Bilevel optimization

Bilevel mixed integer programming (BMIP) models hierarchical decision-making in which a leader anticipates the optimal response of one or more followers, with integer restrictions at one or both levels. BMIPs are important because they capture strategic interactions arising in many real-world systems while posing substantial computational challenges, making them an active area of optimization research. Representative applications include interdiction, pricing, network design, facility location, energy markets, and resource allocation. State-of-the-art solution methodologies primarily include branch-and-bound, branch-and-cut with valid inequalities, single-level reformulations, and problem-specific decomposition algorithms. Because of their integer restrictions, standard single-level reformulations can be challenging; therefore, advanced algorithms are needed for large-scale, problem-specific problems. My current work focuses on single-leader-multi-follower bilevel mixed integer programming problems, designing a decomposition-based algorithm for resource allocation problems with use cases in government incentive optimization. By validating the algorithm using computational experiments, the results demonstrate promising potential for large-scale government incentive optimization problems.