Integer Programming Algorithm Efficiency

This thesis mainly studies of several integer linear programming algorithm efficiency.It is composed of three chapters.In chapter 1,the historical background and the present progress of problem about integer programming, Maple use, Grobner basis of the theory and branch-bound method are introduced and summarized. At the same time, the main work of this paper is concluded.In chapter 2,it describes the theoretical basis of the Grobner basis of knowledge.Items are given polynomial order, Grobner basis, S-polynomials and other definitions, as well as domain and ring on the nature of the Grobner basis,and further shows the calculation of Grobner base methodsIn chapter 3,it compares the solution with the Grobner base integer programming problem, branch and bound and cutting plane method of the efficiency of the algorithm. The use of integer programming problem given in Chapter II the basics of Grobner basis theory, gives the solutions and steps and introduced the branch and bound method and cutting plane method, combined with concrete examples of the three methods the algorithm time and algorithm efficiency are compared.