Speaker: Suresh Bolusani
Date & Time: Friday, February 10, 2023, 3:30 pm
Venue: IEOR 211, Seminar Room, 2nd floor, IEOR Building
Abstract: Mixed integer bilevel linear optimization provides a framework for modeling optimization problems involving two independent decision-makers with two possibly conflicting objectives. We present a generalized Benders’ algorithm for solving general mixed integer bilevel linear optimization problems in which continuous and integer variables are present in both first- and second-level problems. We make minimal assumptions, requiring only that first-level variables participating in the second-level problem be integer variables. Like any Benders’ algorithm, the strategy is to project out the second-level variables in order to obtain a reformulation involving only first-level variables. This reformulation involves the so-called reaction function, which is then iteratively approximated. The result is that the master problem is a single-level optimization problem involving only first-level variables, whereas the subproblem is a two-level lexicographic optimization problem resulting from fixing the first-level variables. We solve this latter problem by reformulating it as a mixed integer linear optimization problem and then generate a Benders’ constraint based on the duality and value function of mixed integer linear optimization problems. A Benders’ constraint is added to the master problem in every iteration of the algorithm to strengthen the reaction function approximation. The details of this talk are available in our paper titled “A framework for generalized Benders decomposition and its application to multilevel optimization.”
Short bio: Suresh Bolusani is a postdoctoral researcher at Zuse Institute Berlin, Germany. Before Zuse Institute, he was at Lehigh University, U.S.A., for his Ph.D. studies, at IIT Bombay, India, for his Master's studies, and IIT
Roorkee, India, for his Bachelor's studies. His research focuses on developing and implementing algorithms for (a) solving mixed integer linear optimization and mixed integer bilevel linear optimization problems and (b) warm starting of mixed integer linear optimization problems. He has contributed to the development of various open-source optimization solvers over the years, such as SCIP (a mixed integer linear and nonlinear optimization solver), MibS (a mixed integer bilevel linear optimization solver), SYMPHONY (a mixed integer linear optimization solver), and Minotaur (a mixed integer nonlinear optimization solver).