# Bilevel Optimization based on Iterative Approximation of Multiple Mappings

arXiv: https://arxiv.org/abs/1702.03394 · HTML: https://mlsanity.com/paper/1702.03394/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Feb 2017.

## Built on by (most cited first, 5 of 5)

- [Fast Continuous and Integer L-shaped Heuristics Through Supervised Learning](https://mlsanity.com/paper/2205.00897/) (2022)
- [Neur2BiLO: Neural Bilevel Optimization](https://mlsanity.com/paper/2402.02552/) (2024)
- [Bilevel Optimization for Neural Architecture Search](https://mlsanity.com/paper/2606.29582/) (2026)
- [A Linear Programming Enhanced Genetic Algorithm for Hyperparameter Tuning in Machine Learning](https://mlsanity.com/paper/2407.00613/) (2024)
- [CR-BLEA: Contrastive Ranking for Adaptive Resource Allocation in Bilevel Evolutionary Algorithms](https://mlsanity.com/paper/2506.06362/) (2025)

## Abstract (arXiv)

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.