A Review on Bilevel Optimization Using Evolutionary Algorithms and Machine Learning Approaches
Abstract
Bilevel Optimization (BLO) is a hierarchical problem structure involving two interdependent levels of optimization tasks. While traditionally approached through evolutionary algorithms (EAs), recent advances in machine learning (ML) have introduced scalable and efficient methods that can address high-dimensional and data-driven BLO problems. This review provides a comprehensive survey of the evolution from EA-based to ML-based BLO approaches. We begin by outlining the mathematical foundations and challenges inherent in BLO problems. We then explore traditional EA methods, highlighting their strengths in non-convex, black-box, and simulation-driven contexts. The core focus of the paper is on ML-based bilevel solvers, including techniques from supervised learning, reinforcement learning, and differentiable programming. We compare the two paradigms across scalability, generalization, interpretability, and efficiency, and discuss emerging applications in neural architecture search, hyperparameter tuning, adversarial learning, and scientific design. The paper concludes with a discussion of open challenges and promising directions for hybrid and automated BLO frameworks. This survey lays the groundwork for future research at the intersection of optimization and learning. Additional resources are available at https://chauhandikshit.github.io/blo-website/.
Authors: Dikshit Chauhan, Hisao Ishibuchi, Kalyanmoy Deb, Anupam Trivedi, Dipti Srinivasan
Published in: IEEE Transactions on Evolutionary Computation (2026)