A reformulation strategy for mixed-integer linear bi-level programming problems

•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. [Dis...

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Bibliographic Details
Published in:Computers & chemical engineering Vol. 153; p. 107409
Main Authors: Medina-González, Sergio, Papageorgiou, Lazaros G., Dua, Vivek
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.10.2021
Subjects:
Lower-level discrete variables
Mixed integer bi-level programming
Nonlinear reformulation
Nonlinear reformulation
Lower-level discrete variables
Mixed integer bi-level programming
ISSN:0098-1354, 1873-4375
Online Access:Get full text
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Summary:•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.
ISSN:0098-1354
1873-4375
DOI:10.1016/j.compchemeng.2021.107409