Swarm robotic systems (SRSs), which are widely used in many fields, such as search and rescue, usually comprise a number of robots with relatively simple mechanisms collaborating to accomplish complex tasks. A challenging task for SRSs is to design local interaction rules for self-organization of robots that can generate adaptive patterns to entrap moving targets. Biologically inspired approaches such as gene regulatory network (GRN) models provide a promising solution to this problem. However, the design of GRN models for generating entrapping patterns relies on the expertise of designers. As a result, the design of the GRN models is often a laborious and tedious trial-and-error process. In this study, we propose a modular design automation framework for GRN models that can generate entrapping patterns. The framework employs basic network motifs to construct GRN models automatically without requiring expertise. To this end, a constrained multi-objective genetic programming is utilized to simultaneously optimize the structures and parameters of the GRN models. A multi-criteria decision-making approach is adopted to choose the preferred GRN model for generating the entrapping pattern. Comprehensive simulation results demonstrate that the proposed framework can obtain novel GRN models with simpler structures than those designed by human experts yet better performance in complex and dynamic environments. Proof-of-concept experiments using e-puck robots confirmed the feasibility and effectiveness of the proposed GRN models.