Phương Pháp Tối Ưu Không Dựa Vào Đạo Hàm Bằng Phương Pháp Lagrangian Tăng Cường: Giảm Chi Phí Trong Mô Hình Hệ Thống Bùn Hoạt Tính Đơn Giản

Abramson, M.A., Audet, C., Dennis Jr. J.E.: Filter pattern search algorithms for mixed variable constrained optimization problems. SIAM J. Optimiz. 11, 573–594 (2004) Afonso, P.N.C.M.: Modelação matemática de reactores biológicos no tratamento terciário de efluentes. Ph.D. Thesis (in portuguese), Universidade do Porto (2001) Alex, J., Benedetti, L., Copp, J., Gernaey, K., Jeppsson, U., Nopens, I., Pons, M., Rosen, C., Steyer, J., Vanrolleghem, P.: Benchmark simulation model no. 1 (BSM1). Technical Report, IWA Taskgroup pn Benchmarking of Control Strategies for WWTPs (2008) Andreani, R., Birgin, E.G., Martinez, J.M., Schuverdt, M.L.: On augmented Lagrangian methods with general lower-level constraints. SIAM J. Optimiz. 18, 1286–1309 (2007) Audet, C., Dennis Jr. J.E.: A pattern search filter method for nonlinear programming without derivatives. SIAM J. Optimiz. 14, 980–1010 (2004) Bartholomew-Biggs, M.: Nonlinear Optimization with Engineering Applications. Springer (2008) Bertsekas, D.: Constrained optimization and Lagrange multiplier methods. Athena Scientific, Belmont (1996) Clara, N.: Neural networks complemented with genetic algorithms and fuzzy systems for predicting nitrogenous effluent variables in wastewater treatment plants. WSEAS Trans. Syst. 7, 695–705 (2008) Conn, A.R., Gould, N.I.M., Toint, Ph.L.: A globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple bounds. SIAM J. Numer. Anal. 28, 545–572 (1991) Elias, A., Ibarra, G., Ormazabal, J., Murgia, I., Zugazti, P.: ADM: A model for water treatment in an anaerobic biological reactor. In: Brebbia, C.A. (ed.) Development and Application of Computer Techniques to Environmental Studies VI, Wessex Institute of Technology, United Kingdom & P. Zannetti, Failure Analysis Associates Inc, California (1996) Ekama, G.A., Barnard, J.L., Günthert, F.W., Krebs, P., McCrquodale, J.A., Parker, D.S., Wahlberg, E.J.: Secondary settling tanks: Theory, modelling, design and operation, Technical Report No. 6, IAWQ - International Association on Water Quality (1997) Espírito Santo, I.A.C.P., Fernandes, E.M.G.P.: Simplified model for the activated sludge system: WWTP cost minimization via an augmented Lagrangian pattern search method. In: Simos, T.E., Psihoyios, G., Tsitouras, Ch. (eds.) Numerical Analysis and Applied Mathematics: ICNAAM 2010, AIP Conference Proceedings ISBN: 978-0-7354-0834-0, Vol. 1281 pp. 971-974 (2010) Espírito Santo, I.A.C.P., Fernandes, E.M.G.P., Araújo, M.M., Ferreira, E.C.: On the secondary settler models robustness by simulation. WSEAS Trans. Inf. Sci. Appl. 12, 2323–2330 (2006) Espírito Santo, I.A.C.P., Fernandes, E.M.G.P., Araújo, M.M., Ferreira, E.C.: An augmented Lagrangian pattern search method for optimal WWTP designs. In: Proceedings of the ICOSSSE ’07, pp. 313–318 (2007) Güçlü, D., Dursum, Ş.: Artificial neural networks modelling of a large-scale wastewater treatment plant operation. Bioproc. Biosyst. Eng. 33, 1051–1058 (2010) Hakanen, J., Miettinen, K., Sahlstedt, K.: Wastewater treatment: New insight provided by interactive multiobjective optimization. Decis. Support Syst. 51, 328–337 (2011) Henze, M., Grady, C.P.L., Gujer, W., Marais, G.V.R., Matsuo, T.: Activated Sludge Model No. 1. Scientific and Technical Report, Vol. 1. IWA Publishing, London (1987) Henze, M., Gujer, W., Mino, T., Van Loosdrecht, M.C.M.: Activated Sludge Models: ASM1, ASM2, ASM2d and ASM3. Scientific and Technical Report, Vol. 9. IWA Publishing, London (2000) Hooke, R., Jeeves, T.A.: Direct search solution of numerical and statistical problems. J. Assoc. Comput. 8, 212–229 (1961) Huyer, W., Neumaier, A.: Global optimization by multilevel coordinate search. J. Glob. Optim. 14, 331–355 (1999) Hydromantis, Inc., Canada, GPS-X V4.1 (2002). http://www.hydromantis.com Jones, D.R., Perttunen, C.D., Stuckman, B.E.: Lipschitzian optimization without the Lipschitz constant. J. Optimiz. Theory App. 79, 157–181 (1993) Kolda, T.G., Lewis, R.M., Torczon, V.: Optimization by direct search: new perspectives on some classical and modern methods. SIAM Rev. 45, 385–482 (2003) Kolda, T.G., Lewis, R.M., Torczon, V.: Stationarity results for generating set search for linearly constrained optimization. SIAM J. Optimiz. 17, 943–968 (2006) Lewis, R.M., Torczon, V.: Pattern search algorithms for bound constrained minimization. SIAM J. Optimiz. 9, 1082–1099 (1999) Lewis, R.M., Torczon, V.: A globally convergent augmented Lagrangian pattern search algorithm for optimization with general constraints and simple bounds. SIAM J. Optimiz. 12, 1075–1089 (2002) Luo, H., Sun, X., Wu, H.: Convergence properties of augmented Lagrangian methods for constrained global optimization. Optim. Method. Softw. 23, 763–778 (2008) Luo, J.: Biegler, L.T.: Dynamic optimization of aeration operations for a benchmark wastewater treatment plant. 18th IFAC Word Congr., 14189–14194 (2011) Neumaier, A.: MINQ - General Definite and Bound Constrained Indefinite Quadratic Programming. WWW-Document (1998). http://www.mat.univie.ac.at/neum/software/minq/ Otterpohl, R., Rolfs, T., Londong, J.: Optimizing operation of wastewater treatment plants by offline and online computer simulation. Water Sci. Technol 30, 165–174 (1994) Seco, A., Serralta, J., Ferrer, J.: Biological nutrient removal model no.1 (BNMR1). Water Sci. Technol 50, 69–78 (2004) Takȧcs, I., Patry, G.G., Nolasco, D.: A dynamic model of the clarification-thickening process. Water Res. 25, 1263–1271 (1991) Torczon, V.: On the convergence of pattern search algorithms. SIAM J. Optimiz. 7, 1–25 (1997) Tyteca, D., Smeers, Y., Nyns, E.J.: Mathematical modeling and economic optimization of wastewater treatment plants. Crit. Rev. Env. Contr. 8, 1–89 (1977) Zhang, X., Zhao, D., Wang, Z., Wu, B., Li, W., Cheng, S.P.: Environmental biological model based optimization of activated sludge process. Int. J. Environ. Sci. Te. 6, 69–76 (2009)