Title: A Journey from Deterministic to Distributionally Ambiguous Combinatorial Optimization: Theory, Algorithms, and Applications
Speaker: Dr. Manish Bansal, Associate Professor, Grado Department of Industrial and Systems Engineering, Virginia Tech, USA
Day, Date, and Time: Thursday, 1st February 2024, 09:30 am to 10:30 am
Venue: Seminar room IE 211, Second Floor, IEOR Building
Abstract: Combinatorial optimization problems arise in a variety of applications ranging from production planning to power systems, and machine learning to bio-informatics. In many applications, it is critical to make strategic long-term combinatorial planning decisions such as locating emergency healthcare or evacuation centers even with uncertain input data parameters. Integer programming is a powerful method to formulate and solve combinatorial optimization problems, but solving integer programs with large-scale deterministic data can still be computationally expensive. To handle the uncertain data, distributionally robust (or risk-averse) integer programs are gaining attention in the research community. We will begin this seminar with an overview of cutting planes and decomposition methods for solving integer programs and distributionally risk-averse integer programs.
Thereafter, we will discuss interdiction problems – a family of combinatorial optimization problems -- that are characterized as games played between two players: an interdictor and defender. The interdictor is a player who makes interdiction decisions using limited resources to degrade the defender’s performance, and the defender makes decisions after observing the interdiction decision. We will introduce new algebraic modeling frameworks that allow uncertainty in the success and impact of the attacks by an interdictor, adjustments based on risk-appetite (risk-receptiveness or risk-aversion) of the players, and incomplete information of probability distribution associated with uncertain data. We will present computationally efficient cutting planes-based and reformulation approaches for solving these distributionally ambiguous (risk-receptive and risk-averse) programs, along with some computational results.
Bio: Dr. Manish Bansal is an Associate Professor and a Grado Early Career Faculty Fellow with Grado Department of Industrial and Systems Engineering at Virginia Tech. He did Bachelors in Electrical Engineering from National Institute of Technology in India, and M.S. with thesis and Ph.D. from Department of Industrial and Systems Engineering at Texas A&M University. Prior to joining Virginia Tech, he was a postdoctoral fellow in Department of Industrial Engineering and Management Sciences at Northwestern University. His research is focused on the theory of mixed integer programming, stochastic and distributionally ambiguous optimization, game theory, and location science along with their applications in homeland security, logistics, and supply chain management. He has received multiple grants from National Science Foundation, Department of Defense, and Cyber Commonwealth Initiatives. He has published papers in journals such as Discrete Applied Mathematics, SIAM Journal on Optimization, Journal on Global Optimization, and Mathematical Programming, among others. Dr. Bansal has served as president of INFORMS Junior Faculty Interest Group, and currently, he is serving as president of Engineering Faculty Organization at Virginia Tech.