This paper introduces a continuous model for Multi-cellular Developmental Design. The cells are fixed on a 2D grid and exchange "chemicals" with their neighbors during the growth process. The quantity of chemicals that a cell produces, as well as the differentiation value of the cell in the phenotype, are controlled by a Neural Network (the genotype) that takes as inputs the chemicals produced by the neighboring cells at the previous time step. In the proposed model, the number of iterations of the growth process is not pre-determined, but emerges during evolution: only organisms for which the growth process stabilizes give a phenotype (the stable state), others are declared nonviable. The optimization of the controller is done using the NEAT algorithm, that optimizes both the topology and the weights of the Neural Networks. Though each cell only receives local information from its neighbors, the experimental results of the proposed approach on the 'flags' problems (the phenotype must match a given 2D pattern) are almost as good as those of a direct regression approach using the same model with global information. Moreover, the resulting multi-cellular organisms exhibit almost perfect self-healing characteristics.

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This paper presents a comparative study of two indirect solution representations, a generative and an ontogenic one, on a set of well-known 2D truss design problems. The generative representation encodes the parameters of a trusses design as a mapping from a 2D space. The ontogenic representation encodes truss design parameters as a local truss transformation iterated several times, starting from a trivial initial truss. Both representations are tested with a naive evolution strategy based optimization scheme, as well as the state of the art HyperNEAT approach. We focus both on the best objective value obtained and the computational cost to reach a given level of optimality. The study shows that the two solution representations behave very differently. For experimental settings with equal complexity, with the same optimization scheme and settings, the generative representation provides results which are far from optimal, whereas the ontogenic representation delivers near-optimal solutions. The ontogenic representation is also much less computationally expensive than a direct representation until very close to the global optimum. The study questions the scalability of the generative representations, while the results for the ontogenic representation display much better scalability.