  Most existing swarm pattern formation methods depend on a predefined gene
regulatory network (GRN) structure that requires designers' priori knowledge,
which is difficult to adapt to complex and changeable environments. To
dynamically adapt to the complex and changeable environments, we propose an
automatic design framework of swarm pattern formation based on multi-objective
genetic programming. The proposed framework does not need to define the
structure of the GRN-based model in advance, and it applies some basic network
motifs to automatically structure the GRN-based model. In addition, a
multi-objective genetic programming (MOGP) combines with NSGA-II, namely
MOGP-NSGA-II, to balance the complexity and accuracy of the GRN-based model. In
evolutionary process, an MOGP-NSGA-II and differential evolution (DE) are
applied to optimize the structures and parameters of the GRN-based model in
parallel. Simulation results demonstrate that the proposed framework can
effectively evolve some novel GRN-based models, and these GRN-based models not
only have a simpler structure and a better performance, but also are robust to
the complex and changeable environments.
