Evolutionary bilevel optimization using KKT proximity measure

Bilevel optimization problems are often reduced to single level using Karush-Kuhn-Tucker (KKT) conditions; however, there are some inherent difficulties when it comes to satisfying the KKT constraints strictly. In this paper, we discuss single level reduction of a bilevel problem using approximate KKT conditions which have been recently found to be more useful than the original and strict KKT conditions. We embed the recently proposed KKT proximity measure idea within an evolutionary algorithm to solve bilevel optimization problems. The idea is tested on a number of test problems and comparison results have been provided against a recently proposed evolutionary algorithm for bilevel optimization. The proposed idea leads to significant savings in lower level function evaluations and shows promise in further use of KKT proximity measures in bilevel optimization algorithm development.

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