We present an algorithm for solving bilevel linear programs that uses simplexpivots on an expanded tableau. The algorithm uses the relationship between multiple objective linear programs and bilevel linear programs a...
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We present an algorithm for solving bilevel linear programs that uses simplexpivots on an expanded tableau. The algorithm uses the relationship between multiple objective linear programs and bilevel linear programs along with results for minimizing a linear objective over the efficient set for a multiple objective problem. Results in multiple objective programming needed are presented. We report computational experience demonstrating that this approach is more effective than a standard branch-and-bound algorithm when the number of leader variables is small.
Bilevel programming (BLP) problems are hierarchical optimization problems having a parametric optimization problem as part of their constraints. From the mathematical point of view, the BLP problem is NP-hard even if ...
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ISBN:
(数字)9783319179964
ISBN:
(纸本)9783319179964;9783319179957
Bilevel programming (BLP) problems are hierarchical optimization problems having a parametric optimization problem as part of their constraints. From the mathematical point of view, the BLP problem is NP-hard even if the objectives and constraints are linear. This paper proposes a cutting plane approach to solve linear BLP problem which is the simplest case of BLP problems. Our approach is based on the idea that is commonly used in computational mathematics: solving a relaxation problem that is easier to solve and giving a tight approximation by introduction of cutting planes. Therefore, by exploring the theoretical properties of linear BLP, we extend the cutting plane approach for solving linear BLP problems. Numerical examples are provided to illustrate the approach.
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