This paper addresses the challenge of learning heuristics for combinatorial optimization problems over graphs, which are NP-hard and commonly encountered in various application domains. The authors propose a novel framework that combines reinforcement learning with graph embedding to automatically design greedy heuristics. The learned policy acts as a meta-algorithm that incrementally constructs solutions based on the current state of the solution, which is represented by a graph embedding network. This approach is applied to three well-known optimization problems: Minimum Vertex Cover (MVC), Maximum Cut (MAXCUT), and Traveling Salesman Problem (TSP). The framework is shown to be effective across different graph types and sizes, outperforming existing methods in terms of solution quality and generalization to larger instances. The learned heuristics are also found to be useful for discovering new algorithms, particularly for less-studied graph optimization problems. The paper includes extensive experimental evaluations on synthetic and real-world datasets, demonstrating the effectiveness and scalability of the proposed framework.This paper addresses the challenge of learning heuristics for combinatorial optimization problems over graphs, which are NP-hard and commonly encountered in various application domains. The authors propose a novel framework that combines reinforcement learning with graph embedding to automatically design greedy heuristics. The learned policy acts as a meta-algorithm that incrementally constructs solutions based on the current state of the solution, which is represented by a graph embedding network. This approach is applied to three well-known optimization problems: Minimum Vertex Cover (MVC), Maximum Cut (MAXCUT), and Traveling Salesman Problem (TSP). The framework is shown to be effective across different graph types and sizes, outperforming existing methods in terms of solution quality and generalization to larger instances. The learned heuristics are also found to be useful for discovering new algorithms, particularly for less-studied graph optimization problems. The paper includes extensive experimental evaluations on synthetic and real-world datasets, demonstrating the effectiveness and scalability of the proposed framework.