In this paper, an improved Grey Wolf Optimizer (GWO) algorithm, termed LGWO, is introduced. The enhanced version is interesting and complementary in terms of the direction of movement of the leader wolf, and a special parameter that allows the faster wolves to prey position. The Le ' vy flight is employed as a special navigation solution for alpha, beta, and delta wolf. In this way, the leader wolf equips a powerful tool to deal with the local search problem. A new principle illustrates the behaviour of omega wolf in hunting is also added to enhance the convergence speed of this algorithm. To investigate the performance of LGWO, a series of problems, namely 23 classical benchmarks, a set of CEC 2019 functions, and three engineering problems...