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arXiv · 1809.10448

Solving Linear Bilevel Problems Using Big-Ms: Not All That Glitters Is Gold

Salvador Pineda·Juan Miguel Morales
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Abstract

The most common procedure to solve a linear bilevel problem in the PES community is, by far, to transform it into an equivalent single-level problem by replacing the lower level with its KKT optimality conditions. Then, the complementarity conditions are reformulated using additional binary variables and large enough constants (big-Ms) to cast the single-level problem as a mixed-integer linear program that can be solved using optimization software. In most cases, such large constants are tuned by trial and error. We show, through a counterexample, that this widely used trial-and-error approach may lead to highly suboptimal solutions. Then, further research is required to properly select big-M values to solve linear bilevel problems.

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Salvador Pineda, Juan Miguel Morales. 2018-09-27. Solving Linear Bilevel Problems Using Big-Ms: Not All That Glitters Is Gold. https://arxiv.org/abs/1809.10448

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