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.

本研究提出了一种用于化学工程中上部结构优化设计的新方法。与文献中建立的大多数优化技术相反，这种近似方法利用特定类型问题的结构，即需要在自然有序离散集上找到处理单元或流的最佳位置的情况。所提出的方法包括用较小的一组称为外部变量的整数变量来重新构成原始混合整数非线性问题（MINLP）的二进制变量。然后，可以将重新构造的优化问题分解为具有线性约束的主整数程序（主IPLC）和原始子问题，形式为固定非线性程序（FNLP），即固定整数变量的非线性程序（NLP）。主IPLC考虑使用离散最速下降算法（D-SDA），而现有的非线性规划（NLP）求解器可求解原始FNLP。通过一个说明性示例讨论了这种方法的主要特征：具有循环和自动催化反应的等温连续搅拌釜反应器（CSTR）网络。新的方法不能保证全局最优。但是，结果表明它可以在很短的计算时间内找到一个局部解。