Review of Mixed‐Integer Nonlinear and Generalized Disjunctive Programming Methods

Abstract

This work presents a review of the applications of mixed-integer nonlinear programming (MINLP) in process systems engineering (PSE). A review on the main deterministic MINLP solution methods is presented, including an overview of the main MINLP solvers. Generalized disjunctive programming (GDP) is an alternative higher-level representation of MINLP problems. This work reviews some methods for solving GDP models, and techniques for improving MINLP methods through GDP. The paper also provides a high-level review of the applications of MINLP in PSE, particularly in process synthesis, planning and scheduling, process control and molecular computing.

Water and energy integration: A comprehensive literature review of non-isothermal water network synthesis

“…Systematic methods based on mathematical programming (MP) and pinch analysis (PA) have been applied over more than 40 years in order to achieve improved energy and water integration in CPI . For further details of these topics the reader is referred to comprehensive review papers relating to recent advances in chemical process optimisation (Biegler, 2014), mixed-integer nonlinear and general disjunctive programming solution methods (Trespalacios and Grossmann, 2014), heat exchanger network (HEN) synthesis (Gundersen andNaess, 1988, Furman andSahinidis, 2002) and retrofit (Sreepathi and Rangaiah, 2014), optimal design of sustainable chemical processes and supply chains (Nikolopoulou and Ierapetritou, 2012), water network (WN) design methods using MP (Jeżowski, 2008), PA (Foo, 2009), and a combination of PA and MP (Bagajewicz, 2000;Jeżowski, 2010). Over the last two decades considerable attention has been devoted to the synthesis problem of heat integration within WNs and is expected to be an active research direction in the near future.…”

Global optimization of an industrial gas network operation

“…These logical decisions were modeled using the corresponding convex hull reformulations. 33 While the convex hull reformulations utilize additional binary and continuous variables and constraints leading to an increase in the size of the model, the continuous relaxations utilized for the solution of these models are tighter than for the corresponding big-M reformulations.…”

Improved Big-M reformulation for generalized disjunctive programs

“…The interest of this work is a modified version of the (BM). We refer the reader to the MINLP and GDP review work [11] for details on the (HR).…”

“…GDP can be considered an extension to the well-known theory of disjunctive programming developed by Balas [21], and has been applied to a number of process systems engineering areas [7,11,14].…”