Journal
IEEE TRANSACTIONS ON POWER SYSTEMS
Volume 34, Issue 3, Pages 2469-2471Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TPWRS.2019.2892607
Keywords
Bilevel programming; optimality conditions; mathematical program with equilibrium constraints (MPEC)
Categories
Funding
- Spanish Ministry of Economy, Industry and Competitiveness [ENE2016-80638-R, ENE2017-83775-P]
- European Research Council under the European Unions Horizon 2020 research and innovation programme [755705]
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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 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 approachmay 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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