Advances in Global Optimization: Novel Function Transformation Approaches

Frequently practitioners need to solve global optimization problems. These problems can be extremely difficult to solve without computationally efficient methods. Filled function methods and tunneling function methods are two kinds of function transformation methods in global optimization, and are computationally efficient as illustrated by numerous papers. In this paper, some advances in these two kinds of global optimization methods are reported. Firstly, we investigate the disadvantages of the early filled function proposed by Ge and the tunneling function proposed by Levy and Montalvo. Secondly, we propose definitions of novel filled functions and modified tunneling functions and construct the corresponding functions. Finally, we propose two filled functions in integer global optimization