Project Description:

Nonconvex optimization has widespread applications in chemical engineering, power systems, and cybersecurity. Global optimization algorithms have been developed to solve nonconvex problems to global optimality. However, unlike convex optimization problems which have polynomial runtime algorithms, nonconvex optimization is known to be NP-hard to solve in general. Due to its computational complexity, state-of-the-art global optimization algorithms are typically limited to the problem size of thousands of variables. On the hand, modern-day energy system planning and operation problems typically involve hundreds of thousands of variables. Solving these large scale-applications, such as optimal power flow problems, to global optimality can lead to annual energy savings in the magnitude of one billion dollars.

In this project, we plan to use machine learning techniques to accelerate global optimization algorithms. Several decisions in the global optimization algorithms, such as branching variable selection, cutting plane selection, the solution of cut generating linear programs, and selecting and warm-starting convex relaxations, can be improved or replaced by machine learning-based policies. We will leverage the high-performance computing infrastructure at Purdue to accelerate data collection, model training, and testing. The proposed machine learning frameworks will be tested within state-of-the-art open-source global optimization solvers like SCIP by considering applications in chemical and power systems, adjustable robust optimization problems.

Start Date:

Any time after February in 2023

Postdoc Qualifications:

PhD in industrial engineering, operations research, chemical engineering, electrical engineering, applied math, computer science, or related fields.
Research expertise in one or more of the followings areas: linear/nonlinear/mixed-integer programming/machine learning/optimization under uncertainty.
Fluent programming in one of the following programming languages: Python/Julia/C++.

Co-Advisors:

Advisor 1:
Name: Can Li
email: canli@purdue.edu
Affiliation: Davidson School of Chemical Engineering
website: https://canli1.github.io/



Advisor 2:
Name: Mohit Tawarmalani
email: mtawarma@purdue.edu
Affiliation: Krannert School of Management
Website: https://web.ics.purdue.edu/~mtawarma/

Outside Collaborators:

Name: Andrea Lodi
Affiliation: Andrew H. and Ann R. Tisch Professor at the Jacobs Technion-Cornell Institute at Cornell Tech and the Technion
Email: andrea.lodi@cornell.edu

Bibliography:

Bengio, Y., Lodi, A., & Prouvost, A. (2021). Machine learning for combinatorial optimization: a methodological tour d’horizon. European Journal of Operational Research, 290(2), 405-421.

Prouvost, A., Dumouchelle, J., Gasse, M., Chételat, D., & Lodi, A. (2021). Ecole: A library for learning inside milp solvers. arXiv preprint arXiv:2104.02828.


Bonami, P., Lodi, A., & Zarpellon, G. (2018, June). Learning a classification of mixed-integer quadratic programming problems. In International Conference on the Integration of Constraint Programming, Artificial Intelligence, and Operations Research (pp. 595-604). Springer, Cham.

Baltean-Lugojan, R., Bonami, P., Misener, R., & Tramontani, A. (2019). Scoring positive semidefinite cutting planes for quadratic optimization via trained neural networks. preprint: http://www. optimization-online. org/DB_ HTML/2018/11/6943. html.

Ghaddar, B., Gómez-Casares, I., González-Díaz, J., González-Rodríguez, B., Pateiro-López, B., & Rodríguez-Ballesteros, S. (2022). Learning for Spatial Branching: An Algorithm Selection Approach. arXiv preprint arXiv:2204.10834.

Gamrath, G., Anderson, D., Bestuzheva, K., Chen, W. K., Eifler, L., Gasse, M., ... & Witzig, J. (2020). The SCIP optimization suite 7.0.