Optimal design of superstructures for placing units and streams with multiple and ordered available locations. Part I: A new mathematical framework. (9th June 2020)

• Record Type: Journal Article
• Authors: Liñán, David A.; Bernal, David E.; Ricardez-Sandoval, Luis A.; Gómez, Jorge M.
• Is Part Of: Computers & chemical engineering. Volume 137(2020)
• Publication Date: 2020-06-09
• Subjects: Superstructures -- Optimal process design -- Decomposition strategy -- Discrete-Steepest Descent Algorithm; CPU Central Processing Unit -- CSTR Continuously Stirred Tank Reactor -- D-SDA Discrete-Steepest Descent Algorithm -- EVR External Variables Reformulation -- FNLP Fixed Nonlinear Program/Problem -- GDP Generalized Disjunctive Programming -- IPLC Integer Program/Problem with Linear Constraints -- MIP Mixed Integer Programming/Program/Problem -- MILP Mixed Integer Linear Programming/Program/Problem -- MINLP Mixed-Integer Nonlinear Programming/Program/Problem -- NLP Nonlinear Programming/Program/Problem -- PFR Plug Flow Reactor -- UIP Unconstrained Integer Programming/Program/Problem; Chemical engineering -- Data processing -- Periodicals; 660.0285
• DOI: 10.1016/j.compchemeng.2020.106794
• Languages: English
• ISSNs: 0098-1354

Abstract

Highlights: A decomposition strategy is used to optimize superstructures. Optimal placement of streams and process units over a superstructure. Optimization of superstructures expressed as Mixed-Integer Nonlinear Problems. A time-efficient Discrete-Steepest Descent Algorithm (D-SDA) is presented. A CSTR network is used to illustrate the implementation of the proposed algorithm. Abstract: A new approach for the optimal design of superstructures in chemical engineering is proposed in this study. Contrary to most of the optimization techniques established in the literature, this approximation exploits the structure of a specific type of problem, i.e., the case where it is necessary to find the optimal location of a processing unit or a stream over a naturally ordered discrete set. The proposed methodology consists of reformulating the binary variables of the original Mixed-Integer Nonlinear Problem (MINLP) with a smaller set of integer variables referred to as external variables . Then, the reformulated optimization problem can be decomposed into a master Integer Program with Linear Constraints ( master IPLC) and primal sub-problems in the form of Fixed Nonlinear Programs (FNLPs), i.e., Nonlinear Programs (NLPs) with integer variables fixed. The use of the Discrete-Steepest Descent Algorithm (D-SDA) is considered for the master IPLC, while the primal FNLPs are solved with existing Nonlinear Programming (NLP) solvers. The main features of this approach are discussed with an illustrative example: an isothermal Continuously Stirred Tank Reactor (CSTR) network with recycle and autocatalytic reaction. The new methodology does not guarantee global optimality; however, the results show that it can find a local solution in a short computational time. Graphical abstract: Image, graphical abstract