A novel single-parameter continuously differentiable filled function for global optimization

The filled function approach is an effective global optimization method. The properties of the filled function directly affect the efficiency of the algorithm and have been discussed by many scholars, resulting in various new forms of filled functions. However, most of existing filled functions are not continuously differentiable and have parameters that are difficult to adjust. To remedy this problem, a new continuously differentiable filled function with an easily adjustable parameter is constructed. According to the theoretical analysis of the filled function, a new easy-to-implement filled function algorithm is designed utilizing the efficient local search algorithm based on gradient information. Numerical experiments show that the proposed filled function algorithm is a feasible and effective global optimization algorithm with less computational cost.