Abstract
Self-organised collective decision making is one of the core components of swarm intelligence, and numerous swarm algorithms that are widely used in optimisation and optimal control have been inspired by the biological mechanisms driving it. Beyond the life sciences and bio-inspired engineering, collective decision making is important in a number of other disciplines, most prominently economics and the social sciences. A paradigmatic model system for collective decision making is the foraging behaviour of mass recruiting ant colonies. While this system has been investigated extensively, our knowledge about its function in dynamic environments is still incomplete at best. We show that the mathematical model of mass foraging is really just a specific instance of a very general class of rational group decision making processes. We analyse this general class using an information-theoretic framework, which allows us to abstract from the specific details of a fixed model system. We specifically investigate how noisy communication can enable groups to share information about changes in an environment more efficiently. In the present paper, we show that an optimal noise level exists and that this optimal level depends on the rate of change in the environment. We explain this on the basis of stochastic resonance theory and show why stochastic attractor switching is a suitable base mechanism for adaptive group decision making in dynamic environments.
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Notes
This is true for purely mass foraging species (Hölldobler and Wilson 1990).
Note that this figure gives the exact plot of a double-well potential function U that we will be defining later in Sect. 4.4.1 and Eq. 19. Here the only property of U that matters is that it is a double-well potential. The exact shape of the potential and thus the parameter values are not relevant at the present point.
There are of course also other channels of communication, for example trophallaxis, but we focus the discussion on pheromone communication here.
Since actual movements have no impact on the simulation outcomes they are not explicitly modelled.
All calculations were performed using numerical integration in Mathematica 11.0 with parameters WorkingPrecision = 16, AccuracyGoal = 2, Method = {GlobalAdaptive, MaxErrorIncreases = 10000}.
For a critical discussion of this claim see Pfeifer (2006).
The sole exception is the approximation by adiabatic elimination, which is entirely dispensable in our approach, as we can rely on EFA instead.
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This work was supported by the Australian Research Council under DP0879239 and DP110101413.
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Meyer, B. Optimal information transfer and stochastic resonance in collective decision making. Swarm Intell 11, 131–154 (2017). https://doi.org/10.1007/s11721-017-0136-7
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DOI: https://doi.org/10.1007/s11721-017-0136-7