Evolving populations of random boolean networks Ney Lemke , Jos´ e C. M. Mombach , and Bardo E. J. Bodmann Centro de Ciˆ encias Exatas e Tecnol´ ogicas, Universidade do Vale do Rio dos Sinos, 93022-000 S˜ ao Leopoldo, RS, Brazil lemke,mombach,bardo @exatas.unisinos.br Abstract. We investigate the adaptation of Random Boolean Networks that are a model for regulatory gene networks. The model considers a general genetic al- gorithm and a fitness function that takes into account the full network dynamical behavior.Our simulations shows a fast decrease on algorithm perfomance when we consider larger networks or networks with more complex dynamical behavior. Fi- nally, we discuss a scenario that describes the adaptation on the proposed fitness landscape. 1. Introduction The cell genome stores all information required for the construction and function of an organism. Its basic units, the genes, interact with each other to perform these tasks in an orchestrated way. Kauffman proposed a cellular automata model for the functioning genome where the dynamics are due to mutuous activations and inactivations of regulatory genes represented by a network of boolean variables. A Kauffman network is a set of boolean variables each one connected randomly to other variables in the set. The state of each variable is determined from a random logical function of the inputs. The underlying dynamics are setup as follows: The state of a variable, at instant is determined from a logical function ( ) evaluating the states of the input variables connected to it at instant , (1) Since the phase space of the networks is discrete and finite, the attractors are cycles with period length between 1 and (the total number of states of a network of size ). The networks are known to possess distinct dynamical behaviors dependent on includ- ing a dynamical transition that separates an ordered phase at from a disordered phase for . For the average period length and the number of cycles scale with while for they scale with and , respectively [1, 2, 3, 4, 5, 6].