A probability distribution estimation based method for dynamic optimization

Engineering optimization of a highly nonlinear complex system is always a challenge methodologically and computationally. This is especially true when multistage dynamic optimization is involved. While significant progress has been made in rigorous deterministic algorithms for dynamic optimization, meta-heuristic-based optimization may offer an attractive alternative. This paper introduces a general mathematical framework, called the Population-based Probability Distribution Estimation (PPDE) method, for tackling constrained multistage complex process dynamic optimization problems. Solution identification is accomplished through probability distribution estimation based search in a continuous space, where special solution migration and penalty assignment techniques are integrated. Besides an optimal parameter estimation problem for a reactor system, an automotive coating curing optimization problem is also investigated, where the PPDE successfully minimizes oven energy consumption under various process/product constraints. Optimization results demonstrate superiorities of the method over the Ant Colony System (ACS) based dynamic optimization method. © 2007 American Institute of Chemical Engineers AIChE J, 2007

[1]  Ian C. Parmee,et al.  The Ant Colony Metaphor for Searching Continuous Design Spaces , 1995, Evolutionary Computing, AISB Workshop.

[2]  R. Horst,et al.  Global Optimization: Deterministic Approaches , 1992 .

[3]  C. Adjiman,et al.  Global optimization of mixed‐integer nonlinear problems , 2000 .

[4]  Luca Maria Gambardella,et al.  Ant colony system: a cooperative learning approach to the traveling salesman problem , 1997, IEEE Trans. Evol. Comput..

[5]  David R. Bauer,et al.  Modeling paint and adhesive cure in automotive applications 1 This paper was presented at the 212th , 1997 .

[6]  Nikolaos V. Sahinidis,et al.  BARON: A general purpose global optimization software package , 1996, J. Glob. Optim..

[7]  Edgar B. Gutoff,et al.  Modern coating and drying technology , 1992 .

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

[9]  Johann Dréo,et al.  A New Ant Colony Algorithm Using the Heterarchical Concept Aimed at Optimization of Multiminima Continuous Functions , 2002, Ant Algorithms.

[10]  Krzysztof Socha,et al.  ACO for Continuous and Mixed-Variable Optimization , 2004, ANTS Workshop.

[11]  Xiaohui Hu,et al.  Engineering optimization with particle swarm , 2003, Proceedings of the 2003 IEEE Swarm Intelligence Symposium. SIS'03 (Cat. No.03EX706).

[12]  David E. Goldberg,et al.  A Survey of Optimization by Building and Using Probabilistic Models , 2002, Comput. Optim. Appl..

[13]  Kalyanmoy Deb,et al.  A population-based algorithm-generator for real-parameter optimization , 2005, Soft Comput..

[14]  Lorenz T. Biegler,et al.  An MPEC formulation for dynamic optimization of distillation operations , 2004, Comput. Chem. Eng..

[15]  H. Miettinen,et al.  alphaPDE: A new multivariate technique for parameter estimation , 2001 .

[16]  Claire S. Adjiman,et al.  A Rigorous Global Optimization Algorithm for Problems with Ordinary Differential Equations , 2002, J. Glob. Optim..

[17]  I. Grossmann.  Review of Nonlinear Mixed-Integer and Disjunctive Programming Techniques , 2002 .

[18]  P. I. Barton,et al.  Global Mixed-Integer Dynamic Optimization , 2005 .

[19]  Helen H. Lou,et al.  Integrated Modeling and Simulation for Improved Reactive Drying of Clearcoat , 2000 .

[20]  P. I. Barton,et al.  Global methods for dynamic optimization and mixed-integer dynamic optimization , 2006 .

[21]  Helen H. Lou,et al.  Cure-Window-Based Proactive Quality Control in Topcoat Curing , 2006 .

[22]  Claire S. Adjiman,et al.  Global optimization of dynamic systems , 2004, Comput. Chem. Eng..

[23]  Helen H. Lou,et al.  ACS–based dynamic optimization for curing of polymeric coating , 2006 .

[24]  Singiresu S. Rao.  Engineering Optimization : Theory and Practice , 2010 .

[25]  Christian Blum,et al.  Training feed-forward neural networks with ant colony optimization: an application to pattern classification , 2005, Fifth International Conference on Hybrid Intelligent Systems (HIS'05).

[26]  Thestatisticalvarianceof theGEM PDFestimateis.  KERNEL PROBABILITY DENSITY ESTIMATION METHODS , 2002 .

[27]  Feng-Sheng Wang,et al.  Hybrid method of evolutionary algorithms for static and dynamic optimization problems with application to a fed-batch fermentation process , 1999 .

[28]  Marco Dorigo,et al.  Ant system: optimization by a colony of cooperating agents , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[29]  Ignacio E. Grossmann,et al.  Retrospective on optimization , 2004, Comput. Chem. Eng..

[30]  Christodoulos A. Floudas,et al.  Deterministic global optimization - theory, methods and applications , 2010, Nonconvex optimization and its applications.

[31]  D. Himmelblau,et al.  Optimization of Chemical Processes , 1987 .