Simplex-bat algorithm for solving system of non-linear equations

In consideration of the fact that bat algorithm (BA) is sensitive to the initial values and simplex algorithm (SA) could often easily fall into local optimal, simplex-bat algorithm is put forward in this paper to solve systems of non-linear equations based on the respective advantages of both algorithms. Such a hybrid algorithm does not only give full play to BA's global searching ability but also make full use of SA's local searching ability. The results of simulation experiments show that this hybrid algorithm can be used to find the roots of all sorts of systems of non-linear equations with high accuracy, and moreover, with strong robustness and fast convergence rate, and therefore, it is indeed an effective method to solve system of non-linear equations.