Combining Reinforcement Learning with Lin-Kernighan-Helsgaun Algorithm for the Traveling Salesman Problem

We address the Traveling Salesman Problem (TSP), a famous NP-hard combinatorial optimization problem. And we propose variable strategy reinforced approach, denoted as VSR-LKH, which combines three reinforcement learning methods (Q-learning, Sarsa and Monte Carlo) with well-known TSP algorithm, called Lin-Kernighan-Helsgaun (LKH). VSR-LKH replaces inflexible traversal operation in LKH, lets program learn to make choice at each search step by learning. Experimental results on 111 benchmarks from TSPLIB up 85,900 cities demonstrate excellent performance of proposed method.