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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| Vydáno v: | Computer Aided Chemical Engineering Ročník 49; s. 1267 - 1272 |
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| Hlavní autoři: | , , , , |
| Médium: | Kapitola |
| Jazyk: | angličtina |
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2022
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| 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. |
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| 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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| Copyright | 2022 Elsevier B.V. |
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| DOI | 10.1016/B978-0-323-85159-6.50211-6 |
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| Keywords | disjunctive programming superstructure optimization derivative free optimization surrogate models |
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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 year: 2021 ident: bb0035 article-title: Optimal design of ethylene and propylene coproduction plants with generalized disjunctive programming and state equipment network models publication-title: Comp. & Chem. Eng. – volume: 140 year: 2020 ident: bb0020 article-title: Surrogate-based optimization for mixed-integer nonlinear problems publication-title: Comp. & Chem. Eng. – year: 2009 ident: bb0025 article-title: The BOBYQA algorithm for bound constrained optimization without derivatives, Technical Report DAMTP 2009/NA06 – volume: 7 start-page: 839 year: 2019 ident: bb0015 article-title: Modern modeling paradigms using generalized disjunctive programming publication-title: Processes – volume: 154 year: 2021 ident: bb0030 article-title: Hybrid model generation for superstructure optimization with Generalized Disjunctive Programming publication-title: Comp. & Chem. Eng. – 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 – volume: 106 start-page: 785 year: 2017 end-page: 795 ident: bb0050 article-title: The ALAMO approach to machine learning publication-title: Comp. & Chem. Eng. – 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 start-page: 250 year: 2018 end-page: 267 ident: bb0010 article-title: Advances in surrogate based modeling, feasibility analysis, and optimization: A review publication-title: Comp. & Chem. Eng. – reference: fo.net – volume: 67 year: 2021 ident: bb0055 article-title: Flexibility index of black-box models with parameter uncertainty through derivative-free optimization publication-title: AIChE Journal |
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| SubjectTerms | derivative free optimization disjunctive programming superstructure optimization surrogate models |
| Title | Surrogate Modeling for Superstructure Optimization with Generalized Disjunctive Programming |
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