The design of optimization algorithms is essential for addressing numerous real-world engineering challenges in the current era. This study focuses on swarm-optimization algorithms (SOAs) that simulate the behavior of swarms in order to address the aforementioned remark due to their exploration-exploitation trade-off, versatility, adaptability and so on. In this paper, we introduce a novel hybrid SOA named as gravitational force Lévy flight grasshopper optimization algorithm-grey wolf optimization (GFLFGOA-GWO) algorithm. The proposed GFLFGOA-GWO algorithm's exploration capability is enhanced through social interaction and Lévy perturbations, while leader-based guidance guarantees exploitation. The performance of the GFLFGOA-GWO is verified by performing two different types of experiments on thirteen benchmark functions (BFs) comparing with the other baseline algorithms (GWO, RWGWO, LFGOA, GFGOA, GFLFGOA, GOA). The first set of experiment is the descriptive statistics metric (mean, standard deviation, median, minimum error, and maximum error). Following this, a non-parametric test (Wilcoxon, Friedman test, and performance index (PI) analysis) has also been performed to observe the optimization of the GFLFGOA-GWO algorithm on BF functions. Through descriptive statistics, GFLFGOA-GWO achieved superiority on 9 out of 13 BFs. Our findings illuminate an overall win rate of $86.2\%$ with no statistically significant loss on any BF based on the non-parametric test.