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.

This paper proposes a novel multiple chaos embedded gravitational search algorithm (MCGSA) that simultaneously utilizes multiple different chaotic maps with a manner of local search. The embedded chaotic local search can exploit a small region to refine solutions obtained by the canonical gravitational search algorithm (GSA) due to its inherent local exploitation ability. Meanwhile it also has a chance to explore a huge search space by taking advantages of the ergodicity of chaos. To fully utilize the dynamic properties of chaos, we propose three kinds of embedding strategies. The multiple chaotic maps are randomly, parallelly, or memory-selectively incorporated into GSA, respectively. To evaluate the effectiveness and efficiency of the proposed MCGSA, we compare it with GSA and twelve variants of chaotic GSA which use only a certain chaotic map on a set of 48 benchmark optimization functions. Experimental results show that MCGSA performs better than its competitors in terms of convergence speed and solution accuracy. In addition, statistical analysis based on Friedman test indicates that the parallelly embedding strategy is the most effective for improving the performance of GSA.