The neuronal network is considered to adopt the specialized structure for the specific functions that the network is responsible for. Also, such a structure is considered to be achieved by the following two principles. One is experience-dependent synaptic plasticity, such as Hebbian plasticity, and the other is the one through genetic or evolutionary processes. However, the organizational principle in the latter process is not fully understood. In this study this principle was assumed as a multi-objective optimization problem whose objective function consists of information transfer to be maximized and maintenance costs to be minimized. The objective is to unravel the underlying principles of circuit formation by investigating wiring patterns and information processing dynamics. The study shows that efficient information transmission requires sparse circuits with internal modular structures characterized by distinct wiring patterns. Significant trade-offs highlight the importance of balancing wiring pattern development. The dynamics of effective circuits exhibit moderate flexibility in response to stimuli, consistent with previous observations in visual system studies. The findings suggest that maximizing information transfer may enable the self-organization of information processing functions akin to biological circuits, transcending specific modalities. This study provides insights into neuroscience and the potential to enhance reservoir computing performance.