This paper proposed an improved bat algorithm based on Lévy flights and adjustment factors (LAFBA). Dynamically decreasing inertia weight is added to the velocity update, which effectively balances the global and local search of the algorithm; the search strategy of Lévy flight is added to the position update, so that the algorithm maintains a good population diversity and the global search ability is improved; and the speed adjustment factor is added, which effectively improves the speed and accuracy of the algorithm. The proposed algorithm was then tested using 10 benchmark functions and 2 classical engineering design optimizations. The simulation results show that the LAFBA has stronger optimization performance and higher optimization efficiency than basic bat algorithm and other bio-inspired algorithms. Furthermore, the results of the real-world engineering problems demonstrate the superiority of LAFBA in solving challenging problems with constrained and unknown search spaces.