Logic-Based Discrete-Steepest Descent: A solution method for process synthesis Generalized Disjunctive Programs

Optimization of chemical processes is challenging due to nonlinearities arising from chemical principles and discrete design decisions. The optimal synthesis and design of chemical processes can be posed as a Generalized Disjunctive Programming (GDP) problem. While reformulating GDP problems as Mixed-Integer Nonlinear Programming (MINLP) problems is common, specialized algorithms for GDP remain scarce. This study introduces the Logic-Based Discrete-Steepest Descent Algorithm (LD-SDA) as a solution method for GDP problems involving ordered Boolean variables. LD-SDA transforms these variables into external integer decisions and uses a two-level decomposition: the upper-level sets external configurations, and the lower-level solves the remaining variables, efficiently exploiting the GDP structure. In the case studies presented in this work, including batch processing, reactor superstructures, and distillation columns, LD-SDA consistently outperforms conventional GDP and MINLP solvers, especially as the problem size grows. LD-SDA also proves superior when solving challenging problems where other solvers encounter difficulties finding optimal solutions.