This work proposes PageRank as a tool to evaluate and optimize the global performance of a swarm based on the analysis of the local behavior of a single robot. PageRank is a graph centrality measure that assesses the importance of nodes based on how likely they are to be reached when traversing a graph. We relate this, using a microscopic model, to a random robot in a swarm that transitions through local states by executing local actions. The PageRank centrality then becomes a measure of how likely it is, given a local policy, for a robot in the swarm to visit each local state. This is used to optimize a stochastic policy such that the robot is most likely to reach the local states that are “desirable,” based on the swarm’s global goal. The optimization is performed by an evolutionary algorithm, whereby the fitness function maximizes the PageRank score of these local states. The calculation of the PageRank score only scales with the size of the local state space and demands much less computation than swarm simulations would. The approach is applied to a consensus task, a pattern formation task, and an aggregation task. For each task, when all robots in the swarm execute the evolved policy, the swarm significantly outperforms a swarm that uses the baseline policy. When compared to globally optimized policies, the final performance achieved by the swarm is also shown to be comparable. As this new approach is based on a local model, it natively produces controllers that are flexible and robust to global parameters such as the number of robots in the swarm, the environment, and the initial conditions. Furthermore, as the wall-clock time to evaluate the fitness function does not scale with the size of the swarm, it is possible to optimize for larger swarms at no additional computational expense.

中文翻译：

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PageRank算法作为通过局部分析优化群体行为的一种方法

这项工作提出了PageRank作为一种工具，可基于对单个机器人的局部行为的分析来评估和优化群体的整体性能。PageRank是一种图形集中度度量，它基于遍历图形时达到节点的可能性来评估节点的重要性。我们使用微观模型将其与一群通过执行局部动作而在局部状态中转换的随机机器人联系起来。然后，根据给定的本地策略，PageRank中心度可以衡量群内机器人访问每个本地状态的可能性。这用于优化随机策略，以使机器人最有可能到达基于群体总体目标的“理想状态”。优化是通过进化算法执行的，因此，适应度函数会最大化这些局部状态的PageRank得分。PageRank分数的计算仅与局部状态空间的大小成比例，并且所需的计算量比群模拟要少得多。该方法应用于共识任务，模式形成任务和聚合任务。对于每个任务，当群集中的所有机器人都执行了已制定的策略时，群集的性能将大大优于使用基准策略的群集。与全球优化的策略相比，该集群实现的最终性能也具有可比性。由于这种新方法基于本地模型，因此它会本地生成对全局参数（如群中机器人的数量，环境和初始条件）具有灵活性和鲁棒性的控制器。此外，