Targeted sampling of enlarged neighborhood via Monte Carlo tree search for TSP

The travelling salesman problem (TSP) is a well-known combinatorial optimization problem with a variety of real-life applications. We tackle TSP by incorporating machine learning methodology and leveraging the variable neighborhood search strategy. More precisely, the search process is considered as a Markov decision process (MDP), where a 2-opt local search is used to search within a small neighborhood, while a Monte Carlo tree search (MCTS) method (which iterates through simulation, selection and back-propagation steps), is used to sample a number of targeted actions within an enlarged neighborhood. This new paradigm clearly distinguishes itself from the existing machine learning (ML) based paradigms for solving the TSP, which either uses an end-to-end ML model, or simply applies traditional techniques after ML for post optimization. Experiments based on two public data sets show that, our approach clearly dominates all the existing learning based TSP algorithms in terms of performance, demonstrating its high potential on the TSP. More importantly, as a general framework without complicated hand-crafted rules, it can be readily extended to many other combinatorial optimization problems.