Robustness and the Halting Problem for Multicellular Artificial Ontogeny

Most works in multicellular artificial ontogeny solve the halting problem by arbitrarily limiting the number of iterations of the developmental process. Hence, the trajectory of the developing organism in the phenotypic space is only required to come close to an accurate solution during a very short developmental period. Because of the well-known opportunism of evolution, there is indeed no reason for the organism to remain close to a good solution in other situations: if the development is continued after the limiting bound; if the environment is perturbed by some noise during the development; if the development takes place in different physical conditions. In order to increase the robustness of the solution against such hazards, a new stopping criterion for the developmental process is proposed, based on the stability of some internal energy of the organism during its development. Such adaptive stopping criterion biases evolution toward solutions in which robustness is an intrinsic property. Experimental results on different “French flag” problems demonstrate that enforcing stable developmental process makes it possible to produce solutions that not only accurately approximate the target shape, but also demonstrate near-perfect self-healing properties, as well as excellent generalization capabilities.