Analysis of emergent symmetry breaking in collective decision making

Abstract

We investigate a simulated multi-agent system (MAS) that collectively decides to aggregate at an area of high utility. The agents' control algorithm is based on random agent-agent encounters and is inspired by the aggregation behavior of honeybees. In this article, we define symmetry breaking, several symmetry breaking measures, and report the phenomenon of emergent symmetry breaking within our observed system. The ability of the MAS to successfully break the symmetry depends significantly on a local-neighborhood-based threshold of the agents' control algorithm that determines at which number of neighbors the agents stop. This dependency is analyzed and two macroscopic features are determined that significantly influence the symmetry breaking behavior. In addition, we investigate the connection between the ability of the MAS to break symmetries and the ability to stay flexible in a dynamic environment.

Analysis of Swarm Behaviors Based on an Inversion of the Fluctuation Theorem

“…This algorithm allows a swarm to aggregate at a maximum of a scalar field although individual agents do not perform a greedy gradient ascent. In addition, a BEECLUST-controlled swarm is able to break symmetries [11] of equal maxima in the scalar field as also observed here (e.g., see Fig. 2).…”

“…It is based on observations of young honeybees [25], was analyzed in many models [12,19,20,11,9], and even implemented in a swarm of robots [21]. This algorithm allows a swarm to aggregate at a maximum of a scalar field although individual agents do not perform a greedy gradient ascent.…”

A Model of Symmetry Breaking in Collective Decision-Making

“…As reported in [12], most macroscopic characteristics of the collective decision processes of these systems can approximately be captured by two features of the symmetry parameter s. First, the mean of the absolute changes…”

“…Initially, the agents have random headings, are in the state 'moving', and are random uniformly distributed in the whole arena (i.e., on average we have initially the same number of robots in the left and in the right half of the arena). The luminance distribution in the test arena is bimodal with maxima of the same value and shape in the left and right half of the arena (for details, see [12,14]). As a measure of symmetry we use s b (t) = L(t)/N ('b' for BEECLUST) where L(t) is the number of robots in the left half of the arena, and N the swarm size.…”

“…We will illustrate this approach and such an analysis with two examples from swarm robotics. The first one is the aggregation behavior of a swarm whose control algorithms are modeled on honeybee behavior [12][13][14], the second one is an emergent density classification task [15].…”