Nature-inspired metaheuristic optimization algorithms have become vital means for solving intricate optimization problems. This paper presents a new hybrid optimization method combining the traditional Grey Wolf Optimizer (GWO) with an Adaptive Genetic Memory (AGM) mechanism to enhance search efficiency and flexibility. Unlike traditional GWO, which discards past solutions at each iteration, the proposed GWO-AGM retains an elite archive of top-performing solutions and is reintroduced strategically based on a dynamic probability function. This probability gradually decreases over time which ensures the algorithm balances exploration and exploitation, preventing stagnation in local optima. A detailed mathematical formulation is done and the developed model is tested on a comprehensive set of 23 benchmark functions and one engineering optimization problem. Experimental results show that GWO-AGM outshines standard GWO, demonstrating faster convergence, higher solution accuracy, and improved reliability.