Research On Global Optimization Algorithms Based On Space-filling Curves

Global optimization is an important branch of mathematical programming.It is widely used many fields,such as industry,finance,social management,science and technology.And many problems can be classified as global optimization problems,so the theory and algorithms of global optimization are being paid more and more attention by scholars.In the past few decades,some new theoretical,algorithmic and computational contributions have been developing and employed for the global optimization problemsThis paper mainly studies the global optimization algorithm based on space filling curve.The idea of algorithm is to transform the 9)-dimension problem into a one-dimensional problem by constructing the auxiliary function,and then the onedimensional global optimization problem is solved,which simplifies the solution process of the problem and can prove the convergence of the algorithm under certain conditions.This paper is divided into the following three chapters:In the first chapter,we mainly introduce the related knowledge of global optimization problems.Firstly,Common local optimization algorithms are given,including steepest descent method,Newton method and DFP quasi-Newton method.Then,several deterministic global optimization algorithms are introduced,including the filled function method,the tunneling function method and the branch and bound method.In the second chapter,we consider the continuously global optimization problem in a hypercube.A space filling curve and its analytic expression in a hypercube is first constructed by a class of series.Based on this space filling curve and an integral function,a global optimization algorithm is presented.Finally,we give the convergence analysis and numerical experiments to illustrate the effectiveness of the algorithm.In the third chapter,we consider unconstrained mixed integer nonlinear programming problem.we first introduce the definition of the mixed local minimizer of the mixed integer nonlinear programming problem,and give the mixed steepest descent algorithm.Then,we correct the mixed steepest descent algorithm based on the algorithm proposed in Chapter 2.Based on the idea of filled function method,we construct an auxiliary function and study its properties.Then we propose a global optimizationalgorithm for solving mixed integer nonlinear programming.Numerical experiments show that the algorithm is reliable and can be solved better for some mixed integer nonlinear programming problems.