Approximation Algorithms Of Optimization Problems Based On Trigonometric Function Dimensionality Reduction

Trigonometric function dimensionality reduction is one of the effective methods to reduce the dimension of objective function for solving optimization problems.In this paper,the corresponding dimensionality reduction forms are proposed respectively f'or the optimization problems with two kinds of constraints.According to the behavior of the functions after dimensionality rceduction,two random search methods are used in the one-dimensional search section.In this paper,the dimensionality reduction technique is applied to the global optimization problem,and a global optimization approximation algorithm based on dimensionality reduction is proposed to solve the nonlinear global optimization problem with box constraints.Firstly,a new dimensionality reduction formula is constructed on the interval[0,?]and the a-density based on the dimensionality reduction curve is discussed.Then the calculation of the approximate algorithm is estimated from the length of the dimensionality reduction curve and the proof is given.A theoretical algorithm is proposed and the numerical results are list to illustrate the effectiveness at last.In addition,from the point of constraint function,an optimization problem algorithm is proposed based on dimension reduction technique for solving curved box constraints.Firstly,the form of dimensionality reduction curve related to the constraint is given.Then the properties of the dimensionality reduction curve are discussed.What's more,the relationship of density parameter based on the dimensionality reduction is obtained.Finally,the theoretical algorithm is proposed and the images of functions before and after dimensionality reduction are given.Moreover,numerical results are list to illustrate the effectiveness.