The rapid growth of renewable integration and active consumer participation has made modern power grids increasingly complex and dynamic, where maintaining balanced and efficient energy distribution remains a central challenge. This paper introduces a symmetry-aware optimized fuzzy deep reinforcement learning-gated recurrent unit (OF-DRL-GRU) model that exploits the natural symmetry and asymmetry in demand–generation behavior to achieve stable and adaptive load balancing. The proposed architecture consists of four core modules: a fuzzy logic layer that formulates symmetrically distributed membership functions for interpretable and balanced state transitions; a DRL agent that governs decision actions through a symmetry-preserving reward mechanism balancing exploration and exploitation; a GRU network that models temporal symmetries while performing controlled symmetry-breaking during dynamic fluctuations to enhance generalization; and an improved multi-objective biogeography-based optimization (IMOBBO) algorithm that optimizes fuzzy parameters and model hyper-parameters through adaptive migration alternating between symmetry preservation and deliberate asymmetry, ensuring efficient convergence and global diversity. The synergy among these modules forms a unified symmetry-aware optimization paradigm, reflecting how symmetric structures sustain stability while purposeful asymmetry enhances robustness and adaptivity. The proposed framework is evaluated using three benchmark datasets (UK-DALE, Pecan Street, and REDD) and compared against several advanced and competitive models. Experimental outcomes show that the proposed OF-DRL-GRU model achieves 99.23% accuracy, 99.69% recall, and 99.83% area under the curve (AUC), alongside faster runtime, lower variance, and improved convergence stability. These results demonstrate that incorporating symmetry–asymmetry principles within AI-driven optimization significantly enhances interpretability, resilience, and energy efficiency, paving the way for intelligent, self-adaptive load management in next-generation smart grids.