The grey wolf optimizer is an efficient metaheuristic algorithm that has received considerable attention in recent years. However, it also suffers from the problems of insufficient population diversity, susceptibility to local optima and an unsatisfactory rate of convergence. Therefore, a hybrid algorithm is proposed utilising a population initialization strategy through Latin hypercube sampling, a nonlinear adaptive convergence factor, and exploitation strategies of the harris hawks optimization, referred to as HGWO. It makes the grey wolf flight capable in position update and balances out the algorithm's exploration and exploitation process. In this paper, HGWO and other popular metaheuristic algorithms as well as other improved schemes of the grey wolf optimizer are evaluated by 23 famous benchmark test functions and 4 real-word engineering problems. The experiment results demonstrate that the HGWO showcases competitiveness by effectively exploring globally, exploiting locally, and achieving both rapidity and accuracy in convergence. Furthermore, the HGWO demonstrates evident advantages in resolving engineering problems, thereby validating its effectiveness and practicality.