Multi-objective optimal control of dynamic bioprocesses using ACADO Toolkit

The optimal design and operation of dynamic bioprocesses gives in practice often rise to optimisation problems with multiple and conflicting objectives. As a result typically not a single optimal solution but a set of Pareto optimal solutions exist. From this set of Pareto optimal solutions, one has to be chosen by the decision maker. Hence, efficient approaches are required for a fast and accurate generation of the Pareto set such that the decision maker can easily and systematically evaluate optimal alternatives. In the current paper the multi-objective optimisation of several dynamic bioprocess examples is performed using the freely available ACADO Multi-Objective Toolkit (http://www.acadotoolkit.org). This toolkit integrates efficient multiple objective scalarisation strategies (e.g., Normal Boundary Intersection and (Enhanced) Normalised Normal Constraint) with fast deterministic approaches for dynamic optimisation (e.g., single and multiple shooting). It has been found that the toolkit is able to efficiently and accurately produce the Pareto sets for all bioprocess examples. The resulting Pareto sets are added as supplementary material to this paper.

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

[2]  Debasis Sarkar,et al.  Genetic algorithms with filters for optimal control problems in fed-batch bioreactors , 2004, Bioprocess and biosystems engineering.

[3]  Eva Balsa-Canto,et al.  DOTcvpSB, a software toolbox for dynamic optimization in systems biology , 2009, BMC Bioinformatics.

[4]  H. Halsall-Whitney,et al.  Multicriteria optimization of gluconic acid production using net flow , 2003, Bioprocess and biosystems engineering.

[5]  H. Bock,et al.  Recent Advances in Parameteridentification Techniques for O.D.E. , 1983 .

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

[7]  Gabriele Eichfelder,et al.  Adaptive Scalarization Methods in Multiobjective Optimization , 2008, Vector Optimization.

[8]  X. Yi.  On Automatic Differentiation , 2005 .

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

[10]  Johannes P. Schlöder,et al.  An efficient multiple shooting based reduced SQP strategy for large-scale dynamic process optimization: Part II: Software aspects and applications , 2003, Comput. Chem. Eng..

[11]  Andreas Griewank,et al.  Evaluating derivatives - principles and techniques of algorithmic differentiation, Second Edition , 2000, Frontiers in applied mathematics.

[12]  W. Ramirez,et al.  Obtaining smoother singular arc policies using a modified iterative dynamic programming algorithm , 1997 .

[13]  Kaisa Miettinen,et al.  Nonlinear multiobjective optimization , 1998, International series in operations research and management science.

[14]  Christian Fonteix,et al.  Multicriteria Optimization for the Production 0f Gluconic Acid , 2001 .

[15]  Wolfgang Marquardt,et al.  Dynamic optimization using adaptive control vector parameterization , 2005, Comput. Chem. Eng..

[16]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[17]  Didier Dumur,et al.  Open-loop optimization and trajectory tracking of a fed-batch bioreactor , 2008 .

[18]  Griewank,et al.  On automatic differentiation , 1988 .

[19]  N. J. Titchener-Hooker,et al.  The application of a Pareto optimisation method in the design of an integrated bioprocess , 2003, Bioprocess and biosystems engineering.

[20]  D. Sarkar,et al.  Pareto-optimal solutions for multi-objective optimization of fed-batch bioreactors using nondominated sorting genetic algorithm. , 2005 .

[21]  K. Tanabe,et al.  Mathematical Programming: Recent Developments and Applications. , 1990 .

[22]  John E. Dennis,et al.  Normal-Boundary Intersection: A New Method for Generating the Pareto Surface in Nonlinear Multicriteria Optimization Problems , 1998, SIAM J. Optim..

[23]  Kazuhiro Maeda,et al.  An integrative and practical evolutionary optimization for a complex, dynamic model of biological networks , 2011, Bioprocess and biosystems engineering.

[24]  J. V. Salcedo,et al.  A new perspective on multiobjective optimization by enhanced normalized normal constraint method , 2008 .

[25]  Johannes P. Schlöder,et al.  An efficient multiple shooting based reduced SQP strategy for large-scale dynamic process optimization. Part 1: theoretical aspects , 2003, Comput. Chem. Eng..

[26]  G. R. Sullivan,et al.  The development of an efficient optimal control package , 1978 .

[27]  G. K. Suraishkumar,et al.  Multi-objective optimization in Aspergillus niger fermentation for selective product enhancement , 2005, Bioprocess and biosystems engineering.

[28]  Peter Deuflhard,et al.  Numerical Treatment of Inverse Problems in Differential and Integral Equations: Proceedings of an International Workshop, Heidelberg, Fed. Rep. of Germany, August 30 - September 3, 1982 , 2012 .

[29]  A. Messac,et al.  Normal Constraint Method with Guarantee of Even Representation of Complete Pareto Frontier , 2004 .

[30]  R. K. Ursem.  Multi-objective Optimization using Evolutionary Algorithms , 2009 .

[31]  Eva Balsa-Canto,et al.  Dynamic optimization of chemical and biochemical processes using restricted second order information , 2001 .

[32]  Moritz Diehl,et al.  ACADO toolkit—An open‐source framework for automatic control and dynamic optimization , 2011 .

[33]  A. Messac,et al.  The normalized normal constraint method for generating the Pareto frontier , 2003 .

[34]  Lorenz T. Biegler,et al.  A software environment for simultaneous dynamic optimization , 2007, Comput. Chem. Eng..

[35]  Filip Logist,et al.  Novel insights for multi-objective optimisation in engineering using Normal Boundary Intersection and (Enhanced) Normalised Normal Constraint , 2012 .

[36]  Filip Logist,et al.  Fast Pareto set generation for nonlinear optimal control problems with multiple objectives , 2010 .

[37]  Christian Kirches,et al.  Efficient multiple objective optimal control of dynamic systems with integer controls , 2010 .

[38]  J. Dennis,et al.  A closer look at drawbacks of minimizing weighted sums of objectives for Pareto set generation in multicriteria optimization problems , 1997 .