Medina-Gonzalez, S; Papageorgiou, LG; Dua, V; (2021) A reformulation strategy for mixed-integer linear bi-level programming problems. Computers & Chemical Engineering , 153 , Article 107409. 10.1016/j.compchemeng.2021.107409.

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Abstract

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.

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