Research On The Filled Function Methods And Theory For Global Optimization

With the rapid development of the computer science and its technology, the global optimization problem has become one of the most important research fields in connection with the theory and algorithms for optimization. In recent years, one of the effective approaches for global optimization, the filled function method(FFM) ,was developed. However the filled function was often composed of the objective function , it made the form of the filled function was complicated. Another difficulty was that more parameters were too hard to adjust in practical computation. Therefore, further research is worthy of continuing on how we can construct filled functions with simpler forms, better properties and more efficient algorithms.This paper mainly concerns the modified filled function methods for nonlinear global optimization problems. It consists of five chapters.The first chapter is the introduction. In this chapter, global optimization model, sorts and some of its main methods are briefly presented. In the second chapter, the thoughts and the research actuality of the FFM are introduced detailedly. In chapter three, the definition of the FFM for continuous global optimization in literature [37] is used and a new filled function is presented, by the function, a new arithmetic is designed finally, the numerical value of experiment and the compared results with the literature [38] are given. In chapter four, a definition of the filled function for nonlinear integer programming problem, which is modified from that of the globally convexized filled function in paper [32], is given. A filled function satisfying the definition is presented, which is modified from that of the box constrained continuous global optimization [48] and contains only one parameter. The properties of the proposed filled function and the method using this filled function to solve nonlinear integer programming problem are also discussed in this chapter. The last chapter makes a summarizing analysis and gives a future prospect of the development of the filled function method.