Bilevel optimization is commonly used by researchers and business professionals to determine their next move based on data from another hierarchical source. However, there is currently less standard practice for using this model, especially when it involves discrete decision-making.
University of Michigan Industrial and Operations Engineering (U-M IOE) Associate Professor Ruiwei Jiang hopes to standardize bilevel optimization with his recent grant awarded from the Air Force Office of Scientific Research.
“We hope to come up with a new library of testing algorithms and instances for bilevel optimization involving discrete decision variables,” said Jiang. “This type of optimization is receiving a lot of growth in interest but there are relatively less testing instances that everyone can try to use, whether that is a researcher or a practitioner.”
Bilevel optimization, as the name suggests, refers to mathematical models involving two decision-makers located in two different intertwined hierarchies. Decisions are made in a sequential manner in which the leading decision, named the leader, first makes a decision and then the second decision, named the follower, follows with its own decision based upon the leader’s decision-making. In this type of problem-solving when the leader makes a decision most anticipate how the follower will react and vice versa.
A classic example of bilevel optimization can be seen in competition decision-making between businesses. Imagine that there are two major players in a certain commodity and they need to decide where to locate their stores. Typically they would solve this problem in a sequential manner by identifying where their competitors are and then following with their own decision.
The goal of this work is to address the properties of this type of optimization and establish a computational algorithm for solving them more effectively. This will be used to develop a software package that people can use to solve their own bilevel optimization problems in many industry and research settings involving discrete decision-making.
This project titled “Theories and Computational Algorithms for Optimizing Bilevel Mixed-integer Nonlinear Programs” is projected to be completed in the early spring of 2026.