This paper presents a novel approach to learning heuristics for combinatorial optimization problems, specifically focusing on routing problems such as the Traveling Salesman Problem (TSP) and variants like the Vehicle Routing Problem (VRP), Orienteering Problem (OP), and Prize Collecting TSP (PCTSP). The authors propose an attention-based model that outperforms existing methods, including the Pointer Network (PN), by using attention layers instead of recurrence to achieve invariance to input order. They also introduce a training method based on REINFORCE with a greedy rollout baseline, which significantly improves the model's performance and convergence speed. The attention model is trained using a single set of hyperparameters, demonstrating its flexibility and efficiency across different routing problems. The results show that the proposed method can achieve near-optimal solutions for TSP instances up to 100 nodes and outperform a wide range of baselines on other routing problems, making it a promising tool for solving practical combinatorial optimization tasks.This paper presents a novel approach to learning heuristics for combinatorial optimization problems, specifically focusing on routing problems such as the Traveling Salesman Problem (TSP) and variants like the Vehicle Routing Problem (VRP), Orienteering Problem (OP), and Prize Collecting TSP (PCTSP). The authors propose an attention-based model that outperforms existing methods, including the Pointer Network (PN), by using attention layers instead of recurrence to achieve invariance to input order. They also introduce a training method based on REINFORCE with a greedy rollout baseline, which significantly improves the model's performance and convergence speed. The attention model is trained using a single set of hyperparameters, demonstrating its flexibility and efficiency across different routing problems. The results show that the proposed method can achieve near-optimal solutions for TSP instances up to 100 nodes and outperform a wide range of baselines on other routing problems, making it a promising tool for solving practical combinatorial optimization tasks.