The Application Of The Filter Fill Function Method In Single-objective And Multi-objective Optimization Problems

The filled function method is one of effective methods for solving global optimization problems.And the filter technique is widely used in local optimization algorithm because of its good numerical results.In order to optimize the filled function method,this paper presents a filled function algorithm based on filter technique for the nonconvex global optimization problems with boxed constrains and trys to use the filter set to supervise the iteration.In the paper,a new filled function is formulated first and then its necessary characteristics are discussed.Based on that,the algorithm dominated by the filter is proposed and its properties are proved.The numerical results are list at last to show the effectiveness of the algorithm.Furthermore,in this paper,the global Pareto optimum and local Pareto optimum are defined,and the filled function algorithm based on filter technique is applied in global multiobjective optimization.At the same time,three filled functions and their charac-teristics are proposed.Based on the ideal point algorithm,the evaluation function algorithm and the steepest descent algorithm of multiobjective optimization,this paper also presents the filled function algorithm of ideal point,the filled function algorithm of summation and the filled function algorithm of direct approach.Eventually,the feasibility of these algorithm are verified.