Making decisions in high-pressure situations is something every general in the United States Army faces while leading troops. If they encounter a problem, they usually need multiple solutions to help form a strategy. It could be a matter of life and death.
That challenge was foremost in the mind of Izuwa Ahanor (PhD/ISE ’23) during his graduate research with ISE Professor Hugh Medal. Ahanor created DiversiTree, a new method for generating diverse sets of near optimal solutions to mixed-integer optimization problems. 
The research study, which was supported by the Army Research Office, represented a different way of thinking about optimization models. Typically, people use optimization models to find a single solution.
“However, models are, by definition, an approximation of reality, so the solution to the model may not be a perfect fit for the real problem,” Medal said. “Thus, it can be useful to provide a decision-maker with a set of solutions that are close to optimal and let them choose which one they prefer.”
DiversiTree’s method, which can be easily incorporated into integer programming solvers, emphasizes diversity within the search for near-optimal solutions. The method showed diversity improvement between 12-190% with a similar runtime as a regular node selection method. Research has shown that having a diverse set of solutions can lead to improved outcomes.
“While optimizers like SCIP can provide a set of near-optimal solutions, they fall short when you need a small yet diverse subset of these solutions—say, 10 solutions,” Ahanor explained. “The existing methods tend to generate solutions that cluster within a narrow part of the solution space, often selecting solutions from a single branch of the search tree. This means the solutions they offer aren’t very distinct from one another. That’s where our approach stands out—our method focuses on generating solutions that are truly diverse, covering a broader range of possibilities.”
Valuable Skill Set
The research study required the team to work with SCIP, a software that allows modifications to its core functionality using C and C++. Ahanor, who earned his bachelor’s degree in computer science from the University of Benin in Nigeria, collaborated closely with his advisors, Dr. Hugh Medal and Dr. Andrew Trapp, to implement and test DiversiTree in SCIP. The group’s efforts have culminated in the release of an open-source version of DiversiTree, now available on Github.
“The project was a good balance of mathematical optimization and coding, requiring us to delve deep into C++ to make specific changes to SCIP,” said Ahanor. “Given my background in computer science, I think my supervisors saw this as a great way to leverage my programming skills. I found the combination of coding with the practical application of mathematical optimization both challenging and rewarding.”
Ahanor is employed as a machine learning engineer for Stripe, a financial infrastructure platform for businesses. However, he hasn’t stopped working on the research project. The group is currently trying to implement the DiversiTree method into machine learning.
“We were looking for even faster ways to do what we had done. We wanted to increase the speed of generating those diverse new optimal solutions,” Ahanor said. “Using machine learning and graph neural networks was the next step.”
Contact
Rhiannon Potkey (865-974-0683, rpotkey@utk.edu)