Abstract
In this paper, the general problem of chemical process optimization defined by a computer simulation is formulated. It is generally a nonlinear, non-convex, non-differentiable optimization problem over a disconnected set. A brief overview of popular optimization methods from the chemical engineering literature is presented. The recent mesh adaptive direct search (MADS) algorithm is detailed. It is a direct search algorithm, so it uses only function values and does not compute or approximate derivatives. This is useful when the functions are noisy, costly or undefined at some points, or when derivatives are unavailable or unusable. In this work, the MADS algorithm is used to optimize a spent potliners (toxic wastes from aluminum production) treatment process. In comparison with the best previously known objective function value, a 37% reduction is obtained even if the model failed to return a value 43% of the time.
Similar content being viewed by others
References
Abramson MA (2007) NOMADm optimization software. http://en.afit.edu/ENC/Faculty/MAbramson/NOMADm.html
Abramson MA (2005) Second order behavior of pattern search. SIAM J Optim 16(2):515–530
Abramson MA, Audet C (2006) Convergence of mesh adaptive direct search to second-order stationary points. SIAM J Optim 17(2):606–619
Aspentech (2007) http://www.aspentech.com/
Audet C, Dennis JE Jr (2004) A pattern search filter approach for nonlinear programming without derivatives. SIAM J Optim 14(4):980–1010
Audet C, Dennis JE Jr (2006) Mesh adaptive direct search algorithms for constrained optimization. SIAM J Optim 17(1):188–217
Audet C, Orban D (2006) Finding optimal algorithmic parameters using the mesh adaptive direct search algorithm. SIAM J Optim 17(3):642–664
Audet C, Béchard V, Le Digabel S (2007) Nonsmooth optimization through mesh adaptive direct search and variable neighborhood search. J Glob Optim. doi:10.1007/s10898-007-9234-1
Béchard V (2004) Optimisation d’un procédé de traitement des brasques. Master’s thesis, Ecole Polytechnique de Montréal
Biegler LT, Grossmann IE (2004) Retrospective on optimization. Comput Chem Eng 28:1169–1192
Biegler LT, Albuquerque J, Gopal V, Staus G, Ydstie BE (1999) Interior point sqp strategies for large-scale structured process optimization problems. Comput Chem Eng 23:543–554
Booker AJ, Dennis JE Jr, Frank PD, Serafini DB, Torczon V (1998) Optimization using surrogate objectives on a helicopter test example. In: Borggaard J, Burns J, Cliff E, Schreck S (eds) Optimal design and control. Progress in systems and control theory. Birkhäuser, Cambridge, pp 49–58
Bowden RO, Hall JD (1998) Simulation optimization research and development. In: The 1998 winter conference on simulation, pp 1693–1698
Choi SH, Manousiouthakis V (1999) A stochastic approach to global optimization of chemical processes. Comput Chem Eng 23:1351–1356
Clarke FH (1990) Optimization and nonsmooth analysis. SIAM classics in applied mathematics, vol 5. SIAM, Philadelphia
Coope ID, Price CJ (2000) Frame-based methods for unconstrained optimization. J Optim Theory Appl 107:261–274
Courbariaux Y (2004) Étude et mise au point d’un procédé de traitement des brasques de l’industrie de l’aluminium. PhD thesis, Ecole Polytechnique de Montreal.
Courbariaux Y, Chaouki J, Guy C (2004) Update on spent potliners treatments: kinetics of cyanides destruction at high temperatures. Ind Eng Chem Res 43:5828–5837
Couture G, Audet C, Dennis JE Jr, Abramson MA (2007) The nomad project. http://www.gerad.ca/NOMAD/
Dantzig GB (1993) Linear programming and extensions. Springer, Berlin
Dolan ED, Lewis RM, Torczon V (2003) On the local convergence properties of pattern search. SIAM J Optim 14(2):567–583
Edgar TF, Himmelblau DM, Lasdon LS (2003) Optimization of chemical processes, 2nd edn. McGraw-Hill, New York
Hanke M, Li P (2000) Simulated annealing for the optimization of batch distillation processes. Comput Chem Eng 24:1–8
Hooke R, Jeeves TA (1961) Direct search solution of numerical and statistical problems. J Assoc Comput Mach 8:212–219
Jones DR, Perttunen CD, Stuckman BE (1993) Lipschitzian optimization without the Lipschitz constant. J Optim Theory Appl 79(1):157–181
Kokkolaras M, Audet C, Dennis JE Jr (2001) Mixed variable optimization of the number and composition of heat intercepts in a thermal insulation system. Optim Eng 2(1):5–29
Lewis RM, Torczon V, Trosset MW (2000) Direct search methods: then and now. J Comput Appl Math 124:191–207
Lin B, Miller DC (2004) Tabu search algorithm for chemical process optimization. Comput Chem Eng 28(11):2287–2306
Lobereiro J, Acevedo J (2004) Process synthesis and design using modular simulators: a genetic algorithm framework. Comput Chem Eng 28:1223–1236
Marsden AL, Wang M, Dennis JE Jr, Moin P (2004a) Optimal aeroacoustic shape design using the surrogate management framework. Optim Eng 5(2):235–262
Marsden AL, Wang M, Dennis JE Jr, Moin P (2004b) Suppression of airfoil vortex-shedding noise via derivative-free optimization. Phys Fluids 16(10):L83–L86
Nelder JA, Mead R (1965) A simplex method for function minimization. Comput J 7:308–313
Ouali MS, Aoudjit H, Audet C (2003) Optimisation des stratégies de maintenance. J Eur Syst Autom 37(5):587–605
Rockafellar RT (1980) Generalized directional derivatives and subgradients of nonconvex functions. Can J Math 32(2):257–280
Rosenbrock HH (1960) An automatic method for finding the greatest or least value of a function. Comput J 3:175–184
Seader JD, Sieder WD, Lewin DR (1999) Process design principles: synthesis, analysis and evaluation. Wiley, New York
Torczon V (1997) Pattern search methods for nonlinear optimization. SIAM J Optim 6:7–11
Zamora JM, Grossmann IE (1998) Continuous global optimization of structured process systems models. Comput Chem Eng 22:1749–1770
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Audet, C., Béchard, V. & Chaouki, J. Spent potliner treatment process optimization using a MADS algorithm. Optim Eng 9, 143–160 (2008). https://doi.org/10.1007/s11081-007-9030-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11081-007-9030-2