Surrogate Modeling for Superstructure Optimization with Generalized Disjunctive Programming - Pedrozo, H.A.; Reartes, S.B. Rodriguez; Vecchietti, A.R.; Diaz, M.S.; Grossmann, I.E. (Computer Aided Chemical Engineering, 2022)
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.