Research On Filter Filling Function Algorithm For Unboxing Constrained Global Optimization Problem

This paper mainly analyzes and studies the filter-filled function method of solving box constraint global optimization problems.The different filled functions are given in different chapters and their filled properties are proved.The filter technology can avoid the difficulty of selecting the penalty parameters and do not need the gradient information of objective function.It only needs to compare the function values of the two objective functions,which is simple,convenient and the effect is more effective.Therefore,the filter technique is introduced and combined with the two different filled functions in different chapters.In this paper,the filter filled function methods are designed.In the iterative process of the algorithm,we use the filter technique to determine whether to accept the current iteration point.Finally,numerical examples are given to test the algorithms,which results can show the feasibility and effectiveness of the algorithms.The structures of the article are as follows.In the first chapter,the optimization problem is introduced and the basic theories of the filled function and filter method are given.In the second chapter,one parameter filled function is given and its properties are proved.The pairs consisted of objective function values and filled function values are used as the elements of filter.We combine filter with the new one-parameter filled function to form the one parameter filter-filled function algorithm.The initial point is randomly generated in the box.In the third chapter,a parametric filled function is given and its properties are proved.This function avoids the shortcoming that there exist exponential terms and parameter terms.The initial point that the filled function can be minimized is randomly generated in the box.We combine filter with the parametric filled function o form the parameter-free filled function algorithm.In the fourth chapter,four numerical examples about global optimization are given.The numerical experiments show that the algorithms of filter-filled function are feasible and effective.