A Benders decomposition framework for the optimization of disjunctive superstructures with ordered discrete decisions

Abstract

AbstractThis study introduces the logic‐based discrete‐Benders decomposition (LD‐BD) for Generalized Disjunctive Programming (GDP) superstructure problems with ordered Boolean variables. The key idea is to obtain Benders cuts that use neighborhood information of a reformulated version of Boolean variables. These Benders cuts are iteratively refined, which guarantees convergence to a local optimum. A mathematical case study, the optimization of a network with Continuous Stirred‐Tank Reactors (CSTRs) in series, and a large‐scale problem involving the design of a distillation column are considered to demonstrate the features of LD‐BD. The results from these case studies have shown that the LD‐BD method exhibited good performance by finding attractive locally optimal solutions relative to existing logic‐based solvers for GDP problems. Based on these tests, the LD‐BD method is a promising strategy to solve optimal synthesis problems with ordered discrete decisions emerging in chemical engineering applications.