Integrated Optimization Strategies for Dynamic Process Operations

Process systems engineering faces increasing demands and opportunities for better process modeling and optimization strategies, particularly in the area of dynamic operations. Modern optimization strategies for dynamic optimization trace their inception to the groundbreaking work Pontryagin and his coworkers, starting 60 years ago. Since then the application of large-scale non-linear programming strategies has extended their discoveries to deal with challenging real-world process optimization problems. This study discusses the evolution of dynamic optimization strategies and how they have impacted the optimal design and operation of chemical processes. We demonstrate the effectiveness of dynamic optimization on three case studies for real-world reactive processes. In the first case, we consider the optimal design of runaway reactors, where simulation models may lead to unbounded profiles for many choices of design and operating conditions. As a result, optimization based on repeated simulations typically fails, and a simultaneous, equationbased approach must be applied. Next we consider optimal operating policies for grade transitions in polymer processes. Modeled as an optimal control problem, we demonstrate how product specifications lead to multistage formulations that greatly improve process performance and reduce waste. Third, we consider an optimization strategy for the integration of scheduling and dynamic process operation for general continuous/batch processes. The method introduces a discrete time formulation for simultaneous optimization of scheduling and operating decisions. For all of these cases we provide a summary of directions and challenges for future integration of these tasks and extensions in optimization formulations and strategies.

[1]  R. Courant,et al.  Methods of Mathematical Physics , 1962 .

[2]  R. V. Gamkrelidze,et al.  Theory of Optimal Processes , 1961 .

[3]  L. S. Pontryagin,et al.  Mathematical Theory of Optimal Processes , 1962 .

[4]  Arthur E. Bryson,et al.  Applied Optimal Control , 1969 .

[5]  G. Reddien Collocation at Gauss Points as a Discretization in Optimal Control , 1979 .

[6]  G. Thompson,et al.  Optimal control theory : applications to management science , 1984 .

[7]  H. Bock,et al.  A Multiple Shooting Algorithm for Direct Solution of Optimal Control Problems , 1984 .

[8]  F. Roush Numerical treatment of inverse problems in differential and integral equations : P. Deuflhard and E. Hairer, Ed., Boston: Birkhauser, 1983, 357 pages, $27.50 , 1984 .

[9]  Ignacio E. Grossmann,et al.  An index for operational flexibility in chemical process design. Part I: Formulation and theory , 1985 .

[10]  C. Floudas,et al.  Active constraint strategy for flexibility analysis in chemical processes , 1987 .

[11]  Costas J. Spanos,et al.  Advanced process control , 1989 .

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

[13]  J. Betts,et al.  Application of sparse nonlinear programming to trajectory optimization , 1992 .

[14]  Brian W. Kernighan,et al.  AMPL: A Modeling Language for Mathematical Programming , 1993 .

[15]  R. Sargent,et al.  Solution of a Class of Multistage Dynamic Optimization Problems. 2. Problems with Path Constraints , 1994 .

[16]  Arne Stolbjerg Drud,et al.  CONOPT - A Large-Scale GRG Code , 1994, INFORMS J. Comput..

[17]  H. J. Pesch A Practical Guide to the Solution of Real-Life Optimal Control Problems , 1994 .

[18]  L. Biegler,et al.  Dynamic Optimization in the Design and Scheduling of Multiproduct Batch Plants , 1996 .

[19]  Richard W. Longman,et al.  Mathematical Optimization in Robotics: Towards Automated High Speed Motion Planning , 1997 .

[20]  Paul I. Barton,et al.  Dynamic Optimization in a Discontinuous World , 1998 .

[21]  Uri M. Ascher,et al.  Computer methods for ordinary differential equations and differential-algebraic equations , 1998 .

[22]  William W. Hager,et al.  Runge-Kutta methods in optimal control and the transformed adjoint system , 2000, Numerische Mathematik.

[23]  Jorge Nocedal,et al.  A trust region method based on interior point techniques for nonlinear programming , 2000, Math. Program..

[24]  G. Thompson,et al.  Optimal Control Theory: Applications to Management Science and Economics , 2000 .

[25]  L. Biegler,et al.  A reduced space interior point strategy for optimization of differential algebraic systems , 2000 .

