The Filled Function Method For Solving Constrained Global Optimization

The content of global optimization is to study the feature of the optimal solutions and the computational method of the nonlinear function. During these years, many new algorithms have been proposed, such as the CUT PEAK method, the TUNNELING method and the FILLED FUNCTION METHOD (FFM). Now it has been developed into an independent branch in the optimization field.The FFM is composed of two phases, which are the minimize phase and the filled phase. In the minimize phase we will find a local minimum of the original problem by using some classical local MINIMIZATION ALGORITHM, and then an auxiliary function which is called the filled function will be constructed by using that local minimum. So in the filled phase another better local minimum of the original problem can be found by using that filled function. These two phases run by turns and will not stop until no better local minimum can be found anymore. In the end the last local minimum is regarded as the approximate global minimum of the original problem. The purpose of researching FFM is to construct an filled function which has simple form and few parameters, so that we can reduce the computational steps and save many time. So to construct a superior auxiliary function is one of the crucial of the FFM.Up to now, the most filled functions are used to solve the unconstrained optimization or the box constrained optimization problem. This paper is aimed at the general constrained optimization problem. We propose a new filled function and design a algorithm for solving the problem concerned. We show the filled properties of the proposed function under suitable assumptions. We also report the preliminary numerical results of the algorithm, and the numerical results show that the proposed algorithm is promising.