This study tenders a new nature-inspired metaheuristic algorithm (MA) based on the behavior of the Genghis Khan shark (GKS), called GKS optimizer (GKSO), which is used for numerical optimization and engineering design. The inspiration for GKSO comes from the predation and survival behavior of GKS, and the entire optimization process is achieved by simulating four different activities of GKS, including hunting (exploration), movement (exploitation), foraging (switch from exploration to exploitation), and self-protection mechanism. These operators are mimicked using various mathematical models to efficiently perform optimization tasks of agents in different regions of the search space. In an effort to validate this method's viability and superiority, an in-depth analysis of the proposed GKSO is carried out from both qualitative and quantitative perspectives. Qualitative analysis verifies that GKSO has good exploration and exploitation (ENE) capability. Simultaneously, GKSO is quantitatively analyzed with eight existing fish optimization algorithms and the other nine well-known MAs on CEC2019 and CEC2022, respectively. Among them, a series of experimental scenarios are conducted to validate the applicability and robustness of GKSO by exploring its performance for CEC2022 at different dimensions and maximum fitness evaluation quantity. Statistical results indicate that GKSO has a strong advantage in the competition between two different types of algorithms. Furthermore, five different kinds of real-world constrained optimization problems (OPs) in CEC2020 benchmark constrained optimization functions, including 50 engineering case suites, are selected to evaluate GKSO's performance and the other seven optimizers, further validating GKSO's extensive usefulness and validity in solving practical complex problems.