Multi-objective Pareto-optimal control: An application to wastewater management

Computational Optimization and Applications

Volumn 46, Issue 1, 2010, Pages 135-157

  Alvarez Vazquez L J ^a   Garcia Chan N ^b   Martinez A ^a   Vazquez Mendez M E ^b  

^a UNIVERSITY OF VIGO   (Spain)

^b UNIVERSITY OF SANTIAGO DE COMPOSTELA   (Spain)

Author keywords

Multi objective; Optimal control; Pareto; Wastewater

Indexed keywords

ECOLOGICAL PROBLEM; GALERKIN DISCRETIZATION; MULTI-OBJECTIVE; MULTI-OBJECTIVE OPTIMAL CONTROL; NUMERICAL ALGORITHMS; NUMERICAL RESULTS; NW SPAIN; OPTIMAL CONTROL PROBLEM; OPTIMAL MANAGEMENT; PARETO OPTIMAL SOLUTIONS; PARETO SOLUTION; PARETO-OPTIMAL; REAL WORLD SITUATIONS; WASTEWATER MANAGEMENT; WASTEWATER TREATMENT SYSTEM; WEIGHTING METHODS;

MULTIOBJECTIVE OPTIMIZATION; NUMERICAL ANALYSIS; PARETO PRINCIPLE; WASTEWATER; WASTEWATER RECLAMATION;

WASTEWATER TREATMENT;

EID: 77950516345     PISSN: 09266003     EISSN: 15732894     Source Type: Journal    
DOI: 10.1007/s10589-008-9190-9     Document Type: Article

References (27)

1. L.J. Alvarez-Vázquez A. Martínez C. Rodríguez M.E. Vázquez-Méndez 2001 Numerical convergence for a sewage disposal problem Appl. Math. Model. 25 1015 1024 01741539 10.1016/S0307-904X(01)00030-0 (Pubitemid 33030912)
2. L.J. Alvarez-Vázquez A. Martínez C. Rodríguez M.E. Vázquez-Méndez 2002 Numerical optimization for the location of wastewater outfalls Comput. Optim. Appl. 22 399 417 1013.90088 10.1023/A:1019767123324 1927428
3. L.J. Alvarez-Vázquez A. Martínez R. Muñoz-Sola C. Rodríguez M.E. Vázquez-Méndez 2005 The water conveyance problem: Optimal purification of polluted waters Math. Models Method. Appl. Sci. 15 1393 1416 1089.49037 10.1142/S0218202505000790 (Pubitemid 41202782)
4. G.M. Bahaa 2003 Quadratic Pareto optimal control of parabolic equation with state-control constraints and an infinite number of variables IMA J. Math. Control Inf. 20 167 178 1029.49023 10.1093/imamci/20.2.167 1987533
5. G.M. Bahaa 2007 Quadratic Pareto optimal control for boundary infinite order parabolic equation with state-control constraints Adv. Model. Optim. 9 37 51 1151.49306 2304383
6. A. Bermúdez C. Rodríguez M.A. Vilar 1991 Solving shallow water equations by a mixed implicit finite element method IMA J. Numer. Anal. 11 79 97 0713.76069 10.1093/imanum/11.1.79 1089549
7. E.G. Birgin J.M. Martínez M. Raydan 2000 Nonmonotone spectral projected gradient methods on convex sets SIAM J. Optim. 10 1196 1211 1047.90077 10.1137/S1052623497330963 1777088
8. Caballero, R., Rey, L., Ruiz, F., González, M.: An algorithmic package for the resolution and analysis of convex multiple objective problems. In: Gunter, F., Gal, T. (eds.) Multiple Criteria Decision Making. Lecture Notes in Econ. and Math. Systems, vol. 448, pp. 275-284. Springer, Berlin (1997) (Pubitemid 127034713)
9. Cea, J.: Optimisation Theorie et Algorithmes. Dunod, Paris (1971)
10. Y. Censor 1977 Pareto optimality in multiobjective problems Appl. Math. Optim. 4 41 59 10.1007/BF01442131 488732
11. Clarke, F.H.: Optimization and Nonsmooth Analysis. Wiley, New York (1983)
12. J. Dutta C. Tammer 2006 Lagrangian conditions for vector optimization in Banach spaces Math. Methods Oper. Res. 64 521 540 1131.90053 10.1007/s00186-006-0079-z 2264799
13. García-Chan, N., Muñoz-Sola, R., Vázquez- Méndez, M.E.: Nash equilibrium for a multiobjective control problem related to wastewater management. ESAIM-Control Optim. Calc. Var. (2008, in press)
14. S. Gass T. Saaty 1955 The computational algorithm for the parametric objective function Nav. Res. Logist. 2 39 45 10.1002/nav.3800020106 127431
15. Jahn, J.: Vector Optimization: Theory Applications and Extensions. Springer, Berlin (2004)
16. W. Kotarski 1989 Characterization of Pareto optimal points in problems with multi-equality constraints Optimization 20 93 106 0681.49026 10.1080/02331938908843418 977222
17. Ladyzenskaja, O.A., Solonnikov, V.A., Ural'ceva, N.N.: Linear and Quasilinear Equations of Parabolic Type. Translations of Mathematical Monographs, vol. 23. Am. Math. Soc., Providence (1968)
18. J.-L. Lions 1986 Contrôle de Pareto de systèmes distribués. Le cas stationnaire C. R. Acad. Sci. Paris Sér. I Math. 302 223 227 0588.49012
19. J.-L. Lions 1986 Contrôle de Pareto de systèmes distribués. Le cas d'évolution C. R. Acad. Sci. Paris Sér. I Math. 302 413 417 0599.49018
20. A. Martínez C. Rodríguez M.E. Vázquez-Méndez 2000 Theoretical and numerical analysis of an optimal control problem related to wastewater treatment SIAM J. Control Optim. 38 1534 1553 0961.49002 10.1137/S0363012998345640 1766429
21. Miettinen, K.M.: Nonlinear Multiobjective Optimization. Kluwer Academic, Boston (1999)
22. M. Minami 1983 Weak Pareto-optimal necessary conditions in a nondifferentiable multiobjective program on a Banach space J. Optim. Theory Appl. 41 451 461 0502.90076 10.1007/BF00935364 728312
23. J. Nash 1951 Non-cooperative games Ann. Math. 54 286 295 10.2307/1969529 43432
24. Pareto, V.: Course d'Economie Politique. Rouge, Lausanne (1896)
25. Pironneau, O.: Finite Element Methods for Fluids. Wiley, Chichester (1989)
26. von Stackelberg, H.: Marktform und Gleichgewicht. Springer, Berlin (1934)
27. L. Zadeh 1963 Optimality and non-scalar-valued performance criteria IEEE Trans. Autom. Control 8 59 60 10.1109/TAC.1963.1105511