Michael Ferris, professor of Computer Sciences, Industrial & Systems Engineering, Mathematics and the theme leader of WID’s Optimization group, has recently been honored as a Fellow at the Society for Industrial and Applied Mathematics (SIAM).
Though Ferris has been a member of the organization for many years, he says the honor recognizes what he’s been able to accomplish with the support of SIAM.
“In my career, I focus on bringing good, rigorous, theoretically-based mathematics and computer science to industrial practice,” Ferris says. “SIAM has been influential in helping me do that.”
Ferris’ years of collaboration and work in solving “complementarity” problems were acknowledged as a part of the award.
Basically, complementarity models “either-or” constraints that are common in nature and physics.
“In some cases, people use complementarity as a way to portray contact mechanics,” Ferris says. “For instance, in video games, when an object falls on a table, it can’t penetrate the table.”
Behind the video game is a mathematical model which has to change dramatically when the object is no longer falling and actually makes contact with the table. Complementarity algorithms are especially useful to the programmer building the game since they encode the change in the underlying physics when the gap between objects becomes zero and when the objects rebound from impact. The results of these models allow the video to appear more natural during contact, Ferris says.
Since Ferris began working on the topic in 1994, he’s expanded his studies to include more problem types. His applications work has influenced approaches in economics and industry.
Unlike other optimization problems with a top-down approach in which actions in a group are orchestrated by one entity, complementarity problems can involve multiple entities, each with its own behavior and desired outcome.
“Complementarity looks at the trade offs between different agents,” Ferris says. “It allows you to generate a system with multiple agents making individual decisions.”
A recent collaboration with the Great Lakes Bioenergy Research Center is one example that draws from Ferris’ work on complementarity. The group created a simulation to track the decision-making of different parties during biofuel production.
Ferris says he’ll continue working on complementarity problems that involve designing, modifying or engineering incentives for multiple agents to solve individual optimization problems to support a common goal.