New Filled Function Method For Global Optimization

The theory and algorithm of optimum is a subject with strong application. Opti-mization problems are widespread in various applications such as economical planning, engineering, management, transport, and military affairs. Therefore, the study of opti-mization has become a highly concerned topic. In recent years, the literature on global optimization can be classified into three categories. The first category includes methods that search for a global minimum among the local minima, more specifically, methods that invoke certain auxiliary functions to move successively from one local minimum to another better one. The second category includes methods that use heuristic or s-tochastic search. The third category includes method that confine their applicability to problems with special structures, such as concave minimization and D.C.programming.In this paper, based on some new contributions, we try to improve the filled function algorithm. This paper mainly consist of three chapters.Chapter 1, we introduce the background of optimization theories and methods, and several global optimization algorithms are presented, such as D.C.programming, the branch and bound method, tunneling function method and filled function method.Chapter 2, a new definition of filled function method is proposed, and based on the new definition, a new filled function with one parameter is proposed, and we verify that it has better properties. An algorithm for unconstrained global optimization is developed from the new filled function. The implementation of the algorithms on several test problems is reported with satisfactory numerical results. The results validate the efficiency of the new algorithm.Chapter 3, an auxiliary function is constructed, which is called the parameter free filled and modified tunneling function. Based on this function, the integral filled func-tion (IFFA) algorithms for the unconstrained global optimization are developed. The implementation of the algorithms on several test problems is reported with numerical results.