2025 AIChE Annual Meeting

(390aq) Superstructure Optimization with Kkt-Hpinn Surrogate Embedded

Authors

Zachary Rasmussen - Presenter, University of Utah
Hao Chen, Purdue University
Superstructure optimization is a systematic approach for process design and synthesis, which solves the optimal process structure and operational conditions simultaneously. A superstructure captures all possible combinations of process units as a network, formulated by interconnection equations and separate unit models. However, its practical application is significantly limited by the physics behind the process units, which are typically governed by nonlinear nonconvex algebraic equations. This often leads to nonconvex mixed-integer nonlinear programming (MINLP) problems that are computationally expensive to solve. Consequently, data-driven surrogate models have been widely explored to replace high-fidelity models of process units and reduce their complexity [1-5].

Among these surrogate models, neural networks have gained significant attention due to their strong expressivity, and mixed-integer programming (MIP) formulations have been developed to embed them into optimization models [6, 7], as demonstrated by various process system engineering (PSE) applications, including fermentation process, compressor plant, cumene process [8], integration of chemical plants [9], and extractive distillation [10]. These case studies focus primarily on optimizing operational conditions with a fixed process structure, and the integration of neural network with superstructure optimization is less studied [11]. This is potentially because neural networks are purely data-driven, which can result in poor extrapolation on unseen instances that are outside the training data distribution and cause cascading errors through interconnected surrogate models [9]. To further leverage prior knowledge, the physics-informed neural networks (PINNs) have been studied to incorporate physics into the loss function as soft constraints [12]. In our prior work, we developed KKT-hPINN, an architecture that employs non-trainable projection layers to strictly enforce additional linear equality constraints. Unlike other PINNs, KKT-hPINN exhibits superior predictive accuracy and, more importantly, ensures that conservation laws are consistently satisfied across all modeled process units [13].

In this work, we examine the integration of KKT-hPINN with superstructure optimization for a distillation column sequence and a heat exchanger network. In these case studies, nonideal thermodynamics, kinetics, and transport properties, as well as capital and operational costs associated with the system, are simulated using high-fidelity models in Aspen and modeled by KKT-hPINN. A traditional neural network counterpart, as proposed in [11], is used as a baseline for comparison, and the resulting surrogate models are then embedded into the superstructure optimization framework. Numerical results indicate that KKT-hPINN is statistically significant in reducing error in the linearly constrained predictions when compared to a traditional neural network, and the formulation embedded with KKT-hPINN results in faster solution time in the branch-and-bound algorithms.

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