| 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. Recently, one of the effective approaches for global optimization was the filled function method (FFM). This thesis studied some issues on FFM.In summary, the first chapter in this thesis stated what is global optimization problem, and discussed the stop conditions and the evaluation standard for one global optimization algorithm.In the second chapter, we introduced some local optimization algorithm, which would be used in the FFM. We also introduced some classes of useful global optimization approaches. For the FFM, we reviewed the existing filled functions, and pointed out their advantages and disadvantages, respectively. We also present a class of generic formation of filled functions with one parameter W(x,B), The lower bound of weight factor B was also discussed theoreticallyIn the third chapter, based on the comparison among different classes of filled functions, we put forward a standard to evaluate different filled functions. Based on these, we proposed two classes of globally convexied filled functions W(x,Ï„) and V(x,Ï„) , which include only one parameter. Because some of the existing other globally convexied filled functions may involve two parameters, the proposed filled functions are superior to others.In the last chapter, we implemented the proposed filled function algorithm to solve some examples. These numerical experiments showed that the proposed algorithms are effective. |
