SplitNet: A Reinforcement Learning Based Sequence Splitting Method for the MinMax Multiple Travelling Salesman Problem

MinMax Multiple Travelling Salesman Problem (mTSP) is an important class of combinatorial optimization problems with many practical applications, of which the goal is to minimize the longest tour of all vehicles. Due to its high computational complexity, existing methods for solving this problem cannot obtain a solution of satisfactory quality with fast speed, especially when the scale of the problem is large. In this paper, we propose a learning-based method named SplitNet to transform the single TSP solutions into the MinMax mTSP solutions of the same instances. Specifically, we generate single TSP solution sequences and split them into mTSP subsequences using an attention-based model trained by reinforcement learning. We also design a decision region for the splitting policy, which significantly reduces the policy action space on instances of various scales and thus improves the generalization ability of SplitNet. The experimental results show that SplitNet generalizes well and outperforms existing learning-based baselines and Google OR-Tools on widely-used random datasets of different scales and public datasets with fast solving speed.