A reformulation strategy for mixed-integer linear bi-level programming problems - Medina-González, Sergio; Papageorgiou, Lazaros G.; Dua, Vivek (Computers & chemical engineering, 2021)
•Convert lower-level mixed-integer formulation to continuous non-linear programming problem.•Formulate optimality conditions for the resulting non-linear programming problem.•Formulate and solve the mixed-integer nonlinear programming problem using global optimization and an iterative strategy. [Display omitted] Bi-level programming has been used widely to model interactions between hierarchical decision-making problems, and their solution is challenging, especially when the lower-level problem contains discrete decisions. The solution of such mixed-integer linear bi-level problems typically need decomposition, approximation or heuristic-based strategies which either require high computational effort or cannot guarantee a global optimal solution. To overcome these issues, this paper proposes a two-step reformulation strategy in which the first part consists of reformulating the inner mixed-integer problem into a nonlinear one, while in the second step the well-known Karush-Kuhn-Tucker conditions for the nonlinear problem are formulated. This results in a mixed-integer nonlinear problem that can be solved with a global optimiser. The computational and numerical benefits of the proposed reformulation strategy are demonstrated by solving five examples from the literature.