A Hybrid Genetic Algorithm for Nonconvex Function Minimization

In this paper, we consider the problem of minimizing a function in several variables which could be multimodal and may possess discontinuities. A new algorithm for the problem based on the genetic technique is developed. The algorithm is hybrid in nature in the sense that it utilizes the genetic technique to generate search directions, which are used in an optimization scheme and is thus different from any other methods in the literature. The algorithm has been tested on the Rosenbrock valley functions in 2 and 4 dimensions, and multimodal functions in 2 and 4 dimensions, which are of a high degree of difficulty. The results are compared with the Adaptive Random Search, and Simulated Annealing algorithms. The performance of the algorithm is also compared to recent global algorithms in terms of the number of functional evaluations needed to obtain a global minimum and results show that the proposed algorithm is better than these algorithms on a set of standard test problems. It seems that the proposed algorithm is efficient and robust.