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Although the exploitation of GWO advances sharply, it has limitations for continuous implementing exploration. On the other hand, the EHO algorithm easily has shown its capability to prevent local optima. For hybridization and by considering the advantages of GWO and the abilities of EHO, it would be impressive to combine these two algorithms. In this respect, the exploitation and exploration performances and the convergence speed of the GWO algorithm are improved by combining it with the EHO algorithm. Therefore, this paper proposes a new hybrid Grey Wolf Optimizer (GWO) combined with Elephant Herding Optimization (EHO) algorithm. Twenty-three benchmark mathematical optimization challenges and six constrained engineering challenges are used to validate the performance of the suggested GWOEHO compared to both the original GWO and EHO algorithms and some other well-known optimization algorithms. Wilcoxon's rank-sum test outcomes revealed that GWOEHO outperforms others in most function minimization. The results also proved that the convergence speed of GWOEHO is faster than the original algorithms.