Engineering optimization problems are often characterized by high dimensionality, constraints, and complex, multimodal landscapes. Traditional deterministic methods frequently struggle under such conditions, prompting increased interest in swarm intelligence algorithms. Among these, the Cuckoo Search (CS) algorithm stands out for its promising global search capabilities. However, it often suffers from premature convergence when tackling complex problems. To address this limitation, this paper proposes a Grouped Dynamic Adaptive CS (GDACS) algorithm. The enhancements incorporated into GDACS can be summarized into two key aspects. Firstly, a chaotic map is employed to generate initial solutions, leveraging the inherent randomness of chaotic sequences to ensure a more uniform distribution across the search space and enhance population diversity from the outset. Secondly, Cauchy and Levy strategies replace the standard CS population update. This strategy involves evaluating the fitness of candidate solutions to dynamically group the population based on performance. Different step-size adaptation strategies are then applied to distinct groups, enabling an adaptive search mechanism that balances exploration and exploitation. Experiments were conducted on six benchmark functions and four constrained engineering design problems, and the results indicate that the proposed GDACS achieves good search efficiency and produces more accurate optimization results compared with other state-of-the-art algorithms.