Proposal and Evaluation of a Robust Pheromone-Based Algorithm for the Patrolling Problem with Various Graph Structure

Abstract

Recently, the urgent necessity to develop an algorithm to resolve patrolling problems has become evident. This problem is modeled using a graph structure and defined as the requirement that an agent or multi-agents patrol each node in the graph at the shortest regular intervals possible. To solve the problem, some central controlled algorithms have been proposed. However, these algorithms require a central control system, and therefore, their reliability strongly depends on the reliability of the central control system. Thus, the algorithm has a lower ability in severe environments, for example, in the case of communication between an agent and the central control system. Instead of a central controlled algorithm, some autonomous distributed algorithms have been proposed. In this paper, we propose an autonomous distributed algorithm, called pheromone and inverse degree-based Probabilistic Vertex-Ant-Walk (pidPVAW), which is an improved version of pheromone-based Probabilistic Vertex-Ant-Walk (pPVAW). pPVAW is based on Probabilistic Vertex-Ant-Walk (PVAW). These algorithms use a pheromone model corresponding to fixed points for agent communication and cooperative patrolling. The difference between pidPVAW and pPVAW is that when an agent determines the neighbor node to which it moves the next time, pidPVAW takes into consideration the degree of each neighbor node, whereas pPVAW does not. This consideration is useful for scale-free or tree-like graphs. It is considered that lower degree nodes cannot easily be visited by agents when they use pPVAW. In contrast, when agents use pidPVAW, they can visit these lower degree nodes with ease. pidPVAW inherits some parts of the useful behavior of pPVAW, such as that agents using pPVAW do not return to the last visited node.