[26]  Christof Büskens,et al.  Sensitivity Analysis and Real-Time Control of Parametric Optimal Control Problems Using Nonlinear Programming Methods , 2001 .

[27]  Christof Büskens,et al.  Real-Time Control of an Industrial Robot under Control and State Constraints , 2001 .

[28]  Lorenz T. Biegler,et al.  Optimal process design with model parameter uncertainty and process variability , 2003 .

[29]  Dominique Bonvin,et al.  Dynamic optimization of batch processes: I. Characterization of the nominal solution , 2003, Comput. Chem. Eng..

[30]  Lorenz T. Biegler,et al.  Dynamic Optimization Strategies for Three-Dimensional Conflict Resolution of Multiple Aircraft , 2004 .

[31]  L. Biegler,et al.  Real Time Optimal Guidance of Low‐Thrust Spacecraft: An Application of Nonlinear Model Predictive Control , 2005, Annals of the New York Academy of Sciences.

[32]  Rüdiger Franke,et al.  Production campaign planning including grade transition sequencing and dynamic optimization , 2005, Comput. Chem. Eng..

[33]  Lorenz T. Biegler,et al.  Dynamic optimization of HIPS open-loop unstable polymerization reactors , 2005 .

[34]  Jaime Cerdá,et al.  State-of-the-art review of optimization methods for short-term scheduling of batch processes , 2006, Comput. Chem. Eng..

[35]  Lorenz T. Biegler,et al.  On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming , 2006, Math. Program..

[36]  L. Biegler,et al.  Convergence rates for direct transcription of optimal control problems with final-time equality constraints using collocation at Radau points , 2006, 2006 American Control Conference.

[37]  Lorenz T. Biegler,et al.  Convergence rates for direct transcription of optimal control problems using collocation at Radau points , 2008, Comput. Optim. Appl..

[38]  John T. Betts,et al.  Practical Methods for Optimal Control and Estimation Using Nonlinear Programming , 2009 .

[39]  Lorenz T. Biegler,et al.  Optimization Strategies for Dynamic Systems , 2009, Encyclopedia of Optimization.

[40]  Lorenz T. Biegler,et al.  Nonlinear Waves in Integrable and Nonintegrable Systems , 2018 .

[41]  Christos T. Maravelias,et al.  General framework and modeling approach classification for chemical production scheduling , 2012 .

[42]  David L. Woodruff,et al.  Pyomo — Optimization Modeling in Python , 2012, Springer Optimization and Its Applications.

[43]  H. J. Pesch,et al.  The Cold War and the Maximum Principle of Optimal Control , 2012 .

[44]  Paul M. Witt,et al.  Optimal Active Catalyst and Inert Distribution in Catalytic Packed Bed Reactors: ortho-Xylene Oxidation , 2013 .

[45]  Lorenz T. Biegler,et al.  Reactor modeling and recipe optimization of polyether polyol processes: Polypropylene glycol , 2013 .

[46]  L. Biegler Nonlinear programming strategies for dynamic chemical process optimization , 2014, Theoretical Foundations of Chemical Engineering.

[47]  Pedro M. Castro,et al.  Scope for industrial applications of production scheduling models and solution methods , 2014, Comput. Chem. Eng..

[48]  N. N. Ziyatdinov,et al.  Optimal design of chemical processes under uncertainty , 2014, Theoretical Foundations of Chemical Engineering.

[49]  L. Biegler,et al.  Extended Discrete-Time Resource Task Network Formulation for the Reactive Scheduling of a Mixed Batch/Continuous Process , 2014 .

[50]  N. N. Ziyatdinov,et al.  Optimization of Chemical Process Design with Chance Constraints by an Iterative Partitioning Approach , 2015 .

[51]  L. Biegler,et al.  Discrete Time Formulation for the Integration of Scheduling and Dynamic Optimization , 2015 .

[52]  Lorenz T. Biegler,et al.  Optimization of grade transitions in polyethylene solution polymerization process under uncertainty , 2016, Comput. Chem. Eng..

[53]  L. Biegler,et al.  Optimization of grade transitions in polyethylene solution polymerization processes , 2016 .

[54]  L. Biegler,et al.  Nested direct transcription optimization for singular optimal control problems , 2016 .

[55]  Anja Vogler,et al.  Lectures On The Calculus Of Variations , 2016 .