Complex nonlinear and high-dimensional optimization problems are solved using metaheuristic optimization algorithms. Nevertheless, there is still a challenge of keeping an effective balance between exploration and exploitation. In this paper, a hybrid metaheuristic algorithm is proposed; it is named Dual-Strategy Walrus-Gazelle Optimizer (DEWGO). The suggested approach involves the exploration ability of the Gazelle Optimization Algorithm (GOA) together with the exploitation approach of the Walrus Optimizer (WO). A dynamically controlled switching parameter is an adaptive iteration-based parameter that dynamically controls the switching between exploration and exploitation in the search process. DEWGO is tested with the CEC2017, CEC2022 suits, and six real-world engineering problems and its performance metrics are compared to ten popular optimization algorithms. The experimental findings indicate that DEWGO performs even better, and achieves the best overall rank on most benchmark functions. The statistical analysis based on the Wilcoxon signed-rank test proves the significance of the obtained improvements.