# Bilevel Optimization based on Iterative Approximation of Multiple Mappings

## TL;DR

This paper introduces an evolutionary optimization method for bilevel problems that reduces computational costs by iteratively approximating key mappings, showing significant performance improvements over existing methods.

## Contribution

It presents a novel combined theory-based and population-based approach using mappings for bilevel optimization, which has not been previously proposed.

## Key findings

- Significant performance gains over existing algorithms
- Effective approximation of lower level mappings
- Validated on numerous test problems

## Abstract

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.