SIAM Journal on Control and Optimization
A control problem arising in the process of waste water purification
Journal of Computational and Applied Mathematics - control of partial differential equations
Theoretical and Numerical Analysis of an Optimal Control Problem Related to Wastewater Treatment
SIAM Journal on Control and Optimization
Recent developments and trends in global optimization
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. IV: optimization and nonlinear equations
Multi-Objective Optimization Using Evolutionary Algorithms
Multi-Objective Optimization Using Evolutionary Algorithms
SIAM Journal on Optimization
Journal of Global Optimization
Deterministic Global Optimization in Nonlinear Optimal Control Problems
Journal of Global Optimization
Numerical Optimization for the Location of Wastewater Outfalls
Computational Optimization and Applications
Deterministic Global Optimization: Theory, Methods and (NONCONVEX OPTIMIZATION AND ITS APPLICATIONS Volume 37) (Nonconvex Optimization and Its Applications)
Evolutionary Algorithms for Solving Multi-Objective Problems (Genetic and Evolutionary Computation)
Evolutionary Algorithms for Solving Multi-Objective Problems (Genetic and Evolutionary Computation)
Brief Numerical treatment of multiobjective optimal control problems
Automatica (Journal of IFAC)
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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 ria 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.