Mixed-Integer Linear Programming Formulation with Embedded Machine Learning Surrogates for the Design of Chemical Process Families

There is a need for design strategies that can support rapid and widespread deployment of new energy systems and process technologies. In a previous work, we introduced process family design as an alternative method to traditional and modular design approaches. In this article, we develop piecewise linear surrogates using Machine Learning (ML) models and the Optimization and Machine Learning Toolkit (OMLT) to show how process families can be designed to reduce manufacturing costs and deployment timelines. We formulate this problem as a nonlinear Generalized Disjunctive Program (GDP), which, following transformation, results in a large-scale mixed-integer nonlinear programming (MINLP) problem. This large-scale problem is intractable using traditional MINLP approaches. By using ML surrogates to predict required system costs and performance indicators, we can approximate the nonlinearities in the GDP to generate an efficient mixed-integer linear programming (MILP) formulation. We apply the ML surrogate approach to two case studies in this work. One case study involves designing a family of carbon capture systems to cover a set of different flue gas flow rates and inlet CO₂ concentrations, while the second case study focuses on a water desalination process, where we design a family of these processes for a variety of salt concentrations and flow rates. In both of these case studies, our approach based on ML surrogates is able to find optimal solutions in reasonable computational time and yield solutions comparable to those of a previously reported approach for solving the problem.