Narrow Results

In the paper, we give a new non-parameter filled function method for finding global minimizer of global optimization programming problems, the filled function consists of a inverse cosine function and a logarithm function, and without parameter. Its theoretical residences are proved. A new filled function algorithm is given based on the proposed new parameterless filled function, The results of numerical with ten experiments verify the efficient and reliability for the algorithm.

Currently, there are four drawbacks for filled function methods: (1) too many local optimal solutions result in huge difficulty to search global optimal solutions; (2) difficult to control the parameter(s); (3) difficult to determine the initial point for minimization of filled function; (4) the shallow basins will affect the solution precision during the minimization of the filled function. To overcome these drawbacks, in this paper, we adopt a flatten function to eliminate many local optimal solutions first, and then a new filled function with one parameter is proposed, and its parameter is easy to control. Furthermore, we propose an efficient method for determining initial point of the filled function by using adaptive step size. Moreover, when some basins of the filled function are shallow ones, it will result in inefficiency of searching these basins during the minimization of the filled function. To tackle this issue and make the search for global optimal solutions much easier, we propose a strategy of basin deepening. By integrating these schemes, we propose a new efficient filled flatten function method. Numerical results indicate the efficiency and effectiveness of the proposed filled function methods.