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