Multi-Agent Deep Reinforcement Learning for Multi-Modal Orienteering Problem

The multi-modal orienteering problem (MM-OP) is common in real life and is to plan diverse tours that can visit as many nodes as possible with limited resources. Researchers used to adopt group intelligence algorithms such as evolutionary algorithms to solve MM-OP, however, show difficulty in designing complex operators and dealing with large-scale cases in real-time. This study first proposes a multi-agent deep reinforcement learning (MA-DRL) method for MM-OP. Our model deploys multiple agents, each trained to independently explore and exploit the solution space, thereby discovering diverse optimal paths. This diversity is critical in multi-modal optimization and is achieved through a unique reward-sharing mechanism implemented within the MA-DRL framework. Empirical evaluation of our model against traditional evolutionary algorithms on various test instances demonstrates its superior optimization accuracy and efficiency, particularly in larger problem sizes. Additionally, the robustness across different instance sizes underscores its great generalization ability.