bi-levelprogramming 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. Th...
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bi-levelprogramming 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. (c) 2021 Elsevier Ltd. All rights reserved.
In this paper, the problem of solving mixed integer bi-level programming problems is discussed. The proposed algorithm is based on the multi-parametric algorithm that using bisection cutting plane techniques to improv...
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In this paper, the problem of solving mixed integer bi-level programming problems is discussed. The proposed algorithm is based on the multi-parametric algorithm that using bisection cutting plane techniques to improve bounds. In fact the paper examines the nature of the so-called separation problem, which is generating a valid inequality arising as the solution to the current sub problem of the multi-parametric algorithm. Some examples are provided to demonstrate the algorithm and evaluate its performance.
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