The principle of modularization has proven to be extremely successful in the field of technical applications and particularly for Software Engineering purposes. The question to be answered within the present article is whether mechanisms can also be identified within the framework of Evolutionary Computation that cause a modularization of solutions. We will concentrate on processes, where modularization results only from the typical evolutionary operators, i.e. selection and variation by recombination and mutation (and not, e.g., from special modularization operators). This is what we call Self-Organized Modularization. Based on a combination of two formalizations by Radcliffe and Altenberg, some quantitative measures of modularity are introduced. Particularly, we distinguish Built-in Modularityas an inherent property of a genotype and Effective Modularity, which depends on the rest of the population. These measures can easily be applied to a wide range of present Evolutionary Computation models. It will be shown, both theoretically and by simulation, that under certain conditions, Effective Modularity (as defined within this paper) can be a selection factor. This causes Self-Organized Modularization to take place. The experimental observations emphasize the importance of Effective Modularityin comparison with Built-in Modularity. Although the experimental results have been obtained using a minimalist toy model, they can lead to a number of consequences for existing models as well as for future approaches. Furthermore, the results suggest a complex self-amplification of highly modular equivalence classes in the case of respected relations. Since the well-known Holland schemata are just the equivalence classes of respected relations in most Simple Genetic Algorithms, this observation emphasizes the role of schemata as Building Blocks (in comparison with arbitrary subsets of the search space).

Natural intelligence and autonomous agents face difficulties when acting in information-dense environments. Assailed by a multitude of stimuli they have to make sense of the inflow of information, filtering and processing what is necessary, but discarding that which is unimportant. This paper aims at investigating the interactions between evolution of the sensorial channel extracting the information from the environment and the simultaneous individual adaptation of agent-control. Our particular goal is to study the influence of learning on the evolution of sensors, with learning duration being the tunable parameter. A genetic algorithm governs the evolution of sensors appropriate for the agent solving a simple grid world task. The performance of the agent is taken as fitness; 'sensors' are conceived as a map from environmental states to agent observations, and individual adaptation is modeled by Qlearning. Our experimental results show that due to the principles of cognitive economy learning and varying the degree thereof actually transforms the fitness landscape. In particular we identify a tradeoff between learning speed (load) and sensor accuracy (error). These results are further reinforced by theoretical analysis: we derive an analytical measure for the quality of sensors based on the mutual entropy between the system of states and the selection of an optimal action, a concept recently proposed by Polani, Martinetz, and Kim.

No abstract

Abstract. The concept of modularity appears to be crucial for many questions in the field of Artificial Life research. However, there have not been many quantitative measures for modularity that are both general and viable. In this paper we introduce a measure for modularity based on information theory. Due to the generality of the information theory formalism, this measure can be applied to various problems and models; some connections to other formalisms are presented.

No abstract