AMARL: An Attention-Based Multiagent Reinforcement Learning Approach to the Min-Max Multiple Traveling Salesmen Problem

In recent years, the multiple traveling salesmen problem (MTSP or multiple TSP) has received increasing research interest and one of its main applications is coordinated multirobot mission planning, such as cooperative search and rescue tasks. However, it is still challenging to solve MTSP with improved inference efficiency as well as solution quality in varying situations, e.g., different city positions, different numbers of cities, or agents. In this article, we propose an attention-based multiagent reinforcement learning (AMARL) approach, which is based on the gated transformer feature representations for min-max multiple TSPs. The state feature extraction network in our proposed approach adopts the gated transformer architecture with reordering layer normalization (LN) and a new gate mechanism. It aggregates fixed-dimensional attention-based state features irrespective of the number of agents and cities. The action space of our proposed approach is designed to decouple the interaction of agents' simultaneous decision-making. At each time step, only one agent is assigned to a non-zero action so that the action selection strategy can be transferred across tasks with different numbers of agents and cities. Extensive experiments on min-max multiple TSPs were conducted to illustrate the effectiveness and advantages of the proposed approach. Compared with six representative algorithms, our proposed approach achieves state-of-the-art performance in solution quality and inference efficiency. In particular, the proposed approach is suitable for tasks with different numbers of agents or cities without extra learning, and experimental results demonstrate that the proposed approach realizes powerful transfer capability across tasks.