A New Filled Function Method with Two Parameters for Global Optimization

The filled function method is an effective approach to find the global minimizer of multi-modal functions. The conventional filled functions are often numerically unstable due to the exponential or logarithmic term and the sensitivity to parameters. In this paper, a new filled function is proposed, which is continuously differentiable, not sensitive to parameters, and not easy to cause overflow. Then a new local search algorithm is given. Based on this, a new filled function method is proposed. The simulations indicate that the proposed method is numerically stable to the variations of the initial points and the parameters. The comparison with some existing algorithms shows that the proposed method is more efficient and effective.