Optimal design of superstructures for placing units and streams with multiple and ordered available locations. Part I: A new mathematical framework

摘要

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.