A New Class of Filled Functions with Two Parameters for Solving Unconstrained Global Optimization Problems

A new class of filled functions for escaping the current local minimizer of unconstrained global optimization is proposed. This kind of filled functions is continuously differentiable. And it has no exponential terms and logarithmic terms, which reduce the possibility of computation overflows. Theoretical properties of the proposed filled functions are studied, including discussing the specific conditions that the proposed functions must meet to qualify as a filled function. Then, a new solution algorithm is developed according to the theoretical analysis. Six benchmark problems are tested, and the performance of the new algorithm is compared with two filled function methods. The numerical results prove that the new algorithm is effective and reliable.