Deep Learning for Combinatorial Optimization: Bridging Discrete Complexity with Neural Innovation

Combinatorial optimization problems (COPs) are pervasive in real-world domains, yet their NP-hard nature makes exact solutions computationally infeasible at scale. While traditional heuristics and approximation algorithms provide partial relief, recent advances in deep learning have opened promising new avenues. This paper presents a comprehensive survey of neural network-based approaches applied to COPs, with a critical focus on both early models (e.g., Hopfield Networks) and modern deep learning architectures, including Pointer Networks, Graph Neural Networks, and reinforcement learning-based frameworks such as GCOMB. We analyze and compare these methods in terms of scalability, generalization, and problem structure adaptability. Furthermore, we highlight current limitations, practical challenges, and propose future research directions for making deep learning-based COP solvers more interpretable, data-efficient, and deployable in real-world scenarios.