Complex networks have become a fundamental paradigm for modeling real-world systems. Synchronization of such networks, particularly under hyperchaotic dynamics, presents a significant control challenge due to the high-dimensional state space and multiple positive Lyapunov exponents. This paper addresses the driver node selection problem in a 4D Hyperchaotic Lorenz complex network, formulating it as a constrained binary optimization task. We evaluate a pool of advanced metaheuristics, including the quantum genetic algorithm (QGA), seahorse optimizer (SHO), and artificial bee colony (ABC), across multiple network experiments conducted over 30 independent runs to guarantee statistical validity. The performance of these solvers is rigorously benchmarked against traditional topological heuristics, a random selection baseline comprising 600 feasible configurations, and verified through Wilcoxon statistical testing. Furthermore, addressing computational sustainability, we introduce a “Green-Artificial Intelligence” architecture based on dual-tier structured query language memoization (SQL-memoization) and provide a detailed runtime comparison evaluating its efficiency. The empirical results indicate that swarm-intelligence methods such as ABC and SHO exhibit robust competitive performance in minimizing synchronization errors while the Green-AI framework consistently and drastically reduces the computation of the repetitive simulations.