Industrial engineering students at the University of Wisconsin-Madison who are interested in learning the basics of optimization—mathematical techniques that can solve problems such as choosing the quickest route from point A to point B—can sign up for one of two introductory courses in the discipline.
PhD students who want to delve deep into the theory behind the full range of optimization models can choose from a series of upper-level courses.
Professor Jim Luedtke saw a gap between those two ends of the optimization knowledge spectrum.
“There wasn’t really a good course for trying to advance the practice of optimization beyond the introductory courses,” says Luedtke, whose work in optimization informs topics such as energy management and cybersecurity. “Most of our students are going into industry, and they’re not necessarily interested in the theory. But some of them want to learn how to use these tools to solve problems that are more challenging than what they see in the introductory courses.”
So, Luedtke created a course, ISyE 603: Advanced Optimization Modeling, to build on students’ basic knowledge of optimization, teach them to apply more advanced modeling techniques and introduce them to real-world considerations like prioritizing computational efficiency. Having launched in spring 2024, it’s open to undergraduates all the way up to PhD students.
Luedtke says he doesn’t know of a similar course at any other university. The class is also unique in that it doesn’t include a traditional exam; Luedtke says the nature of the advanced modeling work, along with writing code and implementing models in software, doesn’t lend itself to an exam format.
Instead, students work through models for challenges—such as power generation and distribution—in class and implement those models using the modeling language JuMP in their homework assignments. They learn to reformulate their models in ways that are easier to solve in existing software.
“Most of the cases, we have limited computational resources or face large amounts of data. How are we going to do that? This course blends in that idea and gives us some techniques to solve that,” says Eddy Yeung, a senior. “It’s really useful.”
Luedtke also added a final project for the spring 2025 semester, allowing students to apply their enhanced optimization skills to a topic of their interest. Kaitlyn Campbell, who’s enrolled in the accelerated industrial engineering master’s program in systems engineering and analytics, studied aerospace engineering as an undergraduate at the University of Florida and hopes to one day work in the aerospace industry. Her group is working on a model to plan flight routes for drones to minimize energy loss from drag while flying to a set of locations.
“It has been a very comprehensive class,” says Campbell. “It’s definitely a significant step up from the introductory course, but at the same time, I feel like Professor Luedtke has made the concepts very digestible and approachable and also very motivated in the real-world applications of all the things we’re doing. So it’s not just complexity for the sake of complexity, but it’s really a focused and intentional walkthrough of solving different problems.”
Photos: Joel Hallberg