Global Optimization of Chemical Processes using Stochastic Algorithms

Many systems in chemical engineering are difficult to optimize using gradient-based algorithms. These include process models with multimodal objective functions and discontinuities. Herein, a stochastic algorithm is applied for the optimal design of a fermentation process, to determine multiphase equilibria, for the optimal control of a penicillin reactor, for the optimal control of a non-differentiable system, and for the optimization of a catalyst blend in a tubular reactor. The advantages of the algorithm for the efficient and reliable location of global optima are examined. The properties of these algorithms, as applied to chemical processes, are considered, with emphasis on the ease of handling constraints and the ease of implementation and interpretation of results. For the five processes, the efficiency of computation is improved compared with selected stochastic and deterministic algorithms. Results closer to the global optimum are reported for the optimal control of the penicillin reactor and the non-differentiable system.

[1]  C. Floudas,et al.  Global optimization for the phase and chemical equilibrium problem: Application to the NRTL equation , 1995 .

[2]  H. Ku,et al.  An evaluation of simulated annealing for batch process scheduling , 1991 .

[3]  R Luus,et al.  Optimization of fed-batch fermentors by iterative dynamic programming. , 1993, Biotechnology and bioengineering.

[4]  Christodoulos A. Floudas,et al.  Global Optimization and Analysis for the Gibbs Free Energy Function Using the UNIFAC, Wilson, and ASOG Equations , 1995 .

[5]  Akio Shindo,et al.  Complex Method for Solving Variational Problems with State-Variable Inequality Constraints , 1972 .

[6]  Rein Luus,et al.  Reliability of optimization procedures for obtaining global optimum , 1978 .

[7]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[8]  L. Petzold Differential/Algebraic Equations are not ODE's , 1982 .

[9]  J. Casares,et al.  Analysis and evaluation of a wastewater treatment plant model by stochastic optimization , 1989 .

[10]  Amy Cha-Tien Sun,et al.  Homotopy-continuation algorithm for global optimization , 1992 .

[11]  R. Salcedo,et al.  An improved random-search algorithm for non-linear optimization , 1990 .

[12]  Luc Devroye,et al.  Progressive global random search of continuous functions , 1978, Math. Program..

[13]  W. F. Ramirez,et al.  Structural analysis and solution of systems of algebraic design equations , 1984 .

[14]  M. J. D. Powell,et al.  A fast algorithm for nonlinearly constrained optimization calculations , 1978 .

[15]  David D. Brengel,et al.  NONLINEAR ANALYSIS IN PROCESS DESIGN , 1991 .

[16]  John W. Eaton,et al.  GNU octave : a high-level interactive language for numerical computations : Octave version 2.0.17 (stable) , 1997 .

[17]  Christodoulos A. Floudas,et al.  Global optimization for the phase stability problem , 1995 .

[18]  L. Ingber Very fast simulated re-annealing , 1989 .

[19]  Gheorghe Maria,et al.  A modified matyas algorithm (MMA) for random process optimization , 1986 .

[20]  M. Michelsen The isothermal flash problem. Part I. Stability , 1982 .

[21]  Chyi Hwang,et al.  OPTIMAL CONTROL COMPUTATION FOR DIFFERENTIAL-ALGEBRAIC PROCESS SYSTEMS WITH GENERAL CONSTRAINTS , 1990 .

[22]  David D. Brengel,et al.  Coordinated design and control optimization of nonlinear processes , 1992 .

[23]  Romualdo Salcedo,et al.  Solving nonconvex nonlinear programming and mixed-integer nonlinear programming problems with adaptive random search , 1992 .

[24]  Eric Walter,et al.  A general-purpose global optimizer: implementation and applications , 1984 .

[25]  Rein Luus Optimization of heat exchanger networks , 1993 .

[26]  W. Schiesser The Numerical Method of Lines: Integration of Partial Differential Equations , 1991 .

[27]  Lester Ingber,et al.  Simulated annealing: Practice versus theory , 1993 .

[28]  Venkat Venkatasubramanian,et al.  Computer-aided molecular design using genetic algorithms , 1994 .

[29]  Shih-Ping Han A globally convergent method for nonlinear programming , 1975 .

