Journal Article

Beyond Neural Solvers: A Critical Review of Machine Learning for Combinatorial Optimization

Ahmed, Alaa E, Ibrahim Mostafa E. A., Daadaa Yassine

2026

Overview

Combinatorial optimization is a key component in critical decision problems such as routing, scheduling, network design, and graph optimization. Although combinatorial optimization methods, including exact algorithms, approximation methods, constraint programming, mixed integer programming, and metaheuristics, are widely available, they often face obstacles, such as limited scalability and adaptability in various applications. In this study, a systematic critical review of machine learning for combinatorial optimization is provided to characterize the usage and evaluation of learning-based approaches. A detailed analysis is used to infer and determine findings and limitations. The paper emphasizes how machine learning for computational optimization has changed over time, moving from end-to-end neural solvers to hybrid systems. Learning components are essential for directing, speeding up, or enhancing traditional solver backbones such as constraint programming and metaheuristics in hybrid systems. The review also critically examines current limits that impact performance in general, including scalability, deployment readiness, generalization, and benchmark consistency. Even though using large language models for problem formulation and heuristic synthesis has potential, more work needs to be done to ensure reliable validation. As a conclusion, this article examines recent studies’ findings, emphasizes the growing trend toward hybrid learning-driven optimization frameworks, and underlines important methodological limits and unresolved issues.

• Publisher: MDPI AG
• Subject: Approximation / Artificial intelligence / Benchmarks / Combinatorial analysis / combinatorial optimization / Constraints / Decision making / Design optimization / Energy consumption / Feasibility / graph neural networks / Heuristic / Heuristic methods / hybrid neuro-symbolic optimization / Hybrid systems / Integer programming / Large language models / Machine learning / Mathematical programming / Mixed integer / Network design / neural combinatorial optimization / Neural networks / Optimization techniques / reinforcement learning / Reproducibility / Solvers