Automated optimization of multilevel models of collective behaviour: application to mixed society of animals and robots.

Animal societies exhibit complex dynamics that require multi-level descriptions. They are difficult to model, as they encompass information at different levels of description, such as individual physiology, individual behaviour, group behaviour and features of the environment. The collective behaviour of a group of animals can be modelled as a dynamical system. Typically, models of behaviour are either macroscopic (differential equations of population dynamics) or microscopic (such as Markov chains, explicitly specifying the spatio-temporal state of each individual). These two kind of models offer distinct and complementary descriptions of the observed behaviour. Macroscopic models offer mean field description of the collective dynamics, where collective choices are considered as the stable steady states of a nonlinear system governed by control parameters leading to bifurcation diagrams. Microscopic models can be used to perform computer simulations or as building blocks for robot controllers, at the individual level, of the observed spatial behaviour of animals. Here, we present a methodology to translate a macroscopic model into different microscopic models. We automatically calibrate the microscopic models so that the resulting simulated collective dynamics fit the solutions of the reference macroscopic model for a set of parameter values corresponding to a bifurcation diagram leading to multiple steady states. We apply evolutionary algorithms to simultaneously optimize the parameters of the models at different levels of description. This methodology is applied, in simulation, to an experimentally validated shelter-selection problem solved by gregarious insects and robots. Our framework can be used for multi-level modelling of collective behaviour in animals and robots.