We might not realize it, but anytime we pack a travel bag, we’re entering the world of optimization.
Every item that goes in bears a volume and a value—and there’s only so much room. This “knapsack problem” is a classic puzzle in combinatorial optimization, a field that seeks the best possible solutions to problems with finite sets of options.
And it’s a conundrum that Carla Michini, the newest faculty member in the Department of Industrial and Systems Engineering at the University of Wisconsin-Madison, takes seriously.
“I am a packing expert,” Michini, who joined the department as an assistant professor in fall 2018, says with a smile.
Of course, Michini’s expertise extends beyond optimally packing her sisters’ suitcases when they visit Madison from her family’s native Italy. Michini works on the theoretical side of combinatorial optimization, examining the structures of problems to identify efficient algorithms that will yield optimal—or near-optimal—solutions.
“I like the rigorous kind of reasoning of math in general, the beauty of simple questions that are hard to answer and the depth of thinking that makes me discover new properties. And, of course, I enjoy the fun and the reward of coming up with my own theorems,” says Michini, who used to tutor her high school classmates in Roseto degli Abruzzi, Italy, so that they could cover more advanced material in class. “It’s a very creative process.”
While she’s new to the Department of Industrial and Systems Engineering, she’s been on campus for the past four years as a postdoctoral associate at the Wisconsin Institute for Discovery.
There, she worked in WID’s optimization group, where she collaborated with future ISyE colleagues Jeffrey Linderoth and James Luedtke and Professor of Computer Sciences Michael Ferris on problems with applications ranging from power networks to traffic congestion to programming languages.
Now she plans to expand her expertise to questions in the field of game theory.
“Instead of looking at a single combinatorial optimization problem, I am interested in a game theoretical framework where there are several players: each player wants to solve his or her own optimization problem, and the decisions of one player influence the decisions of the other players,” she says. “For example, in a road network where there’s congestion, each player wants to go from a certain origin to a certain destination in the shortest possible amount of time. The strategies of each player are all the routes from origin to destination, but the time required to travel each road segment depends on how many players are using it.”
Michini is also excited to interact more with students in her new role, after teaching Linear Programming Methods during the spring 2018 semester.
“My goal is to help the students to develop the skill of thinking in a rigorous way, and hopefully a passion for it,” she says. “One of the most rewarding aspects of teaching is to see the progress of a student gaining a deep understanding of a topic. My ultimate goal in teaching is to inspire the students to learn the subjects that I am passionate about, and to motivate them to work hard.”