# (126d) Data-Driven Optimization with Implicit Constraints: Application to an Ethane Steam Cracking Process

- Conference: AIChE Annual Meeting
- Year: 2018
- Proceeding: 2018 AIChE Annual Meeting
- Group: Computing and Systems Technology Division
- Session:
- Time:
Monday, October 29, 2018 - 1:27pm-1:46pm

The aim of this work is to handle implicit constraints that might exist between the input variables and guide the initial sampling strategy in such a way that the unphysical/numerically unstable combinations of input variables are filtered out, leaving only an appropriate set of samples for simulating the problem. To this end, a supervised machine learning algorithm, Support Vector Machine (SVM) is employed. The problem is formulated as nonlinear SVM classification problem where an optimal hyperplane, separating numerically stable and unstable samples, is built to implement an implicit constraint for the input space. The model is trained and cross-validated using a large set of simulated samples offline, and then incorporated in the AlgoRithms for Global Optimization of coNstrAined grey-box compUTational problems (p-ARGONAUT) [1-3] framework to assess the feasibility of the candidate points *a priori *to sample collection. This methodology has been tested on an ethane steam cracking process, where the continuity, energy and momentum balances are characterized by stiff ODEs in which our objective is to maximize the profitability of operation. The results show that SVM model provides a highly accurate implicit constraint and helps the grey-box optimizer to return feasible profitable solutions to the steam cracking optimization process.

**References**

[1] Boukouvala, F. & Floudas, C.A. ARGONAUT: AlgoRithms for Global Optimization of coNstrAined grey-box compUTational problems. Optimization Letters, 2017, 11:895-913.

[2] Boukouvala, F., Hasan, M.M.F. & Floudas, C.A. Global optimization of general constrained grey-box models: new method and its application to constrained PDEs for pressure swing adsorption. Journal of Global Optimization, 2017, 67:3-42.

[3] Beykal, B., Boukouvala, F., Floudas, C.A., Sorek, N., Zalavadia, H. & Gildin, E. Global Optimization of Grey-Box Computational Systems Using Surrogate Functions and Application to Highly Constrained Oil-Field Operations. Computers & Chemical Engineering, 2018, https://doi.org/10.1016/j.compchemeng.2018.01.005