Improving Convergence Reliability of Chemical Process Flowsheet Optimization using Surrogate Models and Implicit Functions

Core Concepts

Surrogate models and implicit function formulations can significantly improve the convergence reliability of chemical process flowsheet optimization problems compared to the full-space formulation, with a trade-off between solution accuracy and solve time.

Abstract

The paper presents alternative formulations for the optimization of chemical process flowsheets that leverage surrogate models and implicit functions to replace and remove, respectively, the algebraic equations that describe a difficult-to-converge Gibbs reactor unit operation. The authors compare the convergence reliability, solve time, and solution quality of an optimization problem among full-space, ALAMO surrogate, neural network surrogate, and implicit function formulations.
The key findings are:

Both surrogate and implicit function formulations lead to better convergence reliability compared to the full-space formulation, with low sensitivity to process parameters.
The surrogate formulations are faster at the cost of minor solution error, while the implicit function formulation provides exact solutions with similar solve time.
In a parameter sweep on the autothermal reformer flowsheet optimization problem, the full-space formulation solves 33 out of 64 instances, the implicit function formulation solves 52 out of 64 instances, the ALAMO polynomial formulation solves 64 out of 64 instances, and the neural network formulation solves 48 out of 64 instances.
The ALAMO surrogate formulation is the most reliable, while the implicit function formulation may be preferred when solution accuracy is critical or when generating enough simulation data to train an accurate surrogate model is computationally prohibitive.

The authors demonstrate the trade-off between accuracy and solve time that exists in current methods for improving convergence reliability of chemical process flowsheet optimization problems.

Stats

The full-space formulation solves 33 out of 64 instances.
The implicit function formulation solves 52 out of 64 instances.
The ALAMO polynomial formulation solves 64 out of 64 instances.
The neural network formulation solves 48 out of 64 instances.

Quotes

"Both surrogate and implicit function formulations lead to better convergence reliability, with low sensitivity to process parameters."
"The surrogate formulations are faster at the cost of minor solution error, while the implicit formulation provides exact solutions with similar solve time."

Key Insights Distilled From

Process flowsheet optimization with surrogate and implicit formulations of a Gibbs reactor

by Sergio I. Bu... at arxiv.org 04-23-2024

https://arxiv.org/pdf/2310.09307.pdf

Deeper Inquiries

How can the training of surrogate models be further optimized to reduce computational cost while maintaining high accuracy

Training surrogate models can be optimized to reduce computational costs while maintaining high accuracy by implementing more efficient sampling techniques, such as Latin Hypercube Sampling. This method ensures a smaller and more representative dataset of the entire experimental region, potentially leading to higher solution accuracies. Additionally, utilizing advanced optimization algorithms for hyperparameter tuning can streamline the training process and improve the efficiency of surrogate model development. By carefully selecting the hyperparameters and activation functions, the training time can be minimized without compromising the accuracy of the surrogate models. Moreover, leveraging parallel computing resources can significantly speed up the training process by distributing the computational workload across multiple processors or nodes.

What are the potential limitations or drawbacks of the implicit function formulation, and in what types of chemical processes would it be most advantageous to use

The implicit function formulation, while offering improved convergence reliability in certain scenarios, may have limitations and drawbacks. One potential limitation is the need for a non-singular Jacobian (∇yR) for all values of state and input variables, which may not always be feasible in highly complex chemical processes with nonlinear dynamics. Additionally, the implicit function formulation requires solving a square system of equations at every iteration, which can be computationally intensive and may lead to increased solve times compared to other formulations. This approach may be most advantageous in chemical processes where the unit models are well-behaved, and the system of equations can be efficiently solved separately from the main optimization problem. Processes with well-defined and non-singular Jacobians, such as certain reactor systems or separation units, are ideal candidates for the implicit function formulation.

How could the insights from this study be extended to optimize other complex chemical engineering systems beyond just process flowsheets

The insights from this study can be extended to optimize other complex chemical engineering systems beyond process flowsheets by applying similar surrogate and implicit function formulations. For instance, in the design and optimization of multi-component distillation columns, where the system equations are challenging to converge, the implicit function formulation could be beneficial in simplifying the optimization problem and improving convergence reliability. Surrogate models, such as neural networks and ALAMO polynomials, can be utilized to approximate the behavior of intricate unit operations in various chemical processes, enabling faster and more reliable optimization. By adapting the methodologies and strategies employed in this study to different chemical engineering systems, researchers can enhance the efficiency and effectiveness of optimization tasks in diverse industrial applications.