The Dwarf Mongoose Optimization algorithm is a metaheuristic approach designed to solve single-objective optimization problems. However, DMO has certain limitations, including slow convergence rates and a tendency to get stuck in local optima, particularly when applied to multimodal and combinatorial problems. This paper introduces an enhanced version of the DMO, referred to as HDMO, which is based on a hybrid strategy. Firstly, a sine chaotic mapping function is integrated to enhance the diversity of the initial population. Secondly, the study aims to improve the algorithm's performance through the integration of nonlinear control, adaptive parameter tuning, hybrid mutation strategies, and refined exploration-exploitation mechanisms. To evaluate the performance of the proposed HDMO, we conducted tests on the CEC2017, CEC2020, and CEC2022 benchmark problems, as well as 19 engineering design problems from the CEC2020 real-world optimization suite. The HDMO algorithm was compared with various algorithms, including (1) highly cited algorithms such as PSO, GWO, WOA and SSA; (2) recently proposed advanced algorithms, namely, BOA, GBO, HHO, SMA and STOA; and (3) high-performance algorithms like LSHADE and LSHADE_SPACMA. Experimental results demonstrate that, compared to other algorithms, HDMO exhibits superior convergence speed and accuracy. Wilcoxon rank-sum test statistics confirm the significant performance improvement of HDMO, highlight its potential in practical engineering optimization and design problems.