Abstract The paper presents an approach to the numerical investigation of the problems of finding a global optimum of multiextremal functions, based on the use of bioinspired and local search methods. Three combined non-convex optimization algorithms are proposed and implemented. As globalized bioinspired methods, differential evolution, harmony search, and firefly methods are used. For local descents, we used the L-BFGS method. The numerical study of modifications of the implemented approach has been carried out using known non-convex test functions. The developed algorithms have been applied to investigate the problem of the optimal orientation of the aircraft in space. The obtained numerical results allowed us to demonstrate the efficiency of the proposed algorithms.