numerical algorithm to obtain the Pareto-optimal set is proposed and, numerical experiences in the estuary of Vigo (NW Spain) arc presented.