A Filled Flatten Function Method Based on Basin Deepening and Adaptive Initial Point for Global Optimization

Abstract

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.