[30]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[31]  Julio R. Banga,et al.  Optimization of the Thermal Processing of Conduction-Heated Canned Foods: Study of Several Objective Functions , 1991 .

[32]  Linda R. Petzold,et al.  Numerical solution of initial-value problems in differential-algebraic equations , 1996, Classics in applied mathematics.

[33]  W. Seider,et al.  Homotopy-continuation method for stability analysis in the global minimization of the Gibbs free energy , 1995 .

[34]  S. Mitter,et al.  Recursive stochastic algorithms for global optimization in R d , 1991 .

[35]  J. Fontanari,et al.  Stochastic versus deterministic update in simulated annealing , 1990 .

[36]  Rein Luus,et al.  Global optimization of the bifunctional catalyst problem , 1994 .

[37]  Roger J.-B. Wets,et al.  Minimization by Random Search Techniques , 1981, Math. Oper. Res..

[38]  R. Goulcher,et al.  The solution of steady-state chemical engineering optimisation problems using a random-search algorithm , 1978 .

[39]  T. H. I. Jaakola,et al.  Optimization by direct search and systematic reduction of the size of search region , 1973 .

[40]  M. Michelsen The isothermal flash problem. Part II. Phase-split calculation , 1982 .

[41]  G. Bekey,et al.  Random search techniques for optimization of nonlinear systems with many parameters , 1983 .

[42]  Neil L. Book,et al.  The selection of design variables in systems of algebraic equations , 1976 .

[43]  Sandro Ridella,et al.  Minimizing multimodal functions of continuous variables with the “simulated annealing” algorithmCorrigenda for this article is available here , 1987, TOMS.

[44]  Christodoulos A. Floudas,et al.  Decomposition based and branch and bound global optimization approaches for the phase equilibrium problem , 1994, J. Glob. Optim..

[45]  J. J. Casares Long,et al.  INTEGRATED CONTROLLED RANDOM SEARCH: APPLICATION TO A WASTEWATER TREATMENT PLANT MODEL , 1987 .

[46]  C. Floudas,et al.  GLOPEQ: A new computational tool for the phase and chemical equilibrium problem , 1997 .

[47]  R. Luus,et al.  Importance of search-domain reduction in random optimization , 1992 .

[48]  G. Bekey,et al.  A global optimization algorithm using adaptive random search , 1980 .

[49]  R. Luus,et al.  Multiplicity of solutions in the optimization of a bifunctional catalyst blend in a tubular reactor , 1992 .

[50]  Julio R. Banga,et al.  Optimal control of heat and mass transfer in food and bioproducts processing , 1994 .

[51]  Peter T. Cummings,et al.  Process optimization via simulated annealing: Application to network design , 1989 .

[52]  M. Huber Structural optimization of vapor pressure correlations using simulated annealing and threshold accepting: Application to R134a☆ , 1994 .

[53]  J. E. Cuthrell,et al.  Simultaneous optimization and solution methods for batch reactor control profiles , 1989 .

[54]  A. Ravindran,et al.  Engineering Optimization: Methods and Applications , 2006 .

[55]  Serge Domenech,et al.  Separation sequence synthesis how to use simulated annealing procedure , 1993 .

[56]  H. Lim,et al.  Computational algorithms for optimal feed rates for a class of fed‐batch fermentation: Numerical results for penicillin and cell mass production , 1986, Biotechnology and bioengineering.

[57]  Lawrence Davis,et al.  Genetic Algorithms and Simulated Annealing , 1987 .

[58]  Steven G. Louie,et al.  A Monte carlo simulated annealing approach to optimization over continuous variables , 1984 .

[59]  R. Luus Piecewise linear continuous optimal control by iterative dynamic programming , 1993 .

[60]  Joos Vandewalle,et al.  OPTIMAL CONTROL OF THE PENICILLIN G FED-BATCH FERMENTATION: AN ANALYSIS OF A MODIFIED UNSTRUCTURED MODEL , 1992 .

[61]  Rein Luus,et al.  Application of dynamic programming to differential-algebraic process systems , 1993 .

[62]  Philip E. Gill,et al.  Practical optimization , 1981 .