Fuzzy Real-Time Optimization of the Tennessee Eastman Challenge Process

Document Type: Research Article


Faculty of Chemical and Petroleum Engineering, Sharif University of Technology, P.O. Box 11365-8639 Tehran, I.R. IRAN


A Real-Time Optimization (RTO) strategy incorporating the fuzzy sets theory is developed, where the problem constraints obtained from process considerations are treated in fuzzy environment. Furthermore, the objective function is penalized by a fuzzified form of the key process constraints. To enable using conventional optimization techniques, the resulting fuzzy optimization problem is then reformulated into a crisp programming problem. The crisp programming problem is solved using both Sequential Quadratic Programming (SQP) and Heuristic Random Optimization (HRO) techniques for comparison purposes. The proposed fuzzy RTO strategy is demonstrated via the Tennessee Eastman benchmark process, and is also compared with a crisp RTO strategy from the literature. Remarkable economical improvement is found over the crisp RTO. In spite of the fuzzified constraints, the proposed strategy yields smooth operation of the process, while maintaining the product quality within the acceptable range.


[1] Forbes J.F., Marlin T.E., Model Accuracy for Economic Optimizing Controllers: the Bias Update Case, Industrial & Engineering Chemistry Research, 33, p. 1919 (1994).

[2] Chachuat B., Srinivasan B., Bonvin D., Adaptation Strategies for Real-Time Optimization, Computers and Chemical Engineering, 33, p. 1557 (2009).

[3] Chen C.-L., Sun D.-Y., Chang C.-Y., Numerical Solution of Dynamic Optimization Problems with Flexible Inequality Constraints by Iterative Dynamic Programming, Fuzzy Sets and Systems, 127, p. 165 (2002).

[4] Zadeh L.A., Fuzzy Sets, Information and Control, 8, p. 338 (1965).

[5] Duvall P.M., Riggs J.B., On-Line Optimization of the TennesseeEastman Challenge Problem, Journal of Process Control, 10, p. 19 (2000).

[6] Downs J.J., Vogel E.F., A Plant-Wide Industrial Process Control Problem, Computers and Chemical Engineering, 17 (3), p. 245 (1993).

[7] Ricker N.L., Optimal Steady-State Operation of the TennesseeEastman Challenge Process, Computers and Chemical Engineering, 19 (9), p. 949 (1995).

[8] Golshan M., Boozarjomehry R.B., Pishvaie M.R., A New Approach to Real Time Optimization of the Tennessee Eastman Challenge Problem, Chemical Engineering Journal, 112, p. 33 (2005).

[9] McAvoy T,J., Ye N., Base Control for the TennesseeEastman Problem, Computers and Chemical Engineering, 18 (5), p. 383 (1994).

[10] Golshan M., Pishvaie M.R., Boozarjomehry R.B., Stochastic and Global Real Time Optimization of Tennessee Eastman Challenge Problem, Engineering Applications of Artificial Intelligence, 21 (2), p. 215 (2008).

[11] Jockenhövel T., Biegler L.T., Wächter A., Dynamic Optimization of the Tennessee Eastman Process Using the OptControlCentre, Computers and Chemical Engineering, 27, p. 1513 (2003).

[12] Ricker N.L., Lee J.H., Nonlinear Modeling and State Estimation for the Tennessee Eastman Challenge Process, Computers and Chemical Engineering, 19 (9), p. 983 (1995).

[13] Shou Y., Xu J., Multi-Objective Optimization of Oversaturated Signalized Intersection Based on Fuzzy Logic, "Proceedings of the 8th World Congress on Intelligent Control and Automation (WCICA 2010)", 7-9 July 2010, Jinan, China (2010).

[14] Li F.C., Liu L.M., Jin C.X., Study on Fuzzy Optimization Methods Based on Quasi-Linear Fuzzy Number and Genetic Algorithm, Computers and Mathematics with Applications, 57(1), p. 67 (2009).

[15] Bellman R.,  Zadeh L.A., Decision Making in Fuzzy Environment., Management Science, 17, p. B141 (1970).

[16] Zimmermann H.J., Description and Optimization of Fuzzy Systems, International Journal of General Systems, 2, p. 209 (1976).

[17] Zimmermann H.J., "Fuzzy Set Theory and Its Application", Third Edition, Kluwer Academic Publishers (1996).

[18] Li J., Rhinehart R.R. Heuristic Random Optimization, Computers and Chemical Engineering, 22, p. 427 (1998).

[19] Neumaier, A. Complete Search in Continuous Global Optimization and Constraints Satisfaction. Chapter in "Acta Numerica" (A. Iserles, ed.), Cambridge University Press (2004).