Towards swarm calculus: urn models of collective decisions and universal properties of swarm performance

Abstract

Methods of general applicability are searched for in swarm intelligence with the aim of gaining new insights about natural swarms and to develop design methodologies for artificial swarms. An ideal solution could be a 'swarm calculus' that allows to calculate key features of swarms such as expected swarm performance and robustness based on only a few parameters. To work towards this ideal, one needs to find methods and models with high degrees of generality. In this paper, we report two models that might be examples of exceptional generality. First, an abstract model is presented that describes swarm performance depending on swarm density based on the dichotomy between cooperation and interference. Typical swarm experiments are given as examples to show how the model fits to several different results. Second, we give an abstract model of collective decision making that is inspired by urn models. The effects of positive feedback probability, that is increasing over time in a decision making system, are understood by the help of a parameter that controls the feedback based on the swarm's current consensus. Several applicable methods, such as the description as Markov process, calculation of splitting probabilities, mean first passage times, and measurements of positive feedback, are discussed and applications to artificial and natural swarms are reported.

A Reductionist Approach to Hypothesis-Catching for the Analysis of Self-Organizing Decision-Making Systems

“…In this study we discover a different kind of feedback that was not found in the former studies of these models and systems [21,22]. Therefore, we distinguish between standard feedback, which cannot increase above P +F B (k) = 1 with consequent transition probability P s,s f (k) = k and cannot decrease below P +F B (k) = 0 with consequent P s,s f (k) = 1 − k, and super-feedback that is nonlinear in k (e.g., P s,s f (k) < k for k < 0.5).…”

“…The above defined transition probability P s,s f (k) can be modeled and understood by an urn model [21,22] (see Fig. 3 for a schematic overview) similar to common urn models such as the Ehrenfest urn model [23] and the Pólya urn model [24].…”

“…The nonlinearity in k means that drawing a marble with key property is more likely than a mere random draw with probability k in the urn model. When doing measurements based on trivial 2-state Markov chains, super-feedback seems not to be common in natural and artificial systems [22]. Hence, its occurrence seems to depend on the selective definition of states based on local and global features.…”

The Information-Cost-Reward framework for understanding robot swarm foraging

“…These approaches include, for instance, "property-driven design" , "swarm calculus" (Hamann 2013), and other models based on probabilistic finite state machines (PFSMs) (e.g. Liu and Winfield 2010;Reina et al 2015a) and differential equations (DEs) (e.g.…”

Towards a Cognitive Design Pattern for Collective Decision-Making

“…Recent studies have identified optimal decision strategies in decentralised systems [8,13,11].We propose a cognitive design pattern hinged on these studies, to be applied to artificial distributed systems. Although decision-making has been largely studied in this context [2,7,9,12], general purpose solutions are still missing. Our work aims at filling this gap by providing a design methodology that can be applied to several application domains.…”