Studies On Filled Function Algorithm For Global Optimization

The optimization problem has become an independent subject since Dantzing proposed simple algorithm solving the general linear programming problem in1947. The global optimization is an important branch of optimization, which is the study of the optimization problem in the global optimization problems. Since the large number of problems encountered in the real life and the production can be abstracted as global optimization problems, it is widely used in the military, economy, communication, biological engineering, image processing, computer science, system science, transportation and engineering design. Therefore, it has very important theoretical and actual application to study of it. The emergence of the new theories and methods of the research in recent years has made it become a science of theoretical study and practical application.Generally speaking, global optimization problems can be classified into two categories:deterministic and randomized algorithms. The filled function algorithm studied in this article is a deterministic algorithm, it was first proposed by Professor Ge R.P. By solving local optimal solution of the algorithm, the method constantly find smaller optimal solution, and finally to get the global optimal solution. In this paper we generalize the filled function algorithm, and construct some new filled functions, numerical experiments show that the algorithms are effective. The detailed structure is as follows:In first chapter, we summarize the domestic and foreign research status of nonlinear optimization methods, and introduce the idea of the filled function and basic concepts. Further more, we analyze previous filled functions and analysis the advantages and disadvantages of them, which provide new ideas in order to construct better new filled functions.In second chapter, we generalize a previous filled function, and propose a new filled function with single parameter. A simpler algorithm is given. Numerical experiment shows that the algorithm is effective. In third chapter, we construct a new free parameter filled function; it is a clear expression of the objective function. A new free parameter filled function algorithm is obtained. The numerical experiment results show that the filled function algorithm is effective, which generalizes applications of filled function algorithm in solving global optimization problems.In fourth chapter, we conduct a preliminary study in application of discrete filled function algorithm for solving integer global optimization, and generalize a discrete filled function with single parameter. A new discrete filled function with single parameter for solving integer programming is constructed. Theoretical proof and numerical experiments show that the algorithm is effective, which promote the application of filled function algorithm for solving integer global optimization problems.In the last chapter, we summarize the work of this paper, and prospect researches on the filled function providing some ideas and inspiration for the future researches on global optimization.