【Title】Solving Stochastic Bilevel Integer Programs Using Value Functions
【Speaker】Junlong Zhang, Ph.D. Candidate, Department of Industrial & Systems Engineering, North Carolina State University
【Host】Dr. Hai Jiang
【Time】16:00–17:00, March 29th, 2018
【Location】 Room N412 , Shunde Building
 
【Abstract】This talk addresses applications of value functions in optimizing stochastic bilevel integer programs in which the uncertainty only appears in the right-hand sides of the lower-level problem. When solving such problems, many similar bilevel integer programming (BIP) subproblems are required to be solved. Optimizing these BIP subproblems directly one by one often consumes too much computing time. To overcome this difficulty, we compute and store the value functions of bilevel integer programs in advance and use them as a lookup table. Specifically, we derive structural properties of the value functions of bilevel integer programs. Most notably, we propose a level-set characterization of the BIP value functions and show that they can be described by using only the bilevel minimal vectors. Based on the derived properties, we develop efficient approaches to construct the BIP value functions. The constructed value functions are then utilized in a global branch-and-bound algorithm to solve the considered class of stochastic bilevel integer programs through a value function reformulation.
 
【Short Bio】Junlong Zhang is currently a Ph.D. candidate in the Department of Industrial & Systems Engineering at North Carolina State University. He received a bachelor's degree in Automation from Northwestern Polytechnical University, Xi'an, China, and a master's degree in Transportation from the Hong Kong Polytechnic University. His research interests are in methodologies and applications of stochastic optimization, bilevel programming and integer programming. His Ph.D. work focuses on value functions of integer programs and their applications in solving stochastic nonlinear integer programs and stochastic bilevel integer programs. He is a member of INFORMS and IISE, and serves as reviewers for journals including European Journal of Operational Research and Journal of Advanced Transportation.
 
All interested are welcome!