My research focuses on various classes of integer programming problems from both theoretical and practical perspectives. I am currently working with multilevel/multistage mixed integer linear optimization problems (MMILPs) and (single-level/single-stage) mixed integer linear optimization problems (MILPs). In the past, I have worked with mixed integer nonlinear optimization problems. I also have experience working with real-world applications such as security constrained unit commitment, automated timetabling generation, and stock layout planning.
This poster depicts an abstract-level overview of my Ph.D. research. I am working on the development of parametric valid inequalities and their application to both MMILPs and MILPs. These inequalities contain dual functions based on duality and the value functions of these problem classes.
For MMILPs, we have developed an abstract framework based on our parametric valid inequalities for generalizing the principles of Benders’ technique for reformulation, specified an associated algorithmic procedure, and applied this procedure to the solution of optimistic mixed integer bilevel linear optimization problems (MIBLPs). We now have a convergent generalized Benders’ decomposition algorithm for solving MIBLPs. We have implemented a vanilla version of this algorithm in MibS, an open-source MIBLP solver written in C++ and part of the COIN-OR project system. We are currently working on multiple enhancements to this vanilla version. We discussed the theoretical component of this work in this paper.
For MILPs, we are working on warm-starting techniques that utilize our parametric valid inequalities to increase the speed of solving this class of problems. Warm starting MILPs will further increase the speed of our algorithm for solving MIBLPs. We are implementing this work in SYMPHONY, an open-source MILP solver written in C/C++ and is part of the COIN-OR project system.