A data-driven optimization algorithm for differential algebraic equations with numerical infeasibilities.

Support Vector Machines (SVMs) based optimization framework is presented for the data-driven optimization of numerically infeasible Differential Algebraic Equations (DAEs) without the full discretization of the underlying first-principles model. By formulating the stability constraint of the numerical integration of a DAE system as a supervised classification problem, we are able to demonstrate that SVMs can accurately map the boundary of numerical infeasibility. The necessity of this data-driven approach is demonstrated on a 2-dimensional motivating example, where highly accurate SVM models are trained, validated, and tested using the data collected from the numerical integration of DAEs. Furthermore, this methodology is extended and tested for a multi-dimensional case study from reaction engineering (i.e., thermal cracking of natural gas liquids). The data-driven optimization of this complex case study is explored through integrating the SVM models with a constrained global grey-box optimization algorithm, namely the ARGONAUT framework.

[1]  I. Grossmann,et al.  An algorithm for the use of surrogate models in modular flowsheet optimization , 2008 .

[2]  Nikolaos Ploskas,et al.  Tuning BARON using derivative-free optimization algorithms , 2019, J. Glob. Optim..

[3]  Ivan Rusyn,et al.  Optimal Chemical Grouping and Sorbent Material Design by Data Analysis, Modeling and Dimensionality Reduction Techniques. , 2018, ESCAPE. European Symposium on Computer Aided Process Engineering.

[4]  Christodoulos A. Floudas,et al.  Global optimization of general constrained grey-box models: new method and its application to constrained PDEs for pressure swing adsorption , 2017, J. Glob. Optim..

[5]  Arthur K. Kordon,et al.  Fault diagnosis based on Fisher discriminant analysis and support vector machines , 2004, Comput. Chem. Eng..

[6]  Efstratios N. Pistikopoulos,et al.  Process design and control optimization: A simultaneous approach by multi‐parametric programming , 2017 .

[7]  Atharv Bhosekar,et al.  Advances in surrogate based modeling, feasibility analysis, and optimization: A review , 2018, Comput. Chem. Eng..

[8]  Christos T. Maravelias,et al.  Surrogate‐based superstructure optimization framework , 2011 .

[9]  Chris Aldrich,et al.  Improving process operations using support vector machines and decision trees , 2005 .

[10]  Marianthi G. Ierapetritou,et al.  Data-driven feasibility analysis for the integration of planning and scheduling problems , 2019, Optimization and Engineering.

[11]  Meihong Wang,et al.  Modelling and dynamic optimization of thermal cracking of propane for ethylene manufacturing , 2011, Comput. Chem. Eng..

[12]  Zukui Li,et al.  Optimal scenario reduction framework based on distance of uncertainty distribution and output performance: I. Single reduction via mixed integer linear optimization , 2014, Comput. Chem. Eng..

[13]  A. Basudhar,et al.  Constrained efficient global optimization with support vector machines , 2012, Structural and Multidisciplinary Optimization.

[14]  Efstratios N. Pistikopoulos,et al.  Optimal design of energy systems using constrained grey-box multi-objective optimization , 2018, Comput. Chem. Eng..

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

[16]  Efstratios N. Pistikopoulos,et al.  Big data approach to batch process monitoring: Simultaneous fault detection and diagnosis using nonlinear support vector machine-based feature selection , 2018, Comput. Chem. Eng..

[17]  David C. Miller,et al.  Learning surrogate models for simulation‐based optimization , 2014 .

[18]  Selen Cremaschi,et al.  Process synthesis of biodiesel production plant using artificial neural networks as the surrogate models , 2012, Comput. Chem. Eng..

[19]  Efstratios N. Pistikopoulos,et al.  A Nonlinear Support Vector Machine-Based Feature Selection Approach for Fault Detection and Diagnosis: Application to the Tennessee Eastman Process. , 2019, AIChE journal. American Institute of Chemical Engineers.

[20]  Christodoulos A. Floudas,et al.  ARGONAUT: AlgoRithms for Global Optimization of coNstrAined grey-box compUTational problems , 2017, Optim. Lett..

[21]  Christodoulos A. Floudas,et al.  Global optimization of grey-box computational systems using surrogate functions and application to highly constrained oil-field operations , 2018, Comput. Chem. Eng..

[22]  Christodoulos A. Floudas,et al.  Dimensionality reduction for production optimization using polynomial approximations , 2017, Computational Geosciences.

[23]  Styliani Avraamidou,et al.  A hierarchical Food-Energy-Water Nexus (FEW-N) decision-making approach for Land Use Optimization. , 2018, International symposium on process systems engineering.

[24]  L. Biegler,et al.  Simulation and Optimization of the Ethane Cracking Process to Produce Ethylene , 2015 .

[25]  Lan Zhou,et al.  Grouping of complex substances using analytical chemistry data: A framework for quantitative evaluation and visualization , 2019, PloS one.

[26]  Peter Piela.  Ascend: an object-oriented computer environment for modeling and analysis , 1989 .

[27]  Ioannis P E Pistikopoulos,et al.  DOMINO: Data-driven Optimization of bi-level Mixed-Integer NOnlinear Problems , 2020, Journal of global optimization : an international journal dealing with theoretical and computational aspects of seeking global optima and their applications in science, management and engineering.

[28]  P. Daoutidis.  DAEs in Model Reduction of Chemical Processes: An Overview , 2015 .

[29]  Iftekhar A. Karimi,et al.  Design of computer experiments: A review , 2017, Comput. Chem. Eng..