Surrogate Modeling for Superstructure Optimization with Generalized Disjunctive Programming

In this work, we propose an iterative framework to solve superstructure design problems, which includes surrogate models, with a custom implementation of the Logic-based Outer- Approximation algorithm (L-bOA). We build surrogate models (SM) using the machine learning software ALAMO exploiting its ca...

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Published in:Computer Aided Chemical Engineering Vol. 49; pp. 1267 - 1272
Main Authors: Pedrozo, H.A., Reartes, S.B. Rodriguez, Vecchietti, A.R., Diaz, M.S., Grossmann, I.E.
Format: Book Chapter
Language:English
Published: 2022
Subjects:
derivative free optimization
disjunctive programming
superstructure optimization
surrogate models
disjunctive programming
superstructure optimization
derivative free optimization
surrogate models
ISBN:9780323851596, 0323851592
ISSN:1570-7946
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Abstract In this work, we propose an iterative framework to solve superstructure design problems, which includes surrogate models, with a custom implementation of the Logic-based Outer- Approximation algorithm (L-bOA). We build surrogate models (SM) using the machine learning software ALAMO exploiting its capability for selecting low- complexity basis functions to accurately fit sample data. To improve and validate the SM, we apply the Error Maximization Sampling (EMS) strategy in the exploration step. In this step, we formulate mathematical problems that are solved through Derivative Free Optimization (DFO) techniques. The following step applies the L-bOA algorithm to solve the GDP synthesis problem. As several NLP subproblems are solved to determine the optimal solution in L-bOA in the exploitation step, the corresponding optimal points are added to the SM training set. In case that an NLP subproblem turns out to be infeasible, we solve the Euclidean Distance Minimization (EDM) problem to find the closest feasible point to the former infeasible point. In this way, the entire information from NLP subproblems is exploited. As original model output variables are required, we solve EDM problems using DFO strategies. The proposed methodology is applied to a methanol synthesis problem, which shows robustness and efficiency to determine the correct optimal scheme and errors less than 0.2% in operating variables.
AbstractList In this work, we propose an iterative framework to solve superstructure design problems, which includes surrogate models, with a custom implementation of the Logic-based Outer- Approximation algorithm (L-bOA). We build surrogate models (SM) using the machine learning software ALAMO exploiting its capability for selecting low- complexity basis functions to accurately fit sample data. To improve and validate the SM, we apply the Error Maximization Sampling (EMS) strategy in the exploration step. In this step, we formulate mathematical problems that are solved through Derivative Free Optimization (DFO) techniques. The following step applies the L-bOA algorithm to solve the GDP synthesis problem. As several NLP subproblems are solved to determine the optimal solution in L-bOA in the exploitation step, the corresponding optimal points are added to the SM training set. In case that an NLP subproblem turns out to be infeasible, we solve the Euclidean Distance Minimization (EDM) problem to find the closest feasible point to the former infeasible point. In this way, the entire information from NLP subproblems is exploited. As original model output variables are required, we solve EDM problems using DFO strategies. The proposed methodology is applied to a methanol synthesis problem, which shows robustness and efficiency to determine the correct optimal scheme and errors less than 0.2% in operating variables.
Author Grossmann, I.E.
Vecchietti, A.R.
Pedrozo, H.A.
Reartes, S.B. Rodriguez
Diaz, M.S.
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  organization: Department of Chemical Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213, USA
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Keywords disjunctive programming
superstructure optimization
derivative free optimization
surrogate models
Language English
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References Pedrozo, Reartes, Bernal, Vecchietti, Díaz, Grossmann (bb0030) 2021; 154
Pedrozo, Reartes, Vecchietti, Díaz, Grossmann (bb0035) 2021; 149
Powell (bb0025) 2009
Zhao, Grossmann, García-Muñoz, Stamatis (bb0055) 2021; 67
Bhosekar, Ierapetritou (bb0010) 2018; 108
fo.net
Pedrozo, H. A., Rodriguez Reartes, S., Diaz, M. S., Vecchietti, A. R., Grossmann, I. E. (2020), Coproduction of ethylene and propylene based on ethane and propane feedstocks, Computer Aided Chemical Engineering, 48, 907-912.
1.50152-X
Kim, Boukouvala (bb0020) 2020; 140
Chen, Grossmann (bb0015) 2019; 7
T. M. Ragonneau and Z. Zhang, PDFO: Cross-Platform Interfaces for Powell's Derivative-Free Optimization Solvers (Version 1.1), available at h
Wilson, Sahinidis (bb0050) 2017; 106
References_xml – volume: 149
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  article-title: Hybrid model generation for superstructure optimization with Generalized Disjunctive Programming
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– reference: 1.50152-X
– reference: T. M. Ragonneau and Z. Zhang, PDFO: Cross-Platform Interfaces for Powell's Derivative-Free Optimization Solvers (Version 1.1), available at h
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– reference: Pedrozo, H. A., Rodriguez Reartes, S., Diaz, M. S., Vecchietti, A. R., Grossmann, I. E. (2020), Coproduction of ethylene and propylene based on ethane and propane feedstocks, Computer Aided Chemical Engineering, 48, 907-912.
– volume: 108
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Snippet In this work, we propose an iterative framework to solve superstructure design problems, which includes surrogate models, with a custom implementation of the...
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SourceType Publisher
StartPage 1267
SubjectTerms derivative free optimization
disjunctive programming
superstructure optimization
surrogate models
Title Surrogate Modeling for Superstructure Optimization with Generalized Disjunctive Programming
URI https://dx.doi.org/10.1016/B978-0-323-85159-6.50211-6
Volume 49
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