(3bk) Modern Computational Approaches to Nonlinear Discrete Optimization and Their Application to Process Systems Engineering

Optimization problems in Chemical Engineering and Process Systems Engineering (PSE) can be expressed with algebraic equations and decision variables, and solved via mathematical programming. When some of the variables are required to have discrete values, the model becomes a mixed-integer program and if the objective and/or constraints are nonlinear, we have a Mixed-integer Nonlinear Program (MINLP) [1]. Usually, the integer variables are used to model discrete choices, which can be enclosed as logical disjunctions in the Generalized Disjunctive Programming (GDP) framework.

Optimization problems that can be expressed as MINLPs and GDPs have many applications in PSE including process operations, like planning and scheduling, process control and synthesis design, and molecular design. These applications are not exclusive of PSE since it has been successfully used in areas like medicine, civil engineering, and economics [2].

I have an interest in the different solution methods and applications of MINLP and GDP problems focused on chemical engineering. Efficient solution methods include both novel algorithms with rigorous mathematical guarantees and practical computer implementations. We have proposed new algorithms for this broad family of problems [3-5] and provided both commercial [6] and open-source [7, P2] implementations of them.

The complexity of the resulting problems often requires developing tailored algorithms for specific applications that involve a deep understanding of the application itself and the mathematical structure of the resulting model. Considering this, we have developed and published specialized algorithms for refinery planning and scheduling, and catalytic distillation design [8-11]. Developing these tailored algorithms for special applications is another topic that I am interested in.

An area that I am also interested in is quantum computing and its potential to address complex problems relevant to PSE. My background in physics and chemical engineering, together with my research experience provides me with a privileged position to address this interesting topic. The results of this research will be presented at this conference [P1].

Research Experience

During my Ph.D., I have been involved in the Center for Advanced Process Decision Making (CAPD) at the Chemical Engineering Department at Carnegie Mellon University. My main research area is the development of algorithms for discrete nonlinear problems with applications in PSE, under the supervision of Prof. Ignacio Grossmann. Being part of the CAPD has allowed me to collaborate with colleagues in other departments within CMU, different private [P3, 8], national laboratories [P2, 12], and other universities.

Moreover, I have started a new branch in my research by assessing the advantages of quantum computing algorithms for the solution of challenging integer optimization problems in collaboration with Prof. Sridhar Tayur from the CMU Business School. I became a member of the CMU Quantum Computing group and the liaison of this group at the Pittsburgh Quantum Institute (PQI). This project has allowed me to study the possible applications of quantum computing for optimization problems in PSE [P1].

Teaching Experience and Interests

I am committed to excellence in teaching and I keep pushing to become better every day. For this reason, I have joined the Future Faculty Program at the Eberly Center for Teaching Excellence & Educational Innovation at CMU.

In the fall 2020 semester, I am teaching together with Prof. Sridhar Tayur from the CMU Tepper School of Business and Dr. Davide Venturelli from USRA the lecture Quantum Integer Programming (47-779) as main lecturer. This is the first time this lecture is taught, and I have been involved in the complete course design process, including syllabus, slides, and teaching material creation.

During my Ph.D. I have been the teaching assistant for the Ph.D. level Special Topics: Disjunctive Programming (6-805) lecture taught by Prof. Egon Balas†, the Ph.D. level Advanced Process Systems Engineering (6-720) taught by Prof. Ignacio Grossmann, and twice for the undergraduate level Process Design (6-421) taught by Prof. Ignacio Grossmann. I was awarded the Teaching Assistant Mark Denis Karl award from the Chemical Engineering department in 2019.

I have been invited to teach seminars and tutorials on Mixed-integer programming and open-source optimization modeling languages at the Universidad Nacional del Litoral in Santa Fe (2018), Argentina and the Northeastern University in Shenyang, China (2019).

As part of my M.Sc. degree at the Universidad de los Andes, I taught recitations for the Chemical Processes Optimization lecture and the Chemical and Thermodynamic Equilibrium lecture. I was also an undergraduate teaching assistant for different classes in the Chemical Engineering, Physics, and Mathematics departments.

With my teaching experience and background in chemical and systems engineering, I am well-suited for the instruction of a wide range of undergraduate and graduate subjects. I would be particularly interested in courses related to the use of computational tools for Chemical and Process Engineering. I would enjoy as well as developing courses focusing on Process Modeling and Optimization and also in Quantum computing applications.

