Solving Linear Bilevel Problems Using Big-Ms: Not All That Glitters Is Gold
Optimization and Control
2018-09-28 v1
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.
Cite
@article{arxiv.1809.10448,
title = {Solving Linear Bilevel Problems Using Big-Ms: Not All That Glitters Is Gold},
author = {Salvador Pineda and Juan Miguel Morales},
journal= {arXiv preprint arXiv:1809.10448},
year = {2018}
}