Evolution of optimal behaviour in networks of Boolean automata

This paper describes the response to selection for optimal behaviour in networks of Boolean automata. The networks considered are "open" in the sense that they receive an input and produce an output. The task that the nets are selected to solve is to maximize the mean "height" attained in a fixed number of iterations in "landscapes" that vary in their ruggedness. This is analogous to an organism with a fixed time budget that attempts to maximize its food intake in an environment where the food concentration varies in space. The results suggest that it is possible to select simple Boolean nets to respond adaptively to their inputs. Selection on simple environments produces a near "optimal" response. The response to complex environments is worse. The results suggest that nets selected on complex environments perform better on environments of different degrees of complexity than those selected on simple environments. Although nets with larger numbers of automata do not respond markedly better to selection, the variability in the response to selection is reduced. It appears to be difficult to predict the movements of nets from a study of the attractors of net with sensory units clamped at particular values. The cycle of bits in clamped nets can vary greatly with small changes in the inputs to the nets. The actual movement of nets does not, however, reflect this instability. It is concluded that networks of Boolean automata may be useful models with which to investigate different genetic algorithms. Furthermore, perturbations in such systems may give insights into the nature of pleiotropy and epistasis.