  A large number of application problems involve two levels of optimization,
where one optimization task is nested inside the other. These problems are
known as bilevel optimization problems and have been studied by both classical
optimization community and evolutionary optimization community. Most of the
solution procedures proposed until now are either computationally very
expensive or applicable to only small classes of bilevel optimization problems
adhering to mathematically simplifying assumptions. In this paper, we propose
an evolutionary optimization method that tries to reduce the computational
expense by iteratively approximating two important mappings in bilevel
optimization; namely, the lower level rational reaction mapping and the lower
level optimal value function mapping. The algorithm has been tested on a large
number of test problems and comparisons have been performed with other
algorithms. The results show the performance gain to be quite significant. To
the best knowledge of the authors, a combined theory-based and population-based
solution procedure utilizing mappings has not been suggested yet for bilevel
problems.
