<p>Ocial networks are critical platforms for information dissemination, yet optimizing over their large, rugged search spaces remains challenging. We propose a Hybrid Weed–Gravitational Evolutionary Algorithm (HWGEA) that unifies adaptive seed dispersal from Invasive Weed Optimization with attraction dynamics from Gravitational Search in a single reproduction step, complemented by an adaptive mutation that preserves diversity. We further develop a discrete variant, DHWGEA, tailored to influence maximization on graphs via topology-aware initialization, a dynamic neighborhood local search, and an Expected Influence Score surrogate that reduces simulation cost. Across 23 continuous benchmarks, HWGEA attains the best Friedman mean rank (2.41) and shows statistical parity with LSHADE-SPACMA and SHADE, while significantly outperforming GBO, GOA, RSA, PDO, GSA, and GA (Holm-adjusted Wilcoxon tests). On real engineering designs, HWGEA delivers competitive or improved optima with stable convergence. For influence maximization, DHWGEA achieves spreads within 2–5% of CELF at roughly 3–4 × lower runtime and clearly exceeds PageRank’s spread at moderate cost, offering a practical accuracy–efficiency trade-off for medium-to-large networks. Sensitivity studies identify stable parameter ranges and show that adaptive components reduce dependence on manual tuning. Experiments are averaged over 30 runs with independent seeds to ensure reproducibility. Overall, HWGEA/DHWGEA provide a cohesive, scalable framework for continuous and discrete optimization, balancing exploration and exploitation while maintaining robustness across tasks.</p>