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S-system modeling from time series datasets can provide us with an interactive network. However, system identification is difficult since an S-system is described as highly nonlinear differential equations. Much research adopts various evolution computation technologies to identify system parameters, and some further achieve skeletal-network structure identification. However, the truncated redundant kinetic orders are not small enough as compared with the preserved terms. In this paper, we integrate quantitative genetics, bacterium movement, and fuzzy set theory into evolution computation to develop a new genetic algorithm to achieve convergence enhancement and diversity preservation. The proposed exploration and exploitation genetic algorithm (EEGA) can improve the best-so-far individual and ensure global optimal search at the same time. The EEGA enhances evolution convergence by golden section seed selection, normal-distribution reproduction, mixed inbreeding and backcrossing, competition elitism, and acceleration operations. Search-then-conquer evolution direction operations, eugenics-based screen-sifting mutation, eugenic self-mutation, and fuzzy-based tumble migration preserve population diversity to avoid premature convergence. Furthermore, to ensure that a reasonable gene regulation network is inferred, fuzzy composition is introduced to derive a reconstruction index. This performance index let EEGA possess self-interactive multiobjective learning. The proposed fuzzy-reconstruction-based multiobjective genetic algorithm is examined by three dry-lab biological systems. Simulation results show that a safety pruning action is guaranteed (the truncation threshold is set to be 10-15), and only one- or two-step pruning action is taken.