Aiming at the shortcomings of the gazelle optimization algorithm, such as the imbalance between exploration and exploitation and the insufficient information exchange within the population, this paper proposes a multi-strategy improved gazelle optimization algorithm (MSIGOA). To address these issues, MSIGOA proposes an iteration-based updating framework that switches between exploitation and exploration according to the optimization process, which effectively enhances the balance between local exploitation and global exploration in the optimization process and improves the convergence speed. Two adaptive parameter tuning strategies improve the applicability of the algorithm and promote a smoother optimization process. The dominant population-based restart strategy enhances the algorithms ability to escape from local optima and avoid its premature convergence. These enhancements significantly improve the exploration and exploitation capabilities of MSIGOA, bringing superior convergence and efficiency in dealing with complex problems. In this paper, the parameter sensitivity, strategy effectiveness, convergence and stability of the proposed method are evaluated on two benchmark test sets including CEC2017 and CEC2022. Test results and statistical tests show that MSIGOA outperforms basic GOA and other advanced algorithms. On the CEC2017 and CEC2022 test sets, the proportion of functions where MSIGOA is not worse than GOA is 92.2% and 83.3%, respectively, and the proportion of functions where MSIGOA is not worse than other algorithms is 88.57% and 87.5%, respectively. Finally, the extensibility of MSIGAO is further verified by several engineering design optimization problems.