(591c) A Hybrid Stochastic/Gradient-Based Multi-Objective Dynamic Optimization of Vacuum Swing Adsorption

Keywords Bayesian optimization, gradient-free
optimization, gradient-based optimization

Abstract

A two-step approach to complex dynamic multi-objective
optimization problems is proposed. In the first step, a Bayesian
multi-objective optimization algorithm, i.e., Thompson Sampling Efficient
Multi-Objective (TS-EMO) [1], searches the domain globally and approximates a
Pareto front. TS-EMO uses an adaptive sampling technique that generates inputs
for the dynamic simulations. The algorithm builds Gaussian process surrogate
models to approximate the input-output relationship and maximizes a
multi-objective acquisition function to identify the next query point. In the
second step, a local sequential dynamic optimization method, as implemented in
DyOS [2], is initialized at the approximate Pareto points obtained in the first
step and improves the solutions generated from the full set of process models
until local optimality is reached. This two-step approach is then applied to
dynamic optimization of a vacuum swing adsorption (VSA) process.

Stochastic simulation-based optimization has already been reported
for VSA in the literature [3], but the long-time simulation until cyclic steady
is time-consuming and the stochastic approaches typically cannot guarantee (local)
optimality. In the literature, an approach to discretize both temporal and
spatial domains was developed [4,5], but this method generates a large NLP
system, which is expensive for multi-objective optimization.

Our proposed hybrid method performs stochastic multi-objective
optimization in a wide decision domain; the adaptive sampling technique helps to
identify effective input datasets and to avoid unnecessary simulations.
Furthermore, the second step relies on the full model and accurately optimizes
the VSA locally. As shown in Figure 1, several iterations (100 data inputs are
given for each iteration) of TSEMO fail to improve the Pareto front, while the
combination of 1 iteration of TSEMO followed by gradient optimization in DyOS gives
an improved set of solutions.

Figure 1. Pareto solutions
for optimal CO₂ recovery and purity, generated by TSEMO and DyOS.

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E., Schweidtmann M. A., Lapkin A. Efficient multiobjective optimization
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2.       Caspari, A., Hannemann-Tam, R., Bremen, A., Faust M. M. J., Jung,
F., Kappatou, D. C., Sass, S., Vaupel, Y., Mhamdi, A., Mitsos, A. A Framework
for Optimization of Large Scale Differential Algebraic Equation Systems. 29^th European Symposium on Computer-Aided
Process Engineering (ESCAPE-29) 2019

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I. A., & Amanullah, M.
Industrial & Engineering Chemistry Research 2013 52 (11), 4249-4265

4.      
Agarwal, A., Biegler, L. T., & Zitney, S. E.
Industrial & Engineering Chemistry Research 2008 48 (5):
2327-2343.

5.       Tsay, C., Pattison, R. C., & Baldea, M. AIChE Journal 2018 64 (8), 2982-2996.