Multi-objective Optimization and Bilevel Optimization under Uncertainty

Many real word problems, such as transportation system planning problems and network design problems, usually involve multiobjective or bilevel optimization problems with uncertain environments. These problems need to be addressed. This research will focus on two such important problems: (1) the dynamic multiobjective optimization problem and (2) stochastic bilevel optimization problem. For the static multiobjective optimization problem, much research exists; however, the dynamic one is a very hard problem and there are only a few studies. The investigators will try to design efficient algorithms for this problem. The stochastic bilevel optimization problem often arises in the fields of economics and computer science, among others, and it is a strongly NP-hard problem. Most research has focussed on the linear bilevel problem, and the research on the nonlinear or stochastic bilevel optimization problem is very limited. The researchers plan to address the stochastic bilevel optimization problem by proposing some new effective algorithms.