A Distributed Ant Colony System with Pheromone Transfer for Multiagent Traveling Salesmen Problem

The development of multiagent systems (MASs) has given rise to a new type of traveling salesman problem (TSP), namely the multiagent TSP (MATSP). MATSP aims to find multiple routes with the minimum total cost through the cooperation of intelligent agents. Since the distributed nature of MATSP, it is challenging to solve MATSP effectively in a distributed manner. This article focuses on MATSP and proposes a distributed ant colony system with pheromone transfer (DACS) to solve the problem. First, we formally define MATSP, in which each agent has only partial data and independently makes routing decisions. All agents cooperate to make a consensus on the visiting conflicts caused by the loss of global information. To further consider the balanced workloads of agents, the fairness-aware colored MATSP is further formulated. Second, to solve MATSP in a distributed manner, the proposed DACS allows each agent to run an ant colony optimizer and be responsible for the routing under its jurisdiction. To coordinate these agents to avoid conflicts, a bidding-based cooperation mechanism (BCM) is designed to reach a consensus on the allocation of cities. Agents bid for the accessibilities of cities based on market-based economic theory, owning the ability to adapt to complex environments. Two pheromone transfer strategies are designed to improve efficiency. DACS transfers learned pheromones within the same agent and between different agents. Besides, we conduct extensive experiments in nine datasets to certify the effectiveness of DACS. Experimental results show that DACS is effective and efficient even in complex environments.