A New Filled Function with One Parameter to Solve Global Optimization

In this paper, a new filled function with only one parameter is proposed. The main advantages of the new filled function are that it not only can be analyzed easily, but also can be approximated uniformly by a continuously differentiable function. Thus, a minimizer of the proposed filled function can be obtained easily by using a local optimization algorithm. The obtained minimizer is taken as the initial point to minimize the objective function and a better minimizer will be found. By repeating the above processes, we will find a global minimizer at last. The results of numerical experiments show that the new proposed filled function method is effective.