The multiple chaos embedded gravitational search algorithm (CGSA-M) is an optimization algorithm that utilizes chaotic graphs and local search methods to find optimal solutions. Despite the enhancements introduced in the CGSA-M algorithm compared to the original GSA, it exhibits a pronounced vulnerability to local optima, impeding its capacity to converge to a globally optimal solution. To alleviate the susceptibility of the algorithm to local optima and achieve a more balanced integration of local and global search strategies, we introduce a novel algorithm derived from CGSA-M, denoted as CGSA-H. The algorithm alters the original population structure by introducing a multi-level information exchange mechanism. This modification aims to mitigate the algorithm’s sensitivity to local optima, consequently enhancing the overall stability of the algorithm. The effectiveness of the proposed CGSA-H algorithm is validated using the IEEE CEC2017 benchmark test set, consisting of 29 functions. The results demonstrate that CGSA-H outperforms other algorithms in terms of its capability to search for global optimal solutions.