The best-of-n problem with dynamic site qualities: Achieving adaptability with stubborn individuals

Collective decision-making is one of main building blocks of swarm robotics collective behaviors. It is the ability of individuals to make a collective decision without any centralized leadership, but only via local interaction and communication. The best-of-n problem is a subclass of collective decision-making, whereby the swarm has to select the best option among a set of n possible alternatives. Recently, the best-of-n problems has gathered momentum: a number of decision-making mechanisms have been studied focusing both on cases where there is an explicit measurable difference between the two qualities, as well as on cases when there are only delay costs in the environment driving the consensus to one of the n alternatives. To the best of our knowledge, all the formal studies on the best-of-n problem have considered a site quality distribution that is stationary and does not change over time. In this paper, we perform a study of the best-of-n problems in a dynamic environment setting. We consider the situation where site qualities can be directly measured by agents, and we introduce abrupt changes to these qualities, whereby the two qualities are swapped at a given time. Using computer simulations, we show that a vanilla application of one of the most studied decision-making mechanism, the voter model, does not guarantee adaptation of the swarm consensus towards the best option after the swap occurs. Therefore, we introduce the notion of stubborn agents, which are not allowed to change their opinion. We show that the presence of the stubborn agents is enough to achieve adaptability to dynamic environments. We study the performance of the system with respect to a number of key parameters: the swarm size, the difference between the two qualities and the proportion of stubborn individuals.