How does the interaction radius affect the performance of intervention on collective behavior?

The interaction radius r plays an important role in the collective behavior of many multi-agent systems because it defines the interaction network among agents. For the topic of intervention on collective behavior of multi-agent systems, does r also affect the intervention performance? In this paper we study whether it is easier to change the convergent heading of the group by adding some special agents (called shills) into the Vicsek model when r is larger (or smaller). Two kinds of shills are considered: fixed-heading shills (like leaders that never change their headings) and evolvable-heading shills (like normal agents but with carefully designed initial headings). We know that with the increase of r, two contradictory effects exist simultaneously: the influential area of a single shill is enlarged, but its influence strength is weakened. Which factor dominates? Through simulations and theoretical analysis we surprisingly find that r affects the intervention performance differently in different cases: when fixed-heading shills are placed together at the center of the group, larger r gives a better intervention performance; when evolvable-heading shills are placed together at the center, smaller r is better; when shills (either fixed-heading or evolvable-heading) are distributed evenly inside the group, the effect of r on the intervention performance is not significant. We believe these results will inspire the design of intervention strategies for many other multi-agent systems.交互半径r在诸多多智能体系统的群体行为中发挥着关键作用，因其定义了智能体之间的交互网络。针对多智能体系统群体行为干预这一研究主题，交互半径r是否会对干预效果产生影响？本文旨在探究：当交互半径r增大（或减小）时，向维切克模型（Vicsek Model）中引入若干特殊智能体（shills），是否能够更高效地改变群体的收敛航向。本文考虑两类特殊智能体（shills）：一类为固定航向诱导智能体（类似始终保持航向不变的领导者），另一类为可演化航向诱导智能体（与普通智能体类似，但初始航向经过精心设计）。我们已知，随着交互半径r的增大，会同时存在两种相互矛盾的效应：单个诱导智能体的影响范围得以扩大，但其影响力强度却会被削弱。那么究竟哪种效应占据主导地位？通过仿真实验与理论分析，我们意外发现，交互半径r对干预效果的影响在不同场景下存在显著差异：当固定航向诱导智能体集中部署于群体中心时，更大的r能够带来更优的干预效果；当可演化航向诱导智能体集中部署于群体中心时，更小的r则效果更佳；而当两类诱导智能体（固定航向或可演化航向）在群体内部均匀分布时，r对干预效果的影响并不显著。我们认为，上述研究结果将为诸多其他多智能体系统的干预策略设计提供重要启发。