Future Direction

As faculty, I aim to lead a Process Systems Engineering research group in a Chemical Engineering department. This group would use tools from mathematical optimization and computer science to solve problems relevant to chemical engineering applications while also tackling fundamental questions in optimization theory. The group’s work must rely heavily on the use of core chemical engineering principles and advanced computational algorithms and architectures to enhance decision making in complex engineering systems.

As a short-term direction, I consider that the usage of logical- and discrete-based algorithms for decision making is a promising field I would like to be involved in. These algorithms rely especially on methods for MINLP and GDP. Besides its many applications, the computational challenge that these complex optimization problems pose is one that I have spent my graduate research time and would enjoy working on them during my career.

In a longer time-horizon, I want to keep exploring the usage of new computer architectures to solve challenging and relevant problems for Chemical Engineering. The availability of larger amounts of data and more complex models requires constant improvement in the solution methods of optimization problems. Although the classical computer architecture has been successful so far, more challenging instances require specialized hardware to allows for practical solution methods. In particular, the design and application of algorithms for Quantum Computers and Coherent Ising Machines is one topic that I am excited to work in the upcoming years.

Presentations at the current AIChE Annual Meeting

[P1] Use of Quantum Computing to Solve Optimization Problems in Process Systems Engineering. Bernal, D.E. and Grossmann, I.E. Session: CAST Director's Student Presentation Award Finalists.

[P2] Pyomo.GDP: An Ecosystem for Logic-Based Modeling and Optimization Development. Chen, Q., Bernal, D.E., Johnson, E., Valentin, R., Kale, S., Bates, J., Siirola, J.D., and Grossmann, I.E. Session: Software Tools and Implementations for Process Systems Engineering.

[P3] Sample Average Approximation for Stochastic Nonconvex Mixed-Integer Nonlinear Programming Via Outer Approximation. Li, C., Bernal D.E., Furman, K.C. and Grossmann, I.E. Session: Design and Operations Under Uncertainty.

Selected Recent Publications

[1] Bernal, D.E., (2019) On Solving Convex Mixed-integer Nonlinear Programs, Ph.D. Thesis Proposal, Carnegie Mellon University. Available online at https://bit.ly/proposal_deb

[2] Kronqvist, J., Bernal, D.E., Lundell, A. and Grossmann, I.E., (2018). A Review and Comparison of Solvers for Convex MINLP. Optimization and Engineering vol: 20 pp:397-455.

[3] Kronqvist, J., Bernal, D.E., Grossmann, I.E., (2018) Using Regularization and Second Order Information in Outer Approximation for Convex MINLP. Mathematical Programming.

[4] Kronqvist, J., Bernal, D.E., Lundell, A., Westerlund, T., (2018). A Center-Cut Algorithm for Quickly Obtaining Feasible Solutions and Solving Convex MINLP Problems. Computers & Chemical Engineering 2018.

[5] Su, L., Tang, L., Bernal, D.E., Grossmann, I.E., (2017). Improved quadratic cuts for convex mixed-integer nonlinear programs. Computers & Chemical Engineering 2018 vol: 109 pp: 77-95.

[6] Bernal, D.E., Vigerske, S., Trespalacios, F., Grossmann, I.E., (2019). Improving the performance of DICOPT in convex MINLP problems using a feasibility pump. Optimization Methods and Software.

[7] Bernal D.E., Chen, Q., Gong, F., Grossmann, I.E. Mixed-integer Nonlinear Decomposition Toolbox for Pyomo (MindtPy). 13th International Symposium on Process Systems Engineering PSE 2018.

[8] Yang, H., Bernal, D. E., Franzoi, R. E., Engineer, F. G., Kwon, K., Lee, S., & Grossmann, I. E. (2020). Integration of Crude-Oil Scheduling and Refinery Planning by Lagrangean Decomposition. Computers & Chemical Engineering.

[9] Bernal, D.E., Carrillo, C., Gomez, J.M., Ricardez-Sandoval, L.A., (2018). Simultaneous design and control of catalytic distillation columns using rigorous dynamic models. Industrial & Engineering Chemistry Research 57(7), 2587-2608.

[10] Liñán, D. A., Bernal, D. E., Ricardez-Sandoval, L. A., & Gómez, J. M. (2020). Optimal design of superstructures for placing units and streams with multiple and ordered available locations. Part I: A new mathematical framework. Computers & Chemical Engineering, 106794.

[11] Liñán, D. A., Bernal, D. E., Ricardez-Sandoval, L. A., & Gómez, J. M. (2020). Optimal design of superstructures for placing units and streams with multiple and ordered available locations. Part II: Rigorous design of catalytic distillation columns. Computers & Chemical Engineering, 106845.