This paper proposes a framework for learning greedy heuristics for NP-hard combinatorial optimization problems over graphs. The framework combines reinforcement learning with graph embedding to automatically design effective algorithms for problems such as Minimum Vertex Cover (MVC), Maximum Cut (MAXCUT), and Traveling Salesman Problem (TSP). The key idea is to use a graph embedding network to represent the current state of the solution, and then use reinforcement learning to learn a greedy policy that incrementally constructs a solution. The policy selects the next node to add based on the output of the graph embedding network, which captures the current state of the solution. The framework is evaluated on three graph optimization problems: MVC, MAXCUT, and TSP. The results show that the proposed method outperforms existing heuristic and approximation algorithms in terms of solution quality and generalization to larger instances. The method is also efficient in terms of running time, with a polynomial complexity of O(k|E|), where k is the number of greedy steps and |E| is the number of edges. The framework is able to learn effective heuristics for different graph sizes and types, and it is capable of discovering new and interesting algorithms that intuitively make sense but have not been analyzed before. The results suggest that the framework is a promising new tool for designing algorithms for graph problems.This paper proposes a framework for learning greedy heuristics for NP-hard combinatorial optimization problems over graphs. The framework combines reinforcement learning with graph embedding to automatically design effective algorithms for problems such as Minimum Vertex Cover (MVC), Maximum Cut (MAXCUT), and Traveling Salesman Problem (TSP). The key idea is to use a graph embedding network to represent the current state of the solution, and then use reinforcement learning to learn a greedy policy that incrementally constructs a solution. The policy selects the next node to add based on the output of the graph embedding network, which captures the current state of the solution. The framework is evaluated on three graph optimization problems: MVC, MAXCUT, and TSP. The results show that the proposed method outperforms existing heuristic and approximation algorithms in terms of solution quality and generalization to larger instances. The method is also efficient in terms of running time, with a polynomial complexity of O(k|E|), where k is the number of greedy steps and |E| is the number of edges. The framework is able to learn effective heuristics for different graph sizes and types, and it is capable of discovering new and interesting algorithms that intuitively make sense but have not been analyzed before. The results suggest that the framework is a promising new tool for designing algorithms for graph